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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.

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.

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.

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.

The problem of designing Luenberger-like observer for non-linear Lipschitz systems is addressed. Based on using the coordinate transformation, the author classify many practical approaches of observer synthesis into direct and indirect methods. A generalised Lipschitz condition and the related stability condition are then employed to establish a general framework in designing the Luenberger-like observer dealing with both methods. Moreover, the proposed framework is interpreted in terms of some linear matrix inequalities (LMIs) which allows using numerical techniques to obtain a reduced order observer. Finally, some simulation examples are given to exhibit the effectiveness of the proposed observer synthesis approach.

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.

The stability-sufficient condition in designing an observer for non-linear Lipschitz systems is extended such that it does not neglect the structure of given non-linearity and can be less conservative in applying to many non-linear systems. A design procedure based on full control problem is then presented to satisfy the extended condition by means of a constant observer gain. Finally, simulation examples are given to exhibit the effectiveness of the proposed condition and design procedure in dealing with some large Lipschitz non-linearities.