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In this paper, based on event-triggered control, the stabilisation problem of time-varying delay switched linear system with all subsystems unstable is studied. Firstly, the idea of event-triggered mechanism is introduced, and the state feedback controller is designed. Combining the discretised linear Lyapunov function method with the average dwell time technique, the stabilisation schemes for continuous switched system with unstable modes are obtained. Secondly, compared with existing results, the event-triggered mechanism scheme adopted under the current event-triggered control strategy reduces the number of system triggers, effectively saves computational resources, avoids Zeno's behaviour, and has better performance in terms of sampling frequency. Finally, the idea of event-triggered mechanism is first extended to discrete time-varying delay switched systems where all subsystems are unstable. By solving linear matrix inequalities, sufficient conditions for global exponential stability of the system are obtained. The effectiveness of this method was verified through a simulation example of a turbofan engine model. [ABSTRACT FROM AUTHOR]

This study investigates designing optimal controllers on the dynamics performance of active suspension systems. The study incorporates nonlinearities and actuator saturation in the mathematical model of the suspension system for more reasonable representation of the real system. To improve ride comfort and stability performance in the presence of road disturbances, this study proposes two control frameworks including the Proportional-Integral-Derivative (PID) controller and the State Feedback (SF) controller. The focus of the study is to overcome the limitations of existing approaches in handling the actuator saturation in the controller design. To attain a better performance of the two proposed controllers including the input control constraint, a Grey Wolf Optimization (GWO) has been introduced to improve the searching process for the optimal values of the controllers' adjustable parameters. The simulation results using MATLAB show that the proposed controllers exhibit a good performance in normal operation and in a robustness test involving system parameters' changes. In terms of improving the response of the system, the GWO-PID controller shows a better response than that of the GWO-SF controller. Based on the Integral Square Error (ISE) index, the ISE is reduced by 16.67% using the GWO-PID controller compared to the GWOSF controller. [ABSTRACT FROM AUTHOR]

The active suspension systems offer substantial benefits in ride comfort, handling control over traditional passive systems. In this paper, the evaluation of various controllers including the proportional-integral-derivative (PID) controller and the state feedback (SF) controller on the dynamics performance of active suspension systems is presented. Unlike the majority of the previous studies, the nonlinearities and actuator saturation in the mathematical model of the suspension system have been considered for more reasonable representation of the real system. To attain a better performance of the two proposed controllers, a swarm bipolar algorithm (SBA) technique has been introduced to improve the searching process for the optimal values of the controllers' adjustable parameters. The simulation results using MATLAB show that the proposed controllers exhibit a good performance in normal operation and in a robustness test involving system parameters' changes. In terms of improving the response of the system, the SBA-PID controller shows a better response than that of the SBA-SF controller. [ABSTRACT FROM AUTHOR]

This review paper introduces the modeling, measurement, identification and control of direct current motors based on the state space modeling and the transfer function representation. These models are identified by real laboratory measurements, and the simulated results are compared with the measurements. Continuous-time and discrete-time PID (Proportional-Integral-Derivative) controllers, discrete-time state feedback and linear quadratic controllers are designed mathematically. The designed controllers are realized by the microcontroller Arduino UNO, and the behavior of the controllers is compared and analyzed. The noisy current signal has been measured by a discrete-time observer, steady-state Kalman filtering is also studied. The practical results of the implemented controllers support the theoretical results very well. [ABSTRACT FROM AUTHOR]

This paper concerns the energy-to-peak (E2P) control problem for a class of linear discrete-time singular systems in which the external disturbance condition in the regulated output is considered. First, a method for analyzing E2P performance is given to accurately judge whether a closed-loop singular system is admissible and satisfies the required E2P performance index. Furthermore, according to the standard linear matrix inequality (LMI) technique, an E2P controller design scheme is given to ensure that the closed-loop system sufficiently satisfies the required control performance. Finally, an example of a circuit system is adopted to demonstrate the effectiveness of the proposed controller design scheme. [ABSTRACT FROM AUTHOR]

This paper studies robust stabilization problem and state feedback controller design problem for a class of complex production process systems by pattern class variable instead of state variable or output variable. Firstly, the maximum entropy clustering method is introduced and modeling method based on multi-dimensional moving pattern is given. Nonlinear state space models of systems with input-delay are established by using the trajectories of pattern class variable. Then sufficient conditions for robust stabilization of the system are obtained by Linear Matrix Inequality. In addition, a state feedback controller is designed based on this condition. Finally, the effectiveness of the methods is illustrated by taking the actual working conditions data as an example. [ABSTRACT FROM AUTHOR]

This study conducts a comprehensive examination of the nonlinear propeller pendulum system's angular position control, utilizing three distinct control strategies: Proportional-Integral-Derivative (PID) controller, State Feedback (SF) controller, and Sliding Mode Control (SMC). In order to optimize the performance of each controller, Gorilla Troops Optimization (GTO) is employed to identify the optimal value of the controllers' design parameters. The dynamics of the system under each controller are simulated via MATLAB software, and the performance of the controlled system is quantitatively assessed utilizing the Integral Time of Absolute Error (ITAE). The resilience of the controllers under uncertainties is evaluated by introducing an external disturbance to the system. Simulation results indicate that the SMC, tuned by GTO, exceeds the performance of the other controllers in reducing the settling time, eliminating maximum overshoot, and minimizing the ITAE index. Moreover, under external disturbance, the SMC tuned by GTO demonstrates superior robustness compared to other controllers. [ABSTRACT FROM AUTHOR]

For decades in the aerospace and control sciences, the Inertial Stabilized Platform (ISP) system has been studied to improve the accuracy of recipient photos or target tracking. This paper presents a nonlinear observer-based control method for three Degrees Of Freedom (3-DOF) ISP systems. First, a new formula of the state space equation for the 3-DOF ISP system is proposed to make this model suitable for designing an observer-based control. Then, by measuring the angular positions as output feedback, the angular velocities are estimated by the nonlinear observer, and Lyapunov-based nonlinear control techniques are used to design the observer. Furthermore, the exponential stability and convergence of the observer system are proved. Finally, the auxiliary control signal is considered so that the dynamics of the designed observer become a simple linear form and are easily controlled by the state feedback controller. Simulation results illustrate the effectiveness and feasibility of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper presents delay-dependent stabilization criteria for linear time-varying delay systems. A less conservative stabilization criterion is derived by invoking a new Lyapunov{ Krasovskii functional and then, extended reciprocally convex inequality in combination with Wirtinger's inequality is exploited to obtain an improved stabilization criterion where a set of nonlinear matrix inequalities is solved by applying the cone complementarity algorithm. The proposed stabilization technique transforms a non-convex problem into a nonlinear trace minimization problem which is solved by an iterative approach. Numerical examples are considered to demonstrate the effectiveness of the proposed stabilization criteria and the presented iterative algorithm outperforms some existing results. [ABSTRACT FROM AUTHOR]

The state feedback controller design for a class of Generalized Proportional Fractional Order (GPFO) Nonlinear Systems is presented in this paper. The design is based on the combination of the One-Sided Lipschitz (OSL) system class with GPFO modeling. The main contribution of this study is that, to the best of the authors' knowledge, this work presents the first state feedback control design for GPFO systems. The suggested state feedback controller is intended to ensure the system's generalized Mittag Leffler (GML) stability and to deliver optimal performance. The findings of this paper show that the proposed strategy is effective in stabilizing Generalized Proportional Fractional Order Nonlinear Systems. A numerical example is presented to demonstrate the usefulness of the stated theoretical conclusions. [ABSTRACT FROM AUTHOR]

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we will introduce Caputo fractional LC derivative defined in the linear correlated fuzzy-valued number space R F (A) and some of its applications, specifically the feedback control problem in the space R F (A) in the sense of Caputo fractional LC derivative. Firstly, we give definition of the Riemann-Liouville-LC integral and the Caputo fractional LC derivative of a function that takes value in R F (A). Besides, some Caputo factional LC derivative properties of the sum and difference of two functions have also been proved. Moreover, the problem of dynamic systems in space R F (A) is given in both cases where A is a symmetric or non-symmetric fuzzy number. Along with that, the stability theorems of the equilibrium point are also taken into consideration. Finally, we are interested in building a state feedback control function for the fractional differential equation system in space R F (A) to ensure the equilibrium point of the system is asymptotically stable. [ABSTRACT FROM AUTHOR]

The output consensus for a second-order nonlinear multiagent system (MAS) with mismatched input and output vectors is investigated by exploiting the output strict passivity (OSP). By resorting to the Lyapunov functional approach and the state feedback control method, an OSP criterion for the MAS is derived. Based on the OSP and the relationship between output consensus and the OSP, a sufficient condition to ensure the output consensus of the MAS is obtained. At last, a numerical simulation is given to substantiate the merits of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The two-wheeled self-balancing robot (TWSBR) is based on the axletree and inverted pendulum. Its balancing problem requires a control action. To speed up the response of the robot and minimize the steady state error, in this article, a grey wolf optimizer (GWO) method is proposed for TWSBR control based on state space feedback control technique. The controller stabilizes the balancing robot and minimizes the overshoot value of the system. The dynamic model of the system is derived based on Euler formula and linearized to state space representation to enhance the control technique. Then, the GWO optimizes the state feedback controller parameters. Simulation results show that the system reaches the zero steady-state error with less than 2 ms, which proves the effectiveness of the proposed controller over the classical state feedback controller in terms of fast response, very small overall error, and minimum overshoot.

Based on the Lyapunov stability theory, the matrix analysis method and the linear matrix inequality method, etc, the generalized H2 control of singularly perturbed uncertain-control time-varying delay systems with control input and disturbance input, was studied. A memory state generalized H2 controller was designed, and the decision theorem for the specific design method was given. With a new lemma for delay-dependent and delay-independent cases, the relatively less conservative stability criterion was derived. The obtained results were linearized, the selected numerical examples were used to verify the effectiveness and feasibility of the derived conclusions. The results show that, the closed-loop system is asymptotically stable in the whole range from zero to the singular perturbation upper bound, which expands the generalized H2 stability space and reduces the L2-L∞ performance index. The comparison of the stability state parameter index with the related literatures indicate that, the proposed method has certain advantages and less conservatism, and is suitable for standard and non-standard cases. [ABSTRACT FROM AUTHOR]

The finite-time lag consensus problem of nonlinear multi-agent system (MAS) is investigated by applying finite-time passivity (FTP) in this brief. Two sufficient conditions are obtained for insuring FTP of the MAS by choosing the proper state feedback control strategy and adaptive state feedback control strategy. In view of FTP, the finite-time lag consensus criteria for the MAS are developed. Finally, a simulation example which demonstrates the availability of the derived results is proposed. [ABSTRACT FROM AUTHOR]

An averaging tank with variable filling is a nonlinear multidimensional system and can thus be considered a complex control system. General control objectives of such object include ensuring stability, zero steady-state error, and achieving simultaneously shortest possible settling time and minimal overshoot. The main purpose of this research work was the modeling and synthesis of three control systems for an averaging tank. In order to achieve the intended purpose, in the first step, a mathematical model of the control system was derived. The model was adapted to the form required to design two out of three planned control systems by linearization and reduction of its dimensions, resulting in two system variants. A multivariable proportional-integral-derivative (PID) control system for the averaging tank was developed using optimization for tuning PID controllers. State feedback and output feedback with an integral action control system for the considered control system was designed using a linear-quadratic regulator (LQR) and optimization of weights. A fuzzy control system was designed using the Mamdani inference system. The developed control systems were tested using theMATLAB environment. Finally, the simulation results for each control algorithm (and their variants) were compared and their performance was assessed, as well as the effects of optimization in the case of PID and integral control (IC) systems. [ABSTRACT FROM AUTHOR]

The state feedback controller design for a class of Generalized Proportional Fractional Order (GPFO) Nonlinear Systems is presented in this paper. The design is based on the combination of the One-Sided Lipschitz (OSL) system class with GPFO modeling. The main contribution of this study is that, to the best of the authors’ knowledge, this work presents the first state feedback control design for GPFO systems. The suggested state feedback controller is intended to ensure the system’s generalized Mittag Leffler (GML) stability and to deliver optimal performance. The findings of this paper show that the proposed strategy is effective in stabilizing Generalized Proportional Fractional Order Nonlinear Systems. A numerical example is presented to demonstrate the usefulness of the stated theoretical conclusions.

For the modeling and operation of biological computing, chemical reaction networks (CRNs) constitute an ideal programming paradigm for the simulation of various digital and analog circuits. In this manuscript, an originally divergent linear time-invariant (LTI) CRNs system is made stable by constructing a state feedback controller. State feedback controllers control the internal characteristics of a linear system through the state matrix of the system. A static pre-filter based on CRNs is constructed in order to ensure the tracking effect of system response. Next, considering extraneous disturbances to the LTI system, an integration element is added in the first channel of the control system to stably suppress disturbance input. Moreover, the state feedback controller is utilized to build an addition gate control system. When a leak reaction occurs in the addition gate, the addition gate control system produces the correct calculation result, whereas the addition gate calculation is wrong. Finally, a full-dimensional state observer based on CRNs is implemented in this paper. In the case of external disturbance interference or incomplete modeling, the state trajectories of the system are observed by the full-dimensional state observer. [ABSTRACT FROM AUTHOR]

This article investigates the robust exponential stabilization of a class of switched positive systems with uncertainties by co-designing controllers for subsystems and dwell time switching strategy. The uncertainties refer to interval uncertainties. One of the distinguishing features is that none of the forced individual subsystems is assumed to be stabilized. The other feature is that the stabilization for the unforced switched system can not be solvable by designing dwell time switching signal. First, for switched positive systems without uncertainties, a type of multiple time-varying co-positive Lyapunov functions is used, and the computable sufficient conditions on the state feedback controller for each subsystem are derived in the framework of dwell time strategy. Moreover, the exponential stabilization problem is solved by confining the lower and upper bounds of the dwell time, restricting the upper bound of derivative of considered Lyapunov function of the active subsystem, and decreasing the Lyapunov function values at successive switching instants of the overall switched system. Then, the results are extended to the robust exponential stabilization case for switched positive systemswith uncertainties, and sufficient conditions are given in the same framework of the dwell time for that of the forced switched systems by further designing state feedback controllers. Finally, illustration examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, robust H ∞ control for fractional-order switched systems (FOSSs) with uncertainty is studied. Firstly, the fractional-order switching law for FOSSs is proposed. Then, H ∞ control for FOSSs is proven based on the switching law and linear matrix inequalities (LMIs). Moreover, H ∞ control for FOSSs with a state feedback controller is extended. Furthermore, the LMI-based condition of robust H ∞ control for FOSSs with uncertainty is proven. Furthermore, the condition of robust H ∞ control is proposed to design the state feedback controller. Finally, four simulation examples verified the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper deals with the stability and stabilization problems of time-delay systems with nonlinear perturbations. The perturbations are modelled by a nonlinear function of current and/or delayed states. By utilizing Lyapunov–Krasovskii functional, sufficient conditions are obtained in terms of LMIs for the different types of perturbations. The stabilization problem is originally non-convex because of the coupling between the Lyapunov matrices and the controller gains. In order to decouple decision variables, the Young's relation is used in a judicious manner. Numerical examples are given to demonstrate that the proposed method can provide a state feedback controller for a larger delay range than existing methods. [ABSTRACT FROM AUTHOR]

The article proposes a ground-breaking solution to address the challenge of imposing constraints in a full state feedback (FSF) control system. Its simplicity is comparable to the introduction of saturation blocks in the cascaded control system. In the developed control system, a given state variable is stabilized at the threshold value using a separate FSF controller. The overall controller consists then of a set of controllers, the main one with an external reference signal and auxiliary controllers with the internal references set to the desired limits to be imposed on each of the physical states of the investigated plant, operating in parallel fashion (hence the proposed name—multithreaded). This means that in each time instance, the processor executes all FSF controllers. Additionally, if the auxiliary integral states are implemented, a back-calculation algorithm is employed to keep the auxiliary states at the desired level for the controllers that are idling at a given time instance. The median of the calculated control signals is put through to the plant as a control signal. Such an elegant and straightforward way of handling constraints in the state feedback system has never been reported before and is currently patent pending. The proposed method is validated for a servo drive using hardware-in-the-loop setup. All the obtained results confirm technical feasibility of the controller structure and its ability to keep all the state variables within the required intervals. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering (17264073) is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the performance evaluation of two state feedback controllers, Pole Placement (PP) and Linear Quadratic Regulator (LQR). The two controllers are designed for a Mass-Spring-Damper (MSD) system found in numerous applications to stabilize the MSD system performance and minimize the position tracking error of the system output. The state space model of the MSD system is first developed. Then, two meta-heuristic optimizations, Simulated Annealing (SA) optimization and Ant Colony (AC) optimization are utilized to optimize feedback gains matrix K of the PP and the weighting matrices Q and R of the LQR to make the MSD system reach stabilization and reduce the oscillation of the response. The Matlab software has been used for simulations and performance analysis. The results show the superiority of the state feedback based on the LQR controller in improving the system stability, reducing settling time, and reducing maximum overshoot. Furthermore, AC optimization shows significant advantages for optimizing the parameters of PP and LQR and reducing the fitness value in comparison with SA optimization

In this paper, robust H∞ control for fractional-order switched systems (FOSSs) with uncertainty is studied. Firstly, the fractional-order switching law for FOSSs is proposed. Then, H∞ control for FOSSs is proven based on the switching law and linear matrix inequalities (LMIs). Moreover, H∞ control for FOSSs with a state feedback controller is extended. Furthermore, the LMI-based condition of robust H∞ control for FOSSs with uncertainty is proven. Furthermore, the condition of robust H∞ control is proposed to design the state feedback controller. Finally, four simulation examples verified the effectiveness of the proposed methods.

This paper studies the issues of stability analysis and stabilizing controller design for a class of discrete-time semi-Markovian switched linear singular systems. The novel sufficient criteria for such systems to be σ -error mean square admissible are proposed for the first time. By adopting the improved technology of eliminating matrix power terms for singular systems, the existence conditions are proposed for state feedback controller in terms of a group of linear matrix inequalities. An example is presented to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]

When a ship is sailing on the sea, the ship will have violent motions due to the influence of waves, and the roll is the most obvious influence. In order to further reduce roll, a design method of fin stabilizer based on Lyapunov stability theory is studied in this paper. The roll motion model of the ship is constructed, and the roll reduction is realized by state feedback controller. Here, Lyapunov stability theory is used to solve the feasible region of the controller. The controller gain is obtained by using the method of linear matrix inequality. Then, the controller parameter optimization based on optimal phase matching can be realized. The anti-rolling performance of the ship is evaluated by the simulation of zig-zag motion. When a ship is in a zig-zag motion, it will roll more violently than when it is in a straight course because it is constantly changing course. Therefore, it is more meaningful to use zig-zag motion shape to verify the performance of fin stabilizer. Compared with the existing methods, the roll reduction rate of the proposed method is significantly improved, which proves that the proposed method is effective. • Based on the mathematical model of ship motion, the roll model of ship is established. • In order to realize the control of fin stabilizer, a typical state feedback controller is selected. • The controller parameter optimization based on optimal phase matching can be realized. • The anti-rolling performance of the ship is evaluated by zig-zag motion. • The mechanical characteristics of fin stabilizer are considered in the simulation analysis. [ABSTRACT FROM AUTHOR]