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In this paper, we present a generalization of the Zermelo navigation problem considered by E. Zermelo. Our main objective in raising this problem is to find the optimal time of motion of a vehicle with variable speed and limited acceleration, in the presence of strong wind and moving or fixed obstacles. Contrary to other articles, in this paper, the moving speed is not fixed, and the limited acceleration is taken into account. The variable speed makes it possible to avoid collision with moving obstacles and therefore has an impact on the time-optimal trajectory. With the presence of obstacles, the problem involves continuous inequality constraints. To solve this problem, first of all, by parameterizing the problem and using the re-scaling technique, we obtain a set of parameters, such that our goal is to find the best choice of parameters to optimize the objective function. Here, the well-known penalty function is applied, and several examples are given to illustrate the performance of this method.

In this paper, the problem of exponential stabilization is studied for a model of load frequency control of multi-area interconnected power systems with input delays in the control channel. By utilizing a weighted Lyapunov–Krasovskii scheme, tractable analysis and design conditions of a state feedback controller that makes the closed-loop system exponentially stable with a prescribed decay rate are derived in the framework of linear matrix inequalities. The effectiveness of the design schemes proposed in this paper is validated by simulations of a two-area power model.

In this paper, system identification by the deep learning model (DLM) is proposed to compare with the self-learning particle swarm optimization (SLPSO) for a mechatronic motor-table system. Firstly, the complete dynamic formulation containing both mechanical equation with nonlinear frictional force and electrical equation is successfully formulated. Secondly, the governing equations are employed in the DLM and SLPSO to identify the unknown parameters for the mechatronic system. It is shown that the system identification can be successfully performed by using the DLM and SLPSO in this paper. In numerical simulations and experimental results, we discuss their advantage and disadvantage, and it is found that the DLM can identify the unknown parameters better converging toward the real ones when comparing with the SLPSO.

This paper presents discrete robust control of DC/DC buck converter. Regulating the output voltage of the DC/DC converter digitally, irrespective of line voltage and load variation has been driving motivation for investigation of discrete sliding mode control. Average model is used to design discrete sliding mode controller. Extended state observer is designed to estimate state and disturbance of the discrete model. Switch-free controller is designed, estimated value of disturbance is used in controller to compensate its effect. The significant contribution of this paper includes assurance of robust performance by compensating disturbance contributed by load, parameter and supply variations. Proof of existence of sliding modes and stability also has been contribution. It is shown that the proposed method provides robust voltage regulation both in simulation and experiment.

This paper proposes a technique to identify nonlinear dynamical systems with time delay. The sparse optimization algorithm is extended to nonlinear systems with time delay. The proposed algorithm combines cross-validation techniques from machine learning for automatic model selection and an algebraic operation for preprocessing signals to filter the noise and for removing the dependence on initial conditions. We further integrate the bootstrapping resampling technique with the sparse regression to obtain the statistical properties of estimation. We use Taylor expansion to parameterize time delay. The proposed algorithm in this paper is computationally efficient and robust to noise. A nonlinear Duffing oscillator is simulated to demonstrate the efficiency and accuracy of the proposed technique. An experimental example of a nonlinear rotary flexible joint is presented to further validate the proposed method.

This paper transforms the Keller–Miksis (KM) model, which is the main equation describing the bubble behavior, into a state space representation and presents a stability condition for the system using the linearized form of the KM equation. The dynamic of the cavitation bubble is analyzed for different gases, and its burst time is measured. Then, a sliding mode controller (SMC) is designed for the nonlinear system to regulate the radius of a single spherical bubble and prevent collapse occurrence, which has a great importance in some industrial applications. The system's robustness in the presence of uncertainties in bubble parameters is one of its most significant control objectives obtained in the controller designed in this paper. A comparison is also made between this controller and the controller previously designed for the simpler bubble model (Rayleigh–Plesset (RP) model). Also, the chattering created by SMC is eliminated by two methods. Simulation results are presented to show the effectiveness of the proposed method.

Compared with the static cipher, the dynamic cipher has the characteristic of "one cipher at a time" proposed by Shannon theory. Therefore, it is regarded as the safest among many forms of identity authentication. This paper proposes a five-dimensional chaotic system suitable for the construction of dynamic cipher and analyzes its relevant characteristics, including stability, balance, time-domain waveform, Poincare cross sectional diagram, Lyapunov exponent and bifurcation diagram. The results show that the chaotic system has multiple controllable parameters and a wide range of chaos, which is very suitable for constructing chaotic dynamic ciphers. The complexity of the proposed chaotic system is analyzed to verify the high security of the proposed system. On this basis, a dynamic cipher electronic lock based on chaotic system is designed in this paper. In the designed hardware circuit, the fourth order Runge–Kutta solving algorithm is used to discretize the constructed system, and the chaos is successfully implemented in the single-chip microcomputer. The phase diagram obtained from the circuit simulation data is basically consistent with the numerical simulation. Finally, the circuits of the handheld terminal and the electronic lock terminal are designed and simulated. The simulation results show that the preset function can be basically realized, and the generated chaotic dynamic cipher is random and irregular. The five-dimensional chaotic system proposed in this paper has complex dynamic characteristics, which makes the dynamic cipher electronic lock based on the chaotic system extremely safe.

The classical Direct Torque Control has been elaborated to achieve advanced performance of asynchronous motor, especially in speed behaviours. Due to its high level of ripples and variable frequency, several modifications have been proposed to improve it. In this paper, two modified strategies of the direct torque control dedicated to asynchronous motors are presented, the first method is based on the sinusoidal pulse width modulation and PI regulators for regulating torque, speed and stator flux. The second is based on sliding mode control where the principal purpose is to force the system’s trajectory to slide along the switching surface by a well-defined control law. Furthermore, this paper aims to design two observers; the first will be evaluated by the direct calculation method and the second will be formed by sliding mode. These observers can improve control performance while eliminating mechanical sensors and thereby increasing the overall system’s reliability.

The present paper focuses on embedded electrical networks (EEN) under electrical fault conditions. Indeed, the EEN can be affected by small or large disturbances, such as a low voltage ride through or a short-circuit in distribution or consumption parts of the embedded network. In fact, these problems can lead to the network instability and also affect the efficiency of marine vessels. In this work, the EEN can be converted into a flexible network by implementing the dynamic compensation devices. These devices can be considered as a synchronous machine that exchanges only the reactive power with EEN. Indeed, this compensation equipment entitled “Flexible AC Transmission System (FACTS)”, and it is used to improve the dynamic voltage stability of EEN. In this paper, the electrical network performances on the marine vessels are improved when the EEN is affected by small or large disturbances. Moreover, these improvements are achieved by integrating the automatic voltage regulator for ensuring the transient voltage stability, while the static VAr compensator (SVC) and static synchronous compensator (STATCOM) are implemented on the bus-bar of EEN to improve the dynamic voltage stability of the electrical network. The results of this study are obtained by using “Simulink/Matlab” software and a comparative analysis between the efficiency of SVC and STATCOM devices on the EEN stability is also presented.

This paper presents an analytical framework to establish finite gain stability for nonlinear interconnected mixed passive and negative imaginary systems. The stability analysis is presented using the notation of dissipitivity. The proposed stability framework enables us to extend the number of existing results from the linear mixed systems to the wide range of nonlinear mixed systems. Accordingly, the stability analysis of this paper extends the work of Das et al. (in: 2013 Australian control conference. IEEE, pp 445–449, 2013) to nonlinear cases. A numerical example is presented in the paper to test the results of the proposed analytical framework.

This paper deals with the robust stability analysis problem of linear time-invariant systems with a state delay and polytopic uncertainty. The delay parameter is constant which does not limited by any upper bound. The system’s matrices linearly depend on uncertain parameters which belong to the unit simplex known as the uncertain space. An extended uncertain system is introduced based on the original delay model that contains the uncertain parameters and two slack parameters. The slack parameters belong to the boundary of the unit circle in two dimensional real space. Then, it has been proven that the delay system is robust stable if and only if the extended uncertain system is robust stable over the uncertain space and the unit circle’s boundary. Since the unit circle’s boundary is not convex, a containing polygonal space is developed that consists of a group of polygonal subspaces. This paper proposes a novel algorithm to check system’s robust stability via linear dependent Lyapunov functions that correspondingly defined for each polygonal subspace. The algorithm is able to establish robust stability of the model for all positive values of the delay parameter. There simulation examples are provided to clarify the notations and facts of this paper. First example presents the notation and results in an instance uncertain delay system. Two extensive examples compare feasibility performances of the proposed algorithm to some existing methods that reveal the superiority of the prosed algorithm.

Flow control is a very common objective in fluid power systems. Usually, controlling the force, velocity, position, etc. of hydraulic actuator is achieved by adjusting the flow rate of the hydraulic fluid. There are various techniques in which flow can be controlled. Choosing the appropriate flow control method depends on several factors including the systems requirements, the available space and budget. In this paper, a review of the fluid flow control techniques is presented. Those various ways of controlling fluid flow were discussed based on the available literature. The working principle of each flow control method was described. A discussion about those techniques in terms of efficiency, cost, complexity, and the need to accessories is given in this work. Advantages and disadvantages of each flow control strategy are presented. This paper can be used a guide when selecting the most appropriate flow control method when designing a fluid power system.

This paper primarily discusses the solution to multi-degree of freedom linear time invariant fractional order dynamic systems with fractional actuators in detail. This solution is of significant importance due its ease of usage and compatibility with digital systems. Subsequently, a modified model predictive control (MMPC) scheme is introduced that is an infusion of a novel discrete-time robust sliding mode control and model predictive control. The proposed modified model predictive control algorithm is proven to illustrate robustness against uncertainty in system’s parameters and external disturbance while abstaining from the undesirable characteristics of sliding mode control such as chattering. By employing the MMPC scheme, it is possible to constrain the control inputs to be less than pre-determined bounds and by this mean, take a step toward making this algorithm more suitable for practical applications. A general and illustrious plant, represented by the famous Torvik’s three parameter model, is selected and the proposed control scheme is applied to further elucidate the merits, qualities and capabilities of MMPC for fractional systems. The corresponding MATLAB code for the simulation section is also presented in the appendix of the paper. A discussion is also included that examines the effectiveness of MMPC and provides insights for future works.

