Horizontal Platform Systems Research Articles

Disturbance Observer-Based Event-Triggered Adaptive Command Filtered Backstepping Control for Fractional-Order Nonlinear Systems and Its Application

This paper considers the disturbance observer-based event-triggered adaptive fuzzy tracking control issue for a class of fractional-order nonlinear systems (FONSs) with quantized signals and unknown disturbances. To improve the disturbance rejection ability, a fractional-order nonlinear disturbance observer (FONDO) is designed to estimate the unknown composite disturbances. Furthermore, by combining an improved fractional-order command-filtered backstepping control technique and an event-triggered control mechanism, an event-triggered adaptive fuzzy quantized control scheme is established, which guarantees the desired tracking performance can be achieved even in the presence of network constraint. Finally, the validity and superiority of the theoretic results are verified by a fractional-order horizontal platform system.

ADAPTIVE TRACKING CONTROL FOR FRACTIONAL-ORDER NONLINEAR UNCERTAIN SYSTEMS WITH STATE CONSTRAINTS VIA COMMAND-FILTERING AND DISTURBANCE OBSERVER

In this paper, the state-constrained adaptive control problem for a class of uncertain fractional-order nonlinear systems with unknown external disturbances is studied. Using the fuzzy approximation and backstepping control layout, an adaptive disturbance-observer-based control method is proposed, which can effectively estimate the unknown external disturbances through the designed disturbance observers. As we know, the standard backstepping control has inherent computational complexity. Therefore, a design approach of fractional-order command filter is introduced, which takes advantage of fractional-order command filter to pre-estimate the virtual input signal and its fractional derivative. In addition, barrier Lyapunov functions are exploited to cope with the fractional states-constrained control problem. The combination of barrier Lyapunov function technique and backstepping design not only ensures excellent tracking performance, but also enhances the robustness of the system. Furthermore, based on the fractional Lyapunov approach, the relevant stability analysis is established, which demonstrates that all states of the system remain within their constrained scope, and all signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed scheme is verified by numerical simulation examples of RLC circuit and horizontal platform system.

Input-constrained chaos synchronization of horizontal platform systems via a model predictive controller

Horizontal platform systems are mechanical systems that can exhibit both periodic and chaotic behaviour. Various control techniques have been developed to solve their chaos synchronization. However, the avoidance of control saturation is rarely considered in existing control techniques. In this paper, a model predictive controller is developed to address the input-constrained chaos synchronization of horizontal platform systems. To meet the requirements of computational efficiency, the highly efficient symplectic pseudospectral method is taken as the core solver of the model predictive controller. Two methods to impose the terminal boundary condition are considered. And two indices, i.e., the approximate synchronization time and the synchronization-consumed energy, are proposed to evaluate the synchronization performance. Numerical simulations demonstrate that the developed model predictive controller can achieve faster synchronization while owns better robustness under various kinds of external disturbances when compared to several feedback controllers.

Prescribed performance adaptive finite-time control for uncertain horizontal platform systems

This paper presents a new approach to the design of prescribed performance adaptive control for uncertain horizontal platform systems with the finite-time convergence. Following an appropriate performance function and error transformation, a new adaptive control law is proposed by using a novel integral non-singular terminal sliding mode surface. The proposed approach simultaneously guarantees that (i) the transient responses of the closed-loop system possess some advanced properties such as the existence of the prespecified lower bound of the convergence rate and of the pre-established upper bound of the maximum overshoot; and (ii) the finite-time convergence of the state trajectories/tracking errors to zero. The global stability and finite-time convergence are strictly analyzed. The proposed method is clarified and verified through two numerical simulation examples.

Multistability in Horizontal Platform System with and without Time Delays

Chaotic behavior and bifurcation analysis of horizontal platform systems (HPS) have been investigated widely by many researchers. However, the multistable features of such systems have not been investigated, and hence we identified the multistable parameter and investigated the coexisting attractors of the HPS. To understand the effects of time delays on the nonautonomous and autonomous HPS, we introduced a constant time delay in the state feedback variable. Investigation of the bifurcation of the time delayed HPS with time delay and parameters reveals that the system behavior differs between the autonomous and nonautonomous HPS. To investigate the multistability existence in time delayed HPS, we plot the bifurcation of the autonomous HPS and show the multistability and coexisting attractors.

Finite-Time Tracker Design for Uncertain Nonlinear Fractional-Order Systems

This paper considers the problem of finite-time output tracking for a class of nonautonomous nonlinear fractional-order (FO) systems in the presence of model uncertainties and external disturbances. The finite-time control methods indicate better properties in terms of robustness, disturbance rejection, and settling time. Thus, design of a robust nonsingular controller for finite-time output tracking of a time-varying reference signal is considered in this paper, and a novel FO nonsingular terminal sliding mode controller (TSMC) is designed, which can conquer the uncertainties and guarantees the finite-time convergence of the system output toward the desired time-varying reference signal. For this purpose, an appropriate nonsingular terminal sliding manifold is designed, where maintaining the system's states on this manifold leads to finite-time vanishing of error signal (i.e., ensures the finite-time occurrence of both reaching and sliding phases). Moreover, by tacking the fractional derivative of the sliding manifold, the convergence of system's trajectories into the terminal sliding manifold in a finite time is proven, and the convergence time is estimated. Finally, in order to verify the theoretical results, the proposed method is applied to an FO model of a horizontal platform system (FO-HPS), and the computer simulations show the efficiency of the proposed method in finite-time output tracking.

Fuzzy Adaptive Prescribed Performance Control for Uncertain Horizontal Platform System with Unknown Control Gain

This paper proposes a fuzzy adaptive control method for uncertain horizontal platform system with unknown control gain, which is capable of guaranteeing the prescribed performance bounds. An error transformation is introduced to transform the original constrained system into an equivalent unconstrained one. Then, based on the error transformation technique and the predefined performance technique, a fuzzy adaptive controller is designed for the unconstrained system. It is shown that all the variables of the resulting closed-loop system are bounded. Finally, an illustrative example is given to demonstrate the effectiveness and usefulness of the proposed method.

Chaotic behavior in fractional-order horizontal platform systems and its suppression using a fractional finite-time control strategy

The present paper investigates the dynamical properties of a non-autonomous fractional-order horizontal platform system (FOHPS). According to different parameter settings, we show that the FOHPS can possess stable, chaotic and unstable states. Using the maximal Lyapunov exponent criterion, we show that the FOHPS exhibits chaos. Strange attractors of the system are also plotted to validate chaotic behavior of the system. Since the chaotic behavior of the FOHPS may be undesirable, a fractional finite-time controller is introduced to suppress the chaos of the FOHPS with model uncertainties and external disturbances in a given finite time. We use the fractional Lyapunov theory to prove the finite time stability and robustness of the proposed scheme. Finally, computer simulations are given to illustrate the efficiency and applicability of the proposed fractional control method.

An Adaptive Fuzzy Sliding Mode Control Design for a Class of Uncertain Horizontal Platform Systems

This paper presents an adaptive fuzzy sliding mode control design for a class of uncertain horizontal platform systems (HPSs). Firstly, a nonsingular terminal sliding surface is proposed for HPSs. Then, a fuzzy logic system is introduced to estimate the system uncertainties. The adaptive fuzzy sliding mode controller can guarantee the stability of the closed-loop system. The corresponding numerical simulations are demonstrated to verify the effectiveness of the proposed method.

Circuit Implementation and Synchronization Control of Chaotic Horizontal Platform Systems by Wireless Sensors

Horizontal platform system (HPS) produces a nonlinear behavior from precision machinery systems. This mechanical system is implemented mainly in offshore areas or earthquake engineering. However, elucidating or controlling this non-linear behavior of mechanical systems is extremely difficult and time consuming. Therefore, in addition to developing an electronic circuit to implement HPS, this work designs a sliding mode control (SMC) for synchronizing the state trajectories of two horizontal platform systems, subsequently allowing us to easily understand the HPS, perform more detailed analysis, and achieve further control. Experimental results demonstrate the feasibility of implementing the HPS by the proposed electronic circuit system. Comparing the proposed electronic circuitry designs and the HPS of computer simulation reveals that the results of the non-linear dynamic behavior correlate well with each other. Finally, based on use of the control technology, master-slave chaos synchronization with sliding mode control is achieved by wireless sensors.

PRACTICAL SYNCHRONIZATION OF NONAUTONOMOUS SYSTEMS WITH UNCERTAIN PARAMETER MISMATCH VIA A SINGLE STATE FEEDBACK CONTROL

Robust practical synchronization of general second-order nonautonomous systems with uncertain parameter mismatch is investigated by using a single state feedback control. Some simple general algebraic criteria are derived based on practical stability theory of nonautonomous dynamical system. A distinctive feature of this work is that the parameter mismatch not only exists in system parameters, but also in the external excitation ones. More reasonably, the values of parameter mismatch can be uncertain. Besides, a single state feedback control including an approximate differentiation filter only needs to know information about one state, which provides an advantage over the use of full-state model-based observers. It is shown that the approaches developed here further extend the ideas and techniques presented in recent literature. As a direct application of the new theoretical results, the obtained results are applied to a typical horizontal platform system and the representative forced Duffing–Van der Pol oscillator. Subsequently, numerical simulations demonstrate the effectiveness of the criteria and the robustness of the control technique.

Synchronization of chaotic systems under sampled-data control

The problem of global asymptotical synchronization of chaotic Lur’e systems using sampled-data controller is considered in this paper. Sufficient conditions are obtained in terms of effective synchronization linear matrix inequality using a piecewise sawtooth structure of the sampling in time by constructing the new discontinuous Lyapunov functionals. The sampled-data feedback control gain is obtained from the derived condition. The Chua system and horizontal platform system are taken for numerical demonstration to show the effectiveness of the proposed condition.

Finite-time stabilization of a non-autonomous chaotic rotating mechanical system

This paper presents robust adaptive controllers for finite-time stabilization of non-autonomous chaotic horizontal platform systems (HPSs). The effects of uncertainties, unknown parameters and input nonlinearities are fully taken into account. Appropriate adaptation laws are designed to undertake the unknown parameters. Using the adaptation laws and finite-time control theory, first a robust adaptive controller is derived to stabilize the non-autonomous uncertain HPