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Given a multi-input, nonlinear, time-invariant, control-affine system and a controlled-invariant, closed, embedded submanifold N, the local transverse feedback linearization (TFL) problem seeks a coordinate and feedback transformation such that, in transformed coordinates, the dynamics governing the system's transverse evolution with respect to N are linear, time-invariant, and controllable. The transformed system is said to be in the TFL normal form. Checkable necessary and sufficient conditions for this problem to be solvable are known, but, unfortunately, the literature does not present a prescription that constructs the required transformation for multi-input systems. In this article we present an algorithm that produces a virtual output of suitable vector relative degree that, using input-output feedback linearization, puts the system into TFL normal form. The procedure is based on dual conditions for TFL and is fundamentally different from existing methods, such as the GS algorithm proposed by Gardner and Shadwick and the Blended Algorithm, because of the "desired" zero dynamics manifold N. The proposed algorithm is the first to take into consideration the desired zero dynamics manifold. [ABSTRACT FROM AUTHOR]

The paper investigates the problem of adaptive finite-time robust stabilization for a set of high-order uncertain nonlinear systems in the presence of asymmetric output constraint, dynamic uncertainty and complicated external disturbances. Via effectively integrating the artful Barrier Lyapunov Function (BLF) in conjunction with the continuous control armed with a serial of integral functions consisting of embedded sign operations, a continuous controller is generated, which promises that the closed-loop system’s states converge to a compact set within finite time whilst preserving the validity of the output constraint. Preferable to the current techniques, the suggested methodology unifies the construct and theoretical evaluation for the constrained and unconstrained output as well as being able to concurrently handle the output asymmetric constraints, zero dynamics and complex external disturbances. Finally, an instance of simulation is included to illustrate the validity of the established methodology.

This study explores the issue of adaptive stabilization for a class of high-order uncertain nonlinear systems with asymmetric output constraint and zero dynamics. By combining skillful Barrier Lyapunov Function (BLF) with the technique of continuous feedback domination equipped with a group of integral functions including nested sign functions, a continuous state feedback stabilizer is established, which guarantees that the closed-loop system’s states converge to zero asymptotically while keeping the asymmetric output restriction inviolate. Superior to the existing methods, the developed strategy can not only simultaneously cope with the output asymmetric constraints and dynamic uncertainties, but also unifies the construction and theory analysis for the limited and unlimited output. At last, a numerical simulation is offered to verify the efficiency of the developed method.

This article addresses a fundamental issue in power converter control. Namely, the direct output-voltage control of power converters with higher order dynamics. We argue that despite of the burst in the development of new topologies, legacy control design principles—inherited from second-order converter analysis— have been unduly adopted as de facto rules of procedure. In particular, we refer to the minimum-phase requirement on the feedback variable, as the underlying stabilizing mechanism. In this article, we demonstrate that the requirement of minimum-phaseness for higher order converters and the legacy ad hoc solution via ancillary current control, can be bypassed without compromising closed-loop performance. To prove this, we unveil important differences between stability properties of second-order and higher order converters. Then, we introduce new linear and nonlinear control design strategies that permit direct output-voltage control. Experimental results are provided to validate the theory. [ABSTRACT FROM AUTHOR]

Finite‐time non‐smooth stabilization of cascade output‐constrained switched systems via state feedback is investigated. The cascade switched systems consist of subsystems in general form with zero dynamics and mixed powers taken into account. To deal with the finite‐time stabilization problem of such kind of switched systems, some mild assumptions, input‐to‐state stability property of zero dynamics, an appropriate growth rate assumption on nonlinear terms and some well‐known conditions for small signals, have been imposed on subsystems. Then, state feedback controllers are constructed first by revamping adding a power integrator technique and finite‐time stability analysis of the resultant closed‐loop switched systems are implemented by the deliberately constructed tangent‐type barrier Lyapunov function (Tan$$ {T}_{an} $$‐BLF). Meanwhile, the output constraint of switched systems is also implicitly guaranteed by the Tan$$ {T}_{an} $$‐BLF. Switched systems discussed in this article can encompass almost all p$$ p $$‐normal ones because of the inclusion of zero dynamics, mixed powers, and the homogenous upper bounded assumption on nonlinear terms. And, the method proposed in this article operates in a unified framework to tackle finite‐time stabilization of switched systems because the constructed common Tan$$ {T}_{an} $$‐BLF degenerates into a quadratic function when the output constraint tends to infinity. Simulations are carried out to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Reinforcement learning methods often produce brittle policies — policies that perform well during training, but generalize poorly beyond their direct training experience, thus becoming unstable under small disturbances. To address this issue, we propose a method for stabilizing a control policy in the space of configuration paths. It is applied post-training and relies purely on the data produced during training, as well as on an instantaneous control-matrix estimation. The approach is evaluated empirically on a planar bipedal walker subjected to a variety of perturbations. The control policies obtained via reinforcement learning are compared against their stabilized counterparts. Across different experiments, we find two- to four-fold increase in stability, when measured in terms of the perturbation amplitudes. We also provide a zero-dynamics interpretation of our approach. [ABSTRACT FROM AUTHOR]

This paper proposes a sliding mode controller (SMC) with modified Nelder-Mead tuning, for the control of nonlinear chemical processes, which are represented as first order plus dead time process with negative gain (FOPDT-NG). In the controller design, the SMC controller parameter in continuous part is obtained based on the time constant and dead time of the process, and controller parameters in the discontinuous part is obtained using Nelder-Mead tuning equations. Even though the controller parameters of conventional SMC are tuned using Nelder-Mead tuning, zero dynamics are noticed in the closed loop response of few FOPDT-NG processes and, with few other FOPDT-NG processes tracking of set-point is unachievable. This work proposes modification in the Nelder-Mead tuning equations using Nelder-Mead optimization to overcome the above disadvantages. Four different types of FOPDT-NG processes are considered in this work, and for every type the Nelder-Mead tuning equations are modified, for the design of proposed controllers. The performances of proposed controllers are evaluated for FOPDT-NG processes and also for three different chemical processes taken from literature. A simulation results demonstrate that, the proposed controller prevailed the performance of the conventional SMC in tracking the set-point and the elimination of zero dynamic behavior of FOPDT-NG processes. Hence, the proposed controllers provide improved closed loop performances as compared to the conventional SMC. [ABSTRACT FROM AUTHOR]

Modelling errors and robust stabilization/tracking problems under parameter and model uncertainties complicate the control of the flexible underactuated systems. Chattering-free sliding-mode-based input-output control law realizes robustness against the structured and unstructured uncertainties in the system dynamics and avoids the excitation of unmodeled dynamics. The main purpose of this paper was to propose a robust adaptive solution for stabilizing and tracking direct-drive (DD) flexible robot arms under parameter and model uncertainties, as well as external disturbances. A lightweight robot arm subject to external and internal dynamic effects was taken into consideration. The challenges were compensating actuator dynamics with the inverter switching effects and torque ripples, stabilizing the zero dynamics under parameter/model uncertainties and disturbances while precisely tracking the predefined reference position. The precise control of this kind of system demands an accurate system model and knowledge of all sources that excite unmodeled dynamics. For this purpose, equations of motion for a flexible robot arm were derived and formulated for the large motion via Lagrange’s method. The goals were determined to achieve high-speed, precise position control, and satisfied accuracy by compensating the unwanted torque ripple and friction that degrades performance through an adaptive robust control approach. The actuator dynamics and their effect on the torque output were investigated due to the transmitted torque to the load side. The high-performance goals, precision and robustness issues, and stability concerns were satisfied by using robust-adaptive input-output linearization-based control law combining chattering-free sliding mode control (SMC) while avoiding the excitation of unmodeled dynamics. The following highlights are covered: A 2-DOF flexible robot arm considering actuator dynamics was modelled; the theoretical implication of the chattering-free sliding mode-adaptive linearizing algorithm, which ensures robust stabilization and precise tracking control, was designed based on the full system model including actuator dynamics with computer simulations. Stability analysis of the zero dynamics originated from the Lyapunov theorem was performed. The conceptual design necessity of nonlinear observers for the estimation of immeasurable variables and parameters required for the control algorithms was emphasized.

This article is concerned with the leader-following output consensus problem in the framework of distributed nonlinear observers. Instead of certain hypotheses on the leader system, a group of geometric conditions is put forward to develop a novel distributed observers strategy, thereby definitely improving the applicability of the existing results. To be more specific, the improved distributed observers can precisely handle consensus problems for some nonlinear leader systems, which are invalid for the traditional strategies with a certain assumption, such as elastic shaft single linkage manipulator (ESSLM) systems and most of the first-order nonlinear systems. We prove the sufficient conditions for the exponential stability of our distributed observers’ error dynamic by proposing two pioneered lemmas to show the relationship between the maximum eigenvalues of two matrices appearing in Lyapunov type matrices. Then, a partial feedback linearization method with zero dynamic proposed in differential geometry is employed to design the purely decentralized control law for the affine nonlinear multiagent system. With this advancement, the existing results can be regarded as a specific case owing to that the followers can be chosen as an arbitrary minimum phase affine smooth nonlinear system. At last, the novel distributed observers and the improved purely decentralized control law are applied in the distributed control framework to construct a closed-loop system. We also prove the stability of the closed-loop system to achieve leader-following consensus. Our method is illustrated by the ESSLM system and Van der Pol system as leaders. [ABSTRACT FROM AUTHOR]

In this paper we present the modeling of an airship with a load suspended by a flexible heavy cable. The objective is to determine a control law that allows to stabilize the machine and its load under the effect of a gust of wind. In order to overcome the great inertia of the airship and the impossibility of using the accelerations of the latter to attenuate the oscillations of the suspended load, a new actuator was proposed at the exit of the cable in order to control its oscillations, namely a motorized cardan joint. The methodology of the study consisted of extracting a reduced dynamic model, which allowed us to build a robust control vector in order to stabilize the suspended load. The analysis of the stability of the zero dynamics of the system was carried out by means of the phase portraits of Poincaré. Numerical simulations were carried out and demonstrated the interest of our approach. [ABSTRACT FROM AUTHOR]

This article investigates the properties, from a nonlinear control system standpoint, of atomic force microscope (AFM) systems, whenever operated in contact mode and controlled in the vertical direction by proportional-integral control law. By modeling the AFM as a system in which a piezo-electric actuator and a cantilever mutually interact in order to produce the sample topography, ensuing distortions affecting the quality of the yielded topography measurement are naturally cast and analyzed. The proposed investigation considers distortions due to the inception of hysteresis and vibrational dynamics within the piezo-actuator or provoked by system saturation. Both hysteresis and saturation are inherently nonlinear phenomena and are modeled as such. In spite of the inherently nonlinear nature of the AFM dynamics, investigations of the contact mode case from a nonlinear standpoint are lacking within the AFM literature. As the topography yielded by the AFM completely relies on its control algorithm, to the point that the measurement itself corresponds to the control action $v(t)$ , it becomes of paramount importance to understand how $v(t)$ relates to the actual topography, and how such a relationship is affected by the aforementioned distortions. This article hence intends to contribute to the AFM literature, by providing a study in which the very meaning of the image measurement yielded by the AFM is investigated, in the light of distortions due to nonlinear phenomena. The AFM is considered to be operated in contact mode with a PI algorithm. Furthermore, as a byproduct of the derived nonlinear stability analysis, a novel, model-based algorithm for tuning the PI control gains is provided. Finally, experimental results are presented and analyzed in view of the derived theory. [ABSTRACT FROM AUTHOR]

We consider the discretization of continuous-time nonlinear systems described by normal forms. In particular, we consider the case when the input to the system is generated by a B-spline hold device to obtain an approximate discrete-time model. It is shown that the corresponding sampled-data model and its accuracy (measured in terms of the local truncation error) depend on the smoothness of the input and on the applied integration strategy, namely, the truncated Taylor series expansion. Moreover, the sampling zero dynamics of the discrete-time model are asymptotically characterized as the sampling period goes to zero, and it is shown that these zero dynamics converge to the asymptotic sampling zeros of the linear case.

When observabilities of hybrid dynamic systems are considered, the distinguishability of subsystems takes a very important role. Necessary and sufficient conditions for distinguishability of linear dynamic systems are obtained. Some illustrative examples are presented.

This paper focuses on the problem of event-triggered control for nonlinear systems via feedback linearisation. In the design procedure, the static event-triggered mechanisms and dynamic event-triggered mechanisms are applied to deal with nonlinear systems via feedback linearisation. Two cases of feedback linearisation are discussed. Besides, we prove that these two triggering mechanisms guarantee that all the closed-loop signals are asymptotically stable. The effectiveness of the proposed methods is illustrated and compared using simulation examples. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive tracking control problem for underactuated multibody systems with flexible links in the presence of unknown parameters. A four-body system with input signals acting on the first and fourth bodies is chosen as a benchmark model, which can be decomposed into a control dynamics subsystem and a zero dynamics subsystem. A new and detailed stability analysis is conducted to show that such a zero dynamic system is Lyapunov stable and is partially input-to-state stable under the condition that the speeds of first and fourth bodies are synchronous. The physical meaning of such partial input-to-state stability is clarified. An adaptive controller is developed to ensure such a needed system stabilisation condition and thus the boundedness of the desired closed-loop system signal and asymptotic speed tracking of the control dynamics subsystem. Detailed closed-loop system stability and tracking performance analysis are given, in which the tracking errors satisfy the L 1 performance. Extensions to the other multibody systems with flexible links are derived. The developed adaptive controller is applied to a realistic train dynamic model, and simulation results verify the desired system performance. [ABSTRACT FROM AUTHOR]

Finite Control Set Model Predictive Control (FCS-MPC) is an alternative to conventional linear controllers in power converters due to its attractive properties such as its conceptual simplicity, flexibility, direct consideration of non linearities as well as constraints, and fast control response. This last feature imposes computational constraints and short prediction horizons are therefore needed. In fact, in many applications an horizon one FCS-MPC controller is used. However, using FCS-MPC with a short prediction horizon in topologies that exhibit non-minimum phase behavior such as active-front-end rectifiers, dc-dc boost converters, and Z-source converters, among others, may lead to control issues. This work studies the origin of these control issues using nonlinear control theory considering a dc-dc boost converter as a case study. It is shown that the difficulty to directly control the converter output voltage using short horizon FCS-MPC is the resulting unstable internal dynamic, as the short horizon FCS-MPC controller acts like an input-output linearizing controller. To solve the problem of the unstable internal dynamic, a short horizon FCS-MPC controller based on input-state linearization is proposed allowing correct operation of the system. Experimental results show the feasibility of the proposal. [ABSTRACT FROM AUTHOR]

In this article, the adaptive tracking control problem is investigated for a multibody high-speed train dynamic model in the presence of unknown parameters, which is an open adaptive control problem. A four-car train unit model with input signals acting on the second and third cars and output signals being the speeds of the first and third cars is chosen as a benchmark model, in which the aerodynamic resistance force is also considered. To handle the nonlinear term, the feedback linearization method is employed to decompose the system into a control dynamics subsystem and a zero dynamics subsystem. A new and detailed stability analysis is conducted to show that such a zero dynamic system is a Lyapunov stable and is also partially input-to-state stable under the condition that the speed error between the first and third cars is exponentially convergent (to be ensured by a nominal controller) or belongs to the L1 signal space (to be achieved by a properly designed adaptive controller). The system configuration leads to a relative degree 1 subsystem and a relative degree 2 subsystem, for which different feedback linearization-based adaptive controllers and their nominal versions are developed to ensure the needed stabilization condition, the desired closed-loop system signal boundedness, and asymptotic output speed tracking. Detailed closed-loop system stability and tracking performance analysis are given for the new control schemes. Simulation results from a realistic train dynamic model are presented to verify the desired adaptive control system performance. [ABSTRACT FROM AUTHOR]

The development of modern engines with increasing power, fast dynamics, and responsiveness, as well as changes in system architecture, set new requirements on traction control system design for vehicles. We propose a robust nonlinear control design based on input–output linearization to solve the traction control problem. The oscillatory behavior of the powertrain is taken into account explicitly during the controller design phase. Previous work has not addressed this case and no results on stability are available so far. We proove global asymptotic stability of the nonlinear zero dynamics analytically using a parametric Lyapunov function. The traction controller is implemented on different test vehicles and validated for different driving maneuvers and road conditions. Experimental results obtained with test vehicles and by simulation demonstrate stability, high performance, and robustness of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on the adaptive tracking control problem for strict‐feedback nonlinear systems with zero dynamics via prescribed performance. Based on polynomial fitting, an adjustable performance function is firstly proposed, whose parameters can be adjusted in real time according to the tracking error. Furthermore, an adaptive prescribed performance tracking controller is constructed via the backstepping method, which guarantees that all the states in the closed‐loop system are bounded. Meanwhile, the output tracking error falls within an adjustable performance boundary and asymptotically converges to zero. Simulation comparison demonstrates the advantages of the developed controller as follows: (1) the parameters of the adjustable performance function are adjusted online according to the tracking errors for a faster convergent performance boundary; (2) the steady‐state performance of the system is further optimized simultaneously. [ABSTRACT FROM AUTHOR]

It is well-known that such non-conventional digital control schemes, such as generalized sampled-data hold functions, have clear advantages over the conventional single-rate digital control systems. However, they have theoretical negative aspects that deviation of the input can lead to intersample oscillations or intersample ripples. This paper investigates the zero dynamics of sampled-data models, as the sampling period tends to zero, composed of a new generalized hold polynomial function, a nonlinear continuous-time plant and a sampler in cascade. For a new design of generalized hold circuit, the authors give the approximate expression of the resulting sampled-data systems as power series with respect to a sampling period up to the some order term on the basis of the normal form representation for the nonlinear continuous-time systems, and remarkable improvements in the stability properties of discrete system zero dynamics may be achieved by using proper adjustment. Of particular interest are the stability conditions of sampling zero dynamics in the case of a new hold proposed. Also, an insightful interpretation of the obtained sampled-data models can be made in terms of minimal intersample ripple by design, where the ordinary multirate sampled systems have a poor intersample behavior. It has shown that the intersample behavior arising from the multirate input polynomial function can be localised by appropriately selecting the design parameters based on the stability condition of the sampling zero dynamics. The results presented here generalize the well-known notion of sampling zero dynamics from the linear case to nonlinear systems. [ABSTRACT FROM AUTHOR]

The development of a nonlinear controller of stabilization of underactuated mechanical systems (UMSs) is a challenging endeavor due to a larger number of output variables to be controlled than the control input space. This paper proposes an adaptive sliding mode control based on a higher-order nonlinear disturbance observer (HONDO) for stabilizing the rotational pendulum (RP) system falling under the class of UMSs. Firstly, the HONDO is designed in such a way that it can improve accuracy in estimations with its incremental order. As a result, the proposed controller obtained from the sliding surface which is developed with system's states and estimations, forces the states attaining the sliding mode and hence keeps them to their origin forever against disturbances. To achieve this, the sliding coefficients are obtained using inertia matrix of the system. The zero dynamics is stabilized by the proposed controller. This alleviates the chattering problem in the control input. Finally, numerical performance on the underactuated RP model is analyzed to show the efficiency of the proposed controller and it is compared with the established control technique found in the literature. [ABSTRACT FROM AUTHOR]

Highlights • An approximate sampled-data model for nonlinear systems with backward triangle sample and hold function is first derived. • Obtaining a novel expression and stable conditions of zero dynamics in the obtained sampled-data model. • Zero dynamics of the resulting model can be arbitrarily placed by selecting proper parameters from the stable conditions. • Nonlinear systems using those methods in this paper have better control performance. Abstract It is well known that a good approximate sampled-data model is very important in sampled-data controller design of nonlinear continuous-time system because the exact sampled-data model of nonlinear continuous-time system is often unavailable. It is also a truth that unstable zero dynamics of sampled-data model greatly limit the control performance of the system. This paper investigates the properties of approximate sampled-data model and its zero dynamics, which generated during the process of discretization with backward triangle sample and hold (BTSH). Further, a more accurate sampled-data model is obtained for nonlinear systems in BTSH case. The zero dynamics form and stable conditions are also derived. Finally, numerical examples are provided to better show the results developed in this paper. [ABSTRACT FROM AUTHOR]

To overcome the obstructions imposed by high-dimensional bipedal models, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The process begins with trajectory optimization to design an open-loop periodic walking motion of the high-dimensional model and then adding to this solution a carefully selected set of additional open-loop trajectories of the model that steer toward the nominal motion. A drawback of trajectories is that they provide little information on how to respond to a disturbance. To address this shortcoming, supervised machine learning is used to extract a low-dimensional state-variable realization of the open-loop trajectories. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. The design procedure is first developed for ordinary differential equations and illustrated on a simple model. The methods are subsequently extended to a class of hybrid models and then realized experimentally on an Atrias-series 3D bipedal robot. [ABSTRACT FROM AUTHOR]

Highlights • Introduce a new nonlinear coordination method based on zero dynamics (ZD) approach. • Design a super twisting sliding mode control to improve performance of ZD method. • Coordinate controllers of DFIG and STATCOM in multi-machine power systems. • Enhance transient and voltage stability of inter-connected power systems. Abstract This paper proposes a new nonlinear control approach to coordinate doubly fed induction generator (DFIG)-based wind turbines and static synchronous compensator (STATCOM) controllers in multi-machine power systems. Its main objectives are to improve the transient and voltage stability of the inter-connected multi-machine power system via simultaneous design of the voltage of the DFIGs' rotors and reference current of STATCOM. The nonlinear approach is based on a multi input-multi output (MIMO) zero dynamics (ZD) technique augmented by a super twisting sliding mode control (STSMC) to reduce the effects of the linearization error. The proposed approach was implemented to the Kundur's four-machine two-area power system and the IEEE 39-bus power system. Its performance was assessed in the presence of various faulty scenarios and disturbances. The effectiveness of the proposed approach (ZD-STSMC) was evaluated via eigenvalue analysis, transient simulations and transient stability margin analysis (by critical clearing time (CCT)). The merits of the proposed design are further compared to those of the exact feedback linearization (EFL) approach. Enhancing the power and voltage stability of large scale power systems, damping power oscillations and providing faster post-fault recovery time are among the positive features of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: For systems that are not feedback linearizable, a natural question is: how to find the largest feedback linearizable subsystem and, if the partial linearization is not unique, what are the control‐theoretic properties of various partial linearizations. In this paper, we will consider the problem of how to choose a partially linearizing output that renders the zero dynamics asymptotically stable and when such an output exists. We will state general results solving completely the problem for systems whose linearizability defect is one by identifying and describing two classes of systems. For the first class, all maximal partial linearizations lead to the same zero dynamics. For the second class, any asymptotic behavior of the zero dynamics can be achieved by a suitable choice of a partially linearizing output. In the second part, we apply our results to mechanical systems with two‐degrees‐of‐freedom and provide a detailed study of their partial linearizations. We illustrate the obtained results by examples of Acrobot (which belongs to the second class) and Pendubot (which belongs to the first class). [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the problem of asymptotic output tracking of a class of semilinear parabolic equations with pointwise in‐domain actuation. First, the assessment of the well‐posedness of the considered systems is performed, and then, the stability of boundary controlled systems is analyzed via Chaffee‐Infante equation and Fisher's equation. The application of the zero dynamics inverse design results in a dynamic control scheme that is implemented by using the technique of trajectory planning for flat systems and the Adomian decomposition method. The convergence of the solution of the original systems to that of the corresponding zero dynamics and the convergence of the solution expressed by an Adomian series are also analyzed. Numerical simulations are carried out to illustrate the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

Abstract The zero dynamics of infinite-dimensional systems can be difficult to characterize. The zero dynamics of boundary control systems are particularly problematic. In this paper the zero dynamics of port-Hamiltonian systems are studied. A complete characterization of the zero dynamics for port-Hamiltonian systems with invertible feedthrough as another port-Hamiltonian system on the same state space is given. It is shown that the zero dynamics for any port-Hamiltonian system with commensurate wave speeds are a well-posed system, and are also a port-Hamiltonian system. Examples include wave equations with uniform wave speed on a network. A constructive procedure for calculation of the zero dynamics that can be used for very large system order is provided. [ABSTRACT FROM AUTHOR]

Piezoelectric bending actuators have been extensively utilized in recent years. Two major modeling methods, lumped and continuous, have been generally proposed in previous researches for these actuators. The lumped method can only express the transverse vibration of one specified point on the actuator. In addition, the effect of higher vibrational modes has been ignored. Hence, continuous dynamic models have been proposed to rectify the mentioned drawbacks. In this method, linear constitutive equations for low voltage applications are usually applied. But, the main challenge in continuous modeling of piezoelectric actuators is the hysteresis nonlinear phenomenon caused by high excitation voltages. In this paper, piezoelectric nonlinear hysteretic constitutive equations have been employed to carry out the continuous dynamic model for two general types of bimorph bending actuators i.e. Series and Parallel. In addition, zero dynamic analysis for nonlinear systems has been applied to clarify the effect of higher vibrational modes on the actuator dynamic behavior based on the location of target point. Experimental results show the maximum error 1.44 and 1.2% in the identification of first and second vibrational modes, respectively, and the maximum error 2.89% in the modeling of actuator nonlinear behavior by two vibrational modes. These results validate the efficiency of the proposed dynamic model to express the actuator nonlinear behavior, dynamic analysis, and its superiority over conventional models with one vibrational mode. [ABSTRACT FROM AUTHOR]

In this study, the six-degrees-of-freedom flight motion of a tail-controlled bank-to-turn aircraft with two flaps is described as a nonlinear control system. The controllability of this flap-controlled system is analyzed based on nonlinear controllability theory and the system is proved to be weakly controllable. By choosing the angle-of-attack and roll angle as the outputs of this control system, the zero dynamics of the system are analyzed using Lyapunov stability theory, and are proved to be stable under some conditions given by an inequality. Then an autopilot is designed for this system using the feedback linearization technique. Results of the numerical simulation for this control system show the effectiveness of the controllability analysis and autopilot design. [ABSTRACT FROM AUTHOR]

When observabilities of hybrid dynamic systems are considered, the distinguishability of subsystems takes a very important role. Necessary and sufficient conditions for distinguishability of linear dynamic systems are obtained. Some illustrative examples are presented. [ABSTRACT FROM AUTHOR]

This paper discusses a method for achieving high-speed collisionless walking of a point-footed walker. First, we introduce a model of an underactuated rimless wheel with an internal reaction wheel for analysis, and develop two controllers for the single-limb support and double-limb support phases so that they minimize the corresponding control period based on the principle of the minimum-time control. The former is determined under the unilateral constraint condition, whereas the latter is determined under the constraint condition of the zero-moment point for maintaining double-limb support, respectively. Second, we extend the results obtained for generation of the highest speed collisionless walking gait without including double-limb support phases by appropriately setting the initial angular velocity of the reaction wheel. The approximate analytical solution of the target initial angular velocity is derived using the linearized model, and that of the nonlinear model is numerically obtained using a bisection method. The validity of the proposed methods is investigated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a novel adaptive control scheme for half-car active suspension system (HCASS) with unknown dead-zone input. Under the proposed control framework, the overall HCASS is divided into two subsystems. The proposed controller is designed based on the first subsystem, and the second subsystem is regarded as zero dynamics of HCASS. For the first subsystem, a new robust adaptive strategy is first constructed to compensate the adverse effects of unknown dead-zone input nonlinearities. Further, in order to ensure some important state variables within the given restrictive conditions all the time, a novel prescribed performance control strategy (PPC, for short) is designed. For the second subsystem, the corresponding stability analysis of zero dynamics is presented. Finally, the solution of the resulting closed-loop system is ensured to be uniformly ultimately bounded, and the effectiveness of the proposed approach is illustrated by a strict and complete simulation analysis. [ABSTRACT FROM AUTHOR]