This paper presents a literature review on current studies in cooperative control of fixed-wing drones, including maneuvering through adjustments of the tail, rotor, and wing configurations. Cooperative fixed-wing drones are important because of their larger area coverage that allows them to complete the assigned task much faster compared to a single fixed-wing drone. In addition, the endurance of cooperative fixed-wing drones is much higher compared to the endurance of cooperative multi-rotor drones. The papers presented in this review were selected to have as wide a variety as possible in terms of cooperation architectures and strategies, as well as in terms of wing, tail, and rotor configurations. With the rapid advancement of computers, sensors, and actuators which are major components of drones in general, the advancement of fixed-wing drone technology is a logical consequence. And further, this can lead to the advancement of cooperative fixed wing drone which have a much bigger capability compared to a single UAV.

Knee exoskeletons as wearable robots have been increasingly aimed to assist elderly and disabled people to increase their movement abilities through flexion/extension execution of the knee. In this paper, a robust controller was suggested for a new knee joint orthosis. The system is integrated with the orthosis and the human shank and has a nonlinear dynamic model. This paper presents a novel robust controller of an active orthosis for rehabilitation due to no prior knowledge on the dynamical model and unknown the flexion/extension movements as disturbances, an adaptive gain super-twisting algorithm is used to control the knee joint. It is needed to this strategy to cope with the nonlinear nature of the knee exoskeleton with disturbance and model uncertainties that is bounded with unknown bounds. The stability analysis was proven by the Lyapunov approach.

In recent years, data-driven research has attracted significant attention from both industry and academia due to its success in medical, transportation, finance and other fields. How could data tightly integrate with control is a hot issue being explored. This paper provides a brief survey on the relationship of data and control. Four types of data-based control studies are considered, namely post-identification control, direct data control, learning control, and observer-based control. The observer based control can provide real-time observation and estimation of the unknown dynamic systems. It has a great potential in solving complex online control problems. This paper classifies and analyzes the observer integrated control, covering the latest research progress and forecasting the development trend in this direction. This paper concludes with a summary advantages and disadvantages of data-based controls.

A data-driven generalized cell mapping method devoting to conquer the difficulty that how to carry out the global analysis for a model-free and complex system, without prior knowledge of the underlying system, is proposed in this paper to uncover the hidden flow structure existing in the North Pacific Ocean. By this way, the transient attracting region near the 30 degrees north latitude, acting as a short-term attractor in the North Pacific Ocean, is unveiled by investigating the topology of the season-aware transition probability matrix created from the historical data bank of drifters. The predicted probability distributions of drifters are presented to illustrate the evolutions and concentration of ocean currents, which coincides with the real responses of drifters. Furthermore, the purpose of this paper is also to promote the applications of the data-driven cell mapping method in practical engineering.

This article provides a study of modern and classical approaches used for PID tuning and its applications in various domains. Most of the control systems that are implemented to date with the use of PID control because of its simple structure, ease of implementation, and active research in tuning the PID for a long time. The techniques reviewed in the paper are in the order from classical to modern optimization rules used for the PID tuning. This paper attempts to address the literature review of PID control in an era of control system and bio-medical applications. The development of classical PID to the integration of intelligent control to it, has been surveyed by consideration of various application domains. The primary purpose of this document is to provide a detailed point of information for the people to understand the command of PID in different application areas.

The optimum number and location of control devices not only play an important role in effectiveness of the structural control system but also lead to a cost-effective structural design. In the current paper, based on an innovative meta-heuristic optimization method, tug of war optimization (TWO) firstly, an active control algorithm is designed in order to reduce the structural responses and then the optimum number and location of control devices are found to increase the efficiency of the bridge control system. The presented active control algorithm is a neuro-fuzzy adaptive controller that its output functions parameters are optimized by the tug of war optimization method. The optimum number and location of actuators is determined based on the use of the multi-objective mode of TWO and minimization of three objective functions. The first one is maximum of the bridge base shear, second is maximum of mid-span displacement and the third is maximum of mid-span acceleration. In addition, through choosing a predefined performance level for the dynamic responses of the bridge structure, the designer would be able to decide on increasing or decreasing the control devices and minimizing control costs. The optimization results for different number of actuators are shown in this work. The results show that achieving an ideal control plan requires both an appropriate control algorithm and an actuator optimal placement technique. In this paper, using these two factors, the responses of the structure have been desirably less than the responses provided in Ning et al. (Struct Control Health Monit 16(6):639–656, 2009).

The nonlinear behavior of bubble in the blood vessel restricts the applications of bubble technology in the cardiology. In this paper, a novel engineering solution is proposed to control the radius of the bubble and prevent bubble collapse. For this purpose, the nonlinear dynamics of the bubble in the blood vessel is introduced and then presented into the state-space form. The next part of this paper is devoted to designing a nonlinear control method, where the ultrasonic wave plays the role of control input and the output is the radius of the bubble in the blood vessel. In order to achieve faster, finite-time convergence and higher control precision, fast terminal sliding mode is proposed. The stability of the closed-loop system is ensured through the Lyapunov stability analysis. In order to tackle the chattering problem, the switching gain is adaptively tuned according to the fuzzy rule. In this method, the tracking error and its differential are considered as the inputs and the switching gain is considered as the output of the fuzzy logic system. Simulation results confirm the effectiveness of the proposed control method. Finally, the results of this research are of immediate interest for modern medical applications such as ultrasonic imaging, targeted drug delivery, and cancer treatment.

Position control and mechanical vibration suppression are still open problems in compliant link mechanisms. Operation and accuracy improvements of manipulators can be made by finding solutions for these problems. This paper presents a comprehensive performance comparison between controllers (two of them robust controllers) to control position and reduce mechanical vibration over a compliant link-manipulator in a three-dimensional environment: (i) linear quadratic regulator, (ii) model predictive controller, (iii) $$H_{\infty }$$ loop shaping, and (iv) $$\mu $$ -synthesis. The comparisons of controllers are made based on position tracking, vibration damping and control effort in the simulation environment by taking the gravity effect into account. Finally, the paper makes a conclusion by providing some information about main purpose, advantages and disadvantages of each controller in compliant link-manipulator applications.

This paper shows the ability of Fractional-Order (FO) dynamics in adaptation laws of indirect adaptive fuzzy logic control (AFLC). The parameters of the FO-adaptive laws are optimized using Particle Swarm Optimization algorithm without the presence of the disturbance. The optimal FO-AFLC (OFO-AFLC) is introduced in this paper to overcome the drawbacks of AFLC. The complexity in AFLC is due to using the projection algorithm to keep the adapted parameters bounded. Also the AFLC uses a complex control to guarantee the error convergence. It has proven that the OFO-AFLC can guarantee the error convergence without using neither the projection algorithm nor complex control. The applicability and efficiency of the proposed method is compared to the ordinary AFLC, and demonstrated through simulations made on inverted pendulum model. Furthermore, simulation results show that the control signal in OFO-AFLC is smoother with less oscillations.

The established guidance laws in literature are generally designed to capture the target while considering all the states of the interceptor model to be measurable. This paper demonstrates the use of an input output observer for the unmeasured state of the missile-target model with semi-global exponential results. A well-established guidance law called pure proportional navigation law is incorporated in this paper to demonstrate the application of the proposed observer. The missile’s angle of attack is the unmeasured state, which also appears non-linearly in the remaining two kinematic equations of the missile. The occurrence of the unmeasured state in the nonlinear form makes it more challenging to theoretically prove its convergence. The Lyapunov analysis is used to show the convergence of the observed state. Different scenarios consisting of the tail chase and head-on engagements with non-maneuvering and maneuvering targets are considered in the simulations to establish the effectiveness of the proposed guidance strategy.

In this paper, a bifurcation tree of an independent period-3 motion to chaos in a flexible nonlinear rotor system is developed semi-analytically. The period-3 motion was traditionally called the subharmonic periodic motion of order-1/3, but one did not achieve the corresponding solutions yet. Herein, stable and unstable periodic solutions on the bifurcation tree in the flexible rotor system are achieved and the corresponding stability is analyzed by eigenvalue analysis. Harmonic frequency-amplitude characteristics for periodic motions on the bifurcation tree are presented. For comparison of analytical and numerical results, numerical simulation of periodic motions is completed. Phase trajectories, displacement orbits and velocity planes are illustrated, and harmonic amplitude spectrums of period-3 and period-6 motions are presented to show harmonic terms effects. Such studies presented in this paper help one better understand the subharmonic periodic oscillation of order-1/3 in nonlinear rotor systems.

Vortex-induced vibration is a common phenomenon observed in many engineering applications and it is detrimental to the performances and health of the system. It is, therefore, imperative for engineers to make suitable design modifications or arrange for some type of control device to mitigate such oscillations. In this paper, the performance of the acceleration feedback control is compared with that of the simple passive vibration absorber. The effect of time-delay in the feedback loop is also investigated. The acceleration of the primary system is measured and passed through a second-order compensator. The active absorber is designed by setting the filter frequency same as the natural frequency of vibration and the optimum filter damping is numerically obtained. Nonlinear analysis is performed using the Describing Function method and the results are validated using direct numerical simulation performed in MATLAB Simulink. In the present paper, vortex shedding frequencies are selected from two different regions, one with vortex shedding frequency less than the natural frequency of the system and other having vortex shedding frequency higher than the natural frequency of the system. It is observed that the acceleration feedback control can effectively reduce the amplitude of vibration to a great extent. It is also observed that the amplitude of the system changes marginally (up to a certain value of time-delay) in the pre-locking and locking region. However, the effect of time-delay in post-locking zone is detrimental. Beyond a certain value of the time-delay, the amplitude becomes large and even the system may become unstable.

This paper illustrates various techniques to achieve the best optimization method under the Linear quadratic control strategy that is used for a multiple input multiple output system. The objective of the paper is to find the control criteria using the principle of extended state observer. An advanced optimized iteration method was introduced to select the weighted matrix Q from the control parameters. Another method is simulink response optimization method which also can fulfil the desired output result shown in the paper. Both the variables, the weighted matrix Q and the observer gain La, was modified after applying these optimization methods. The method responses were as per the minimal damping ratio of control logic. Among all these algorithms, the best iterative result was initiated.

Control of the bubble radius is essential in many medical and industrial applications. In this paper, the nonlinear governing dynamic of single spherical bubble in a perfect incompressible liquid is introduced. In continuation, the state space form of the nonlinear dynamic is presented and then observability and controllability are checked by Lie derivative concepts and finally the linearized state space is obtained around its equilibrium point. Second part of this paper is devoted to designing control strategies for the nonlinear governing dynamics of bubble, where the ultrasonic pressure plays the role of control input and the output is radius of bubble which is intended to follow desired radius in order to prevent from bubble collapse phenomenon. A novel robust control is proposed to ensure the desired level of performance in the presence of parametric uncertainty. In this method, the stability of the closed loop system is guaranteed by Lyapunov theorem and the stabilizing gain is achieved by Linear Matrix Inequality (LMI) optimization approach. For comparison, Linear Quadratic Regulator method is selected which is a very classical approach. The optimal feedback gain is also achieved through LMI approach. Simulation results indicate the effectiveness and efficiency of the robust over optimal controller.

This paper investigates the control of vibration of a self-excited system, namely Rayleigh Oscillator, by using Acceleration Feedback Control method. In this control scheme, acceleration of the vibrating system is fed back to a second-order compensator and the control force is produced by amplifying the signal obtained from the compensator. Linear and non-linear stability analyses are performed. Linear stability analysis is used to obtain the stability regions and the optimal system parameters. Non-linear analysis is performed using Describing Function method. Acceleration feedback control is found to be effective in controlling the self-excited vibration. The presence of time-delay is also studied in this paper. It is observed that the presence of uncertain time-delay in the feedback loop can be detrimental. The optimal system (optimized for no delay case) can result in instability of the static equilibrium leading to finite amplitude oscillation. However, one can improve the situation by increasing the loop-gain. In order to circumvent this problem, it is proposed that a pre-determined time-delay may be introduced in the feedback circuit and the control parameters are re-optimized considering this time-delay. As a result, the system equilibrium can be stabilized even in the presence of time-delay. The results of theoretical analysis are validated with the simulation results performed in MATLAB Simulink.

The paper is dealing with the concept of positive real and strictly positive real properties of linear time-invariant systems. Although strict positive realness is the most important subset of positive real systems and extensively used in stabilizing control systems, there are inconsistencies in the literature for its necessary and sufficient conditions. Also, many frequency properties of such systems are less attended by the scholars. In this paper, a comprehensive discussion on definitions, properties, lemmas, and theorems related to multi-input multi-output positive real and strictly positive real systems will be presented. Further, several frequency domain properties are presented to characterize these functions. Also, three equivalent high frequency condition presented in the literature for strictly positive real systems are compared. The main results have been supported via several illustrative examples.

In this paper, we propose the minimum energy control input based on Hamiltonian strategy for the motor-table system. The energy equation of the motor-table system contains of the input energy, dissipation energy, potential energy and output energy, and includes electrical and mechanical energies. The methods of the minimum control effort (MCE), minimum input energy control (MIEC), minimum dissipation energy control (MDEC) and trapezoidal trajectory energy control are compared for the motor-table system. From the numerical results, we can find that the MIEC and MDEC approaches can obtain the same minimum input energy. Traditionally, the MCE approach was regarded as the minimum energy control in the previous study. However, we have demonstrated that the MCE approach is not the minimum energy control in this paper.

This paper presents related literature review on drones or unmanned aerial vehicles that are controlled in real-time. Systems in real-time control create more deterministic response such that tasks are guaranteed to be completed within a specified time. This system characteristic is very much desirable for drones that are now required to perform more sophisticated tasks. The reviewed materials presented were chosen to highlight drones that are controlled in real time, and to include technologies used in different applications of drones. Progress has been made in the development of highly maneuverable drones for applications such as monitoring, aerial mapping, military combat, agriculture, etc. The control of such highly maneuverable vehicles presents challenges such as real-time response, workload management, and complex control. This paper endeavours to discuss real-time aspects of drones control as well as possible implementation of real-time flight control system to enhance drones performance.

This paper introduces a new method (notation and theory) in engineering dynamics. The goal of this paper is to apply this new method to the analysis of multi-body systems, specifically for the analysis of the motion of a Remotely Operated Vehicle (ROV). Norway conducts operations on a variety of structures in the North Sea. Research that can improve the efficiency of these operations are of high interest. This paper researches the motion of an ROV induced by the motion of the robotic manipulators, motor torques, and buoyancy. This research also introduces a new method in engineering dynamics: the Moving Frame Method (MFM). The MFM draws upon Lie group theory and Cartan’s Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. While others have applied pieces and aspects of these mathematical tools, the notation presented here brings them together; it is accessible, programmable and simple. The notation for multi-body dynamics and single rigid body dynamics is the same. Most important, this paper presents a restricted variation of the angular velocity to use in Hamilton’s Principle to extract the equations of motion. This research solves the equations using a relatively simple numerical integration scheme. The Cayley-Hamilton theorem and Rodriguez’s formula reconstructs the rotation matrix for the ROV. This work displays the rotating ship in 3D, viewable on mobile devices. This paper presents the results qualitatively as a 3D simulation. This research demonstrates that the MFM is suitable for the analysis of “smart ROVs” as the next step in this work.

This paper develops a novel approach for discrete time proportional integral derivative (PID) control, namely PID+, with application to manipulator arm with four-degrees of freedom. The approach utilizes extra proportional and input compensators to counteract the influence of the discrete time transfer functions higher than second order and having samples time delay more than unity, respectively. These plus compensators allow the exploiting of the full state feedback signals to construct the state variable feedback control law for the proposed PID+ controller. The work introduces two tuning approaches for the compensators of the novel PID+ controller; they are the Linear Quadratic (LQ) cost function by exploiting the non-minimal state space, namely the novel NMSS-PID+ form, and the pole placement. Simulation results verify the applicability of the proposed PID+ controller. Both tuning approaches, PID+/LQ and PID+/pole placement, show satisfactory steady state response with good control action, along with deadbeat response when applying the pole placement approach, in simulation. Finally, the paper shows successful practical implementation for the PID+ controller, when applied to the four degrees of freedom manipulator arm, for which all the control design criteria (tracking with acceptable response time, and input/output disturbance rejection) are met.

In this paper, dynamic formulation, system identification and motion control for a liquid crystal display (LCD) glass-handling robot system are studied. Hamilton’s principle is employed to derive Lagrange’s equations of both flexible and rigid models for an LCD glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The real-coded genetic algorithm is adopted to identify all the parameters of the robot and PMSM simultaneously, and to search for the unknown coefficients of polynomials for the point-to-point trajectories by minimizing the input absolute electrical energy (IAEE). In this paper, variable structure controller (VSC) is realized to track the minimum IAEE point-to-point trajectory with a sliding-mode observer. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. In comparisons of numerical simulations and experimental results, it is demonstrated that identification results of the dynamic model present well matching with the system. Finally, the VSC tracking control based on the minimum IAEE trajectory is realized and its robustness and energy-saving performance is demonstrated simultaneously. The proposed methodology to design the minimum IAEE trajectory can also be applied to any other mechatronic system driven by a PMSM.

This paper improves upon experience mapping based predictive controller (EMPC) for an under-damped type 1 system which is a fairly new concept presented in literature. EMPC has been earlier demonstrated for an under-damped type 1 system. However, the earlier EMPC controller did not address changes in system parameters and hence the performance in terms of rise time and overshoots deteriorated with change in friction and inertia. This paper develops a theoretical basis for EMPC presented earlier. An adaptation technique is proposed for EMPC to control under-damped type 1 systems for variations in load friction and inertia. The present control action is decided based on the steady state error due to the previous control action. The general nth order type-1 under-damped system is simulated and the results of simulation for system variation and various demands are presented. EMPC is shown to perform robustly with adaptation. Adaptive EMPC controller is shown to outperform proportional derivative controller and a Model reference based adaptive controller. The system is also simulated and practically implemented with a PMDC motor based positioning system coupled to a load through a flexible shaft. The results of these simulations and experiments are presented and it is observed experimentally that adaptive EMPC performs well.

Majority of wheelchair users with neuromuscular diseases experience upperbody muscular weakness, which limit their ability to perform common activities of daily living. A Wheelchair Mounted Robotic Arm (WMRA) can assist these individuals to perform various tasks independently. This research paper is focused on designing a control system and interfacing mechanism to a newly designed WMRA. The proposed interfacing mechanism is based on virtual image and voice activated signals. The paper outlined the implementation through three dimensional imagining and a virtual workspace model of the real world for the arm to navigate through. The user speaks a simple command through a microphone and then be run through a control algorithm to drive the robotic arm. Inverse dynamics based control scheme is implemented to command the active joints of the robot, based on an input from the virtual CAD environment. The preliminary simulation results show that the virtual model joint trajectories are well tracked with minimal error. The paper also outlined the overall implementation of the system using Robot Operating System based interfacing system.

In this paper we investigate the effect of the tool-workpiece mode interaction on the stability of a flexible-tool, flexible-workpiece turning process. The workpiece dynamics are modeled by classical beam theory while for the tool we consider a description in terms of eigenmodes with an arbitrary orientation. The focus here is on elucidating the coupling effects due to the flexibility of both structures. Specifically, we show how the tool location along the workpiece and the dynamics of both the workpiece and the tool affect stability. Another contribution of this paper is the utilization of a novel analytical force model for cutting with round inserts. Using this force model, we further show that when round inserts are present, commonly used frequency domain methods can no longer be utilized to capture the system stability. Consequently, we use the spectral element approach, a highly-efficient time-domain approach, for studying the system stability.

This paper studies the problem of optimal control of switched systems under state constraints. It suggests a hybrid approach based on Continuous Hopfield Neural Network (CHNN). To deal with this issue, we need first to determine the optimal switching instants as well as the optimal control input, which guarantees the minimization of a performance criterion while respecting the constraints imposed on the system. Hence, this paper divides the issue under study into two stages. In the first, it starts with the transformation of the problem into an equivalent problem based on parameterization of the switching instants. This step would allow us to calculate the optimal control law and to determine the optimal cost’s derivatives’ expressions at the same time. These expressions are used in the second stage by the CHNN to define the optimal switching instants. In order to respect the state inequalities constraints of the system, the Karush-Kuhn-Tucker conditions and the Lagrange multipliers method associated with the Pontryagin Maximum Principle are used, which we apply on the equivalent problem. The results of this approach have been illustrated through a hydraulic system under state constraints.

In this paper, a new control strategy of a variable speed based SEIG wind energy conversion is presented. Nonlinear control strategy is proposed to extract maximum available energy from the wind turbine and regulate the rotor flux magnitude of SEIG and the DC-link voltage in the generator side as well as the load voltage magnitude in the inverter load side under wind speed, load and rotor/stator resistances variations. The proposed nonlinear adaptive controller is robust given its insensitivity to SEIG variation of the rotor and stator resistances. The global convergence and stability analysis taking into account the interconnections between the stator electrical angular position, the rotor flux and rotor resistance estimators and the nonlinear controller have been proved by using the separation principle. Another contribution of this paper is the robustness of the proposed method with respect to the variation of the driven speed and relatively low wind speed operation. Thus, the proposed stand-alone variable speed based SEIG wind energy conversion system can be used in remote and isolated areas where the mean value of the wind speed profile is relatively low.

This paper is an extension of the work presented by Reddy and Saha (Int J Dyn Control 2016) i.e. Part I of this series of papers. Reddy and Saha (2016) developed Wiener type nonlinear models using orthogonal basis filters which were proved to be ideal candidates for modeling nonlinear resonating systems such as continuous stirred tank reactor(s). Those nonlinear models have further been employed in the present work for developing nonlinear model based control strategies and their closed-loop control performance have been evaluated through simulation case studies involving same continuous stirred tank reactor(s). Two types of model based control strategies are adopted viz. nonlinear model predictive control and nonlinear internal model control. In case of nonlinear internal model controller, the problem of model inversion has been addressed, first of its kind in approach, through tactful modification of Wiener model coupled with optimization technique. Deletion of positive zeros from orthogonal basis filters while modifying Wiener model is the uniqueness of this paper and it ensures stability of the controller.

In this paper, we develop extended one-step methods for solving optimal control problem for systems governed by delay differential equations(DDEs). The optimal control problem governed by ordinary differential equations have been considered in this paper as a case of the DDEs with the absence of delays. The proposed problem is reduced to either a constrained or unconstrained minimization problem according to the nature of the dynamic system and the given conditions. Pontryagin’s maximum (or minimum) principle is used to characterize the optimal controls. Numerical results with simulations compared with other methods are presented to show the efficiency of the methodology.

This paper deals with adaptive control of a nonlinear autonomous underwater vehicle (AUV) in the presence of actuator saturation. Despite the importance of actuator saturation as a practical involvement in the control of autonomous vehicles, it has been considered less in control of AUVs. Therefore, the adaptive $$\mu $$ -modification control method is utilized in this paper for pitch channel autopilot of the REMUS AUV. The designed adaptive $$\mu $$ -modified controller has been applied to the nonlinear six degrees of freedom model of the vehicle. Coefficients of the model are assumed unknown to be coped with an adaptive controller. Performance of the designed controller is compared with that of a direct Model reference adaptive control (MRAC) in six degrees of freedom through simulations. Problems of the MRAC in the presence of input constraints are shown. Shortcomings of conventional adaptive methods in the presence of input constraints are studied. It is finally deduced that how the adaptive controller with $$\mu $$ -modification can perform suitable performance in the presence of the actuator saturation.

This paper is a note on the stability and robustness of the Nash Game (Vamvoudakis et al. in Adaptive optimal control algorithm for zero-sum nash games with integral reinforcement learning, 2012; Ning et al. in Optim Control Appl Methods. doi: 10.1002/oca.2042 , 2012; Bouyer et al. in Concurrent games with ordered objectives, 2012) based mixed $${\mathcal {H}}_{2}/{\mathcal {H}}_{\infty }$$ Model Predictive Controllers (Aadaleesan and Saha in Mixed $$\mathcal {H}_{2}/\mathcal {H}_{\infty }$$ Model Predictive Control for Unstable and Non-Minimum Constrained Processes, 2008; Aadaleesan in Nash Game based Mixed $$\mathcal {H}_{2}/\mathcal {H}_{\infty }$$ Model Predictive Control applied with Laguerre-Wavelet Network Model, 2011) for linear state feedback systems addressed in Part 1 (Aadaleesan and Saha in Int J Dyn Control, 2016) of this series. The mixed $${\mathcal {H}}_{2}/{\mathcal {H}}_{\infty }$$ MPC proposed in Part 1 (Aadaleesan and Saha in Int J Dyn Control, 2016) and that developed by Orukpe et al. (Model predictive control based on mixed $$\mathcal {H}_2/\mathcal {H}_{\infty }$$ control approach, 2007) are compared in this Part 2. The issues of stability and robustness of the multi-criterion optimal control are dealt in this paper using set theoretic concepts.

Mathematical model of permanent magnet synchronous motor (PMSM), which is also popularly known as sinusoidal BLDC motor, is highly nonlinear. Speed control of this motor is a cascade control structure which has two distinct loops: an inner current control loop and outer speed control loop. In this paper, we present the design of fractional proportional-integral (PI) controller using small-signal model of PMSM. The basic scheme used for speed control is field-oriented control wherein constant torque angle control is obtained by zero direct-axis current. This requires three PI controllers: one for direct-axis current to keep at zero; another for quadrature axis current to maintain at maximum; and the third for the speed to keep at the reference level. In this paper, we have replaced all three PI controllers with fractional-order (FO) PI controllers, where order of integrator is fractional. These three FOPI controllers are tested on integer-order nonlinear model as well as fractional-order nonlinear model of PMSM using MATLAB simulink and FOMCON toolbox. The comparative analysis shows superior performance of the FOPI controllers for FO PMSM.

Recent developments in the space industry and the great tendency to define efficient, precise and low cost missions are the main reasons for the growing interest in satellites formation flight. Regarding the aforementioned, the study of multiple satellites control methods is the subject of the present paper. In this paper, two linear robust control strategies are applied to position control system of certain satellites in the virtual structure formation flight. The proposed controllers are designed considering different parametric uncertainties such as semimajor axis and eccentricity changes as well as some disturbances like second term of gravitational acceleration function ( $$j_{2}$$ ) and drag acceleration which are resulted in asymmetrical shape of the Earth and low density atmosphere in high altitude. In the presence of all parametric and un-modeled dynamic uncertainties, the robust stability and performance of the nonlinear system are guaranteed and good tracking, disturbance and noise rejection characteristics are achieved. Computer simulations show that these approaches have very promising performance when position controllers are applied with PWPF modulators while they are working in their pseudo linear range.

A passive bipedal walking robot can descend down a small slope without any exertion of external force and only by using the gravity force. By exerting a proper energy to a passive biped robot, its walking speed can be controlled and also it can be forced to walk on flat planes and ascending slopes. In this paper, the proper energy is applied to the robot in three different methods: applying a proper moment to the robot joints, applying a proper moment to the robot’s stance leg, and applying a proper movement to the robot’s upper body. It is found that the first method is not practical, but the second and third methods enhance the stability and speed regulation of the robot. Additionally, the robot can walk on flat planes, ascending or descending slopes. The controlling algorithm used in this paper is a nonlinear algorithm based on tracking of a given mechanical energy pass of a bipedal walking robot.

The paper studies the classical stochastic Merton’s terminal wealth portfolio problem without transaction costs and also some related problems which may serve as efficient benchmarks for developing relevant analytical techniques as applied to problems with transaction costs. Very few analytical solutions are available for all these types of the Merton’s problem, whereas effective applications of substantially numerical approaches are strongly restricted. Hence, even for quite narrow classes of problems, the development of analytical techniques constructing exact representations for optimal value functions and the corresponding optimal feedback controls is of great theoretical and practical importance. Despite some advancements, sufficiently simple single-input control-affine systems without state constraints and the subject of optimal control synthesis are investigated rather poorly in analytical and qualitative aspects. The present paper is devoted to an entirely analytical construction of the global optimal control synthesis in a certain class of stochastic Merton’s terminal wealth problems. A significant feature of the obtained optimal feedback controls is their capability to be interpreted naturally and adequately from a financial point of view as well as to observe a significant qualitative difference between stochastic and limiting deterministic cases.

Experience mapping based prediction controller (EMPC) is a novel controller based on the human motor control mechanism. The application of EMPC for the precise position control of PMDC motors and the performance analysis using step responses is present in literature. However, the performance of the EMPC control concepts in trajectory tracking applications is not studied. This paper investigates the trajectory control of a PMDC motor using EMPC. The ability of EMPC to control the position along an arbitrarily selected trajectory and the limitations of the quasi-open-loop control structure of EMPC in trajectory tracking applications are studied. A modification to the control strategy which retains the quasi-open-loop control structure is suggested to improve the performance. Further, a novel method is developed within the existing framework of EMPC in this paper for the prediction of duty-cycle to achieve the required steady-state velocity output of the DC motor system and this is employed for smooth trajectory tracking. The proposed method is tested in simulation and the results are analyzed and compared with that of MRAC and LQG techniques. The robustness of the proposed technique to changes in system parameters is also studied. All the proposed techniques are also implemented on a practical laboratory setup and the results are provided. The proposed methods are used for plotting and drawing on a XY plotter and the results are presented and discussed.

This paper develops a novel approach for pole placement method of discrete proportional-integral-derivative (PID) control with industrial application of Bitumen system. The approach utilizes first order discrete-time transfer function (TF) with samples time delay more than unity for tuning the PID compensators, in order to achieve a priori set point of Bitumen mixing temperature. The work also introduces the well established Ziegler Nichols (ZN) and Chien-Hrones-Reswick (CHR) tuning techniques of discrete PID control, when applied to the same TF of Bitumen system, as benchmark. Bitumen system, sited at INSUMAT Company, is considered as a demonstrator for which the discrete PID control with the novel discrete pole placement approach is applied. Here, it is required to achieve a certain temperature for the Bitumen prior to the mixing process with the additives (polymers and fillers) in order to achieve a certain properties for insulation purposes. The key factor for the mixing process is the temperature of Bitumen which should not exceed $$\pm 5\,\%$$ of the specified temperature, which ranges from 90 to $$180\,^{\circ }\hbox {C}$$ , to avoid reaching self-ignition state for the vapor inside the tank ( $$\sim $$ 220 $$\,^{\circ }\hbox {C}$$ ). This explains the avoidance of using conventional online tuning for PID compensators. Simulation results verify the applicability of the new approach and show satisfactory steady state response with very good control action when compared to the noisy control action of the ZN and CHR techniques. Finally, the paper shows successful implementation ‘onsite’ for the discrete PID control using the new approach for pole placement technique, for which all the control design criteria are verified.

The importance of robust feedback control for uncertain negative imaginary system lies in its practical relevance and engineering applications, for example, lightly damped flexible structures with collocated position sensors and force actuators. This article investigates an LMI based robust static state internally stabilizing feedback controller of the negative imaginary system in presence of strictly negative imaginary uncertainties. The paper first presents some basic theory of negative imaginary systems and then, a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems. The paper provides a systematic controller synthesis procedure based on negative imaginary lemma to achieve robustness in the feedback control of negative imaginary systems. To show the effectiveness of controller synthesis method, one design example is considered and a static state-feedback controller is constructed to force the plant to be stable. The simulation results of this article demonstrate the usefulness of the design method and we believe that feedback control of the negative imaginary system can benefit control engineering practitioners in a number of ways.