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This brief considers sliding mode control of hysteresis in piezoelectric actuators. For modeling of hysteresis, the Bouc–Wen model that is based on differential equations is utilized. One of the states of this model is unmeasurable. Therefore, a state observer is proposed, and the proper selection of observer parameters is discussed. Based on the observed state, a control rule is proposed, and asymptotic stability of the observer-based closed-loop system is proven using the Lyapunov theory. This brief also presents a design method, i.e., sufficient conditions on design parameters for closed-loop stability are derived explicitly. Furthermore, the mass, stiffness, and damping coefficients in the model are assumed unknown. The values of these parameters are estimated using an online adaptation rule, and the control rule is modified based on the estimated parameters. The adaptation rule is extracted so that the asymptotic stability of the whole system is guaranteed. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed scenarios.

The output feedback stabilization of Lipschitz nonlinear systems is addressed. The synthesis of reduced-order controller is formulated as static output feedback problem. Based on coupled algebraic Riccati inequalities, the stability analysis of closed loop dynamic is presented. By utilizing some structural knowledge of Lipschitz nonlinearity, the sufficient conditions to obtain static as well as dynamic output feedback gains are given. For the class of Lipschitz nonlinearity, it is shown that the proposed condition is a necessary and sufficient condition to achieve static gain. The cone complementary linearization method is then applied to satisfy the proposed stability condition and to obtain an output feedback regulator. The effectiveness of proposed method is finally demonstrated through simulation results on some practical systems.

Asymptotic stabilization of a class of nonlinear systems with known constant long input delay is addressed in the presence of external disturbance by applying sliding mode control method. Modified prediction variable scheme is employed to compensate long delays in the input, where conventional prediction variable approaches cannot be employed. This is mainly due to the fact that the external disturbance appears in the prediction variable, which renders the controller dependent on the external disturbance. In order to tackle this problem, the nonlinear disturbance observer based predictor is used. A suitable disturbance observer is designed to estimate the external disturbance that appears in the prediction variable. Respected to some existing results, the prediction-based control for more general class of the nonlinear systems in the presence of external disturbance is the main contribution of this paper. Actuator and sensor delays exist in the most common dynamic systems. So, the proposed control scheme can be employed in many conventional systems. The simulation results indicate the robustness and efficiency of the proposed controller.

In this study, stabilisation of input-delay non-linear systems in the presence of disturbance based on prediction variable is studied. For both disturbance estimation and delay compensation, an extended prediction variable as well as adaptive sliding mode controller are proposed in which the open-loop system is not required to be stable. In the proposed prediction variable one needs to estimate disturbance in the future. In order to solve this problem a new non-linear disturbance observer (NDOB) is proposed. Considering the NDOB in the closed-loop system, the stability analysis of error dynamic is performed. And the asymptotic stability of non-linear system with input delay is guaranteed for some class of disturbance. Simulation results finally validate the good performance and robustness of the proposed controller based on disturbance observer.

The mechanical impedance of the human arm can be measured to quantitatively assess the motor function. In this paper, an adaptive least square estimation method is proposed for online measurement o...

This paper proposes a cascade high-gain observer for a class of triangular nonlinear systems with large and diverse time delays at states and output equation. Compared with some existing re...

An observer-based controller for Lipschitz nonlinear systems is presented. The necessary and sufficient condition to ensure stability of state-observer as well as nonlinear system with state-feedback control law is derived. According to the separation principle, the closed-loop stability is guaranteed based on dual problems concerning stability of state-observer and stability of state-feedback parts. Also, the stability region for locally Lipschitz nonlinearities is obtained. A practical synthesis approach to achieve controller parameters is then given which yields the closed-loop convergence with less conservative results. The effectiveness of the proposed synthesis method is finally demonstrated by simulation results.

A robust nonlinear observer for a class of nonlinear time-delay systems is introduced. The generalized sector constraint is employed to deal with many commonly encountered nonlinearity in dynamic equation. It is assumed that time-varying delay exists in both state and output equations, and further it directly appears in nonlinear function. By utilizing two correction terms in nonlinear observer related to the dynamic equation as well as system’s nonlinearity, the stability analysis of observer error dynamic is presented. For uncertain systems, a synthesis method to obtain robust nonlinear observer is then given in terms of some LMI’s. The effectiveness of proposed observer and related synthesis method are finally demonstrated through simulation examples.

The aim of this paper is to propose an identification scheme for linear switched systems with state space description. The method consists of two stages: first, output matrix elements are identified by Kaczmarz Algorithm and then by k-means clustering algorithm, switching time is estimated; Second, by passing the estimated switching time to an adaptive observer in serial-parallel form, input and state matrices are estimated. Identification method is tested on numerical simulation.

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities.

In this paper, a novel observer-based force control scheme is proposed to guarantee the position and force tracking in nonlinear teleoperation systems, subject to constant communication time delay. Stability of the teleoperation system is analytically proved using the Lyapunov stability theorem. Enough condition for asymptotic convergence of the force and position are derived. The transparency is also improved by force tracking capability of the system. The teleoperation controller is then applied to a pair of planar 2-DOF robots, connected via a communication channel with constant time delay. The experimental and simulation results demonstrate the effectiveness of the proposed control algorithm, in force estimation and dealing with time delay.

In this paper, a sliding mode observer for the class of Lipschitz nonlinear systems with uncertainty is proposed. The uncertainty is assumed to be bounded and the matching condition is first taken into account. The generalized Lipschitz condition is employed to consider some structural knowledge of Lipschitz nonlinearity. This yields less conservative results in stability analysis of proposed observer dynamics. The results are then extended to the unmatched uncertainty. Moreover, a synthesis method in terms of some linear matrix inequalities is established to achieve the proposed sliding mode observer. The simulation results on manipulator with revolute joints actuator are finally given to exhibit the effectiveness of the proposed observer and related synthesis method.

A new method is proposed in this article in order to determine a guaranteed interval of time delay in input signal for a class of non-linear control systems with state feedback. This method is based on the stability sufficient condition of a non-linear control system using the Lyapunov direct approach. For this purpose, the dynamic equations of the non-linear input-delayed system are reformulated as a non-linear system without delay, but with delay-dependent coefficients in the state-space description. The control strategy is considered a linear state feedback. Then, by introducing an appropriately related Lyapunov candidate, the stability sufficient condition of the closed-loop system is satisfied, leading to a guaranteed interval of delay according to the state feedback gain. The main results are gathered and proved as a lemma. The effectiveness of this proposed method is investigated by simulating the state feedback control of a non-linear synchronous generator with a delay in input.

This paper proposes an observer for the class of triangular nonlinear systems including the model uncertainty, with constant delays in the state and input equations. It is assumed that the nonlinear perturbations satisfy the Lipschitz condition and the uncertain part is bounded. The main idea is based on the designing a high-gain observer in combination with the sliding mode observer which leads to a robust high-gain observer that has not been sufficiently studied previously. A compensation term is included in the observer dynamics that is designed based on the solution of a Lyapunov inequality. For stability analysis, if the matching condition is satisfied, by using a suitable Lyapunov-Krasovski functional, simple sufficient conditions are provided that guarantees the observation error converges to the origin asymptotically. The simulation results for a nonlinear system in triangular form illustrate the effectiveness of the proposed approach.

In this paper, a finite time control method for an uncertain nonlinear system is proposed. An adaptive sliding mode disturbance observer is designed to estimate the disturbance in finite time. The assumptions on the disturbance are relaxed in the sense that, its first derivative upper bound is considered to be unknown and only the order of its second derivative upper bound is known. Based on the output of proposed disturbance observer, a terminal sliding mode control scheme for the uncertain nonlinear system is presented. The designed control law is continuous and nonsingular. Furthermore, compared with some existing sliding mode controllers, the conditions on the controller parameters bounds are relaxed. It is proved that the disturbance observer error as well as the system states converges to the origin in finite time. Finally, the effectiveness of the proposed method is shown by numerical simulations.

Aim of this paper is to estimate time delays in nonlinear dynamic systems with unknown time-delays, such that time-delays appear in both state and output equations. The problem of estimating unknown delays is formulated as a dynamic optimization problem in which the cost function is defined based on the least-squares error between predicted and actual system output. Using proposed estimation method derives unknown time-delays by evaluating the gradient of cost function. Since, the gradient cannot be obtained analytically by standard differentiation rules, a practical computational method is presented to compute gradient and related cost function. The effectiveness of proposed algorithm is finally demonstrated by applying it to a practical example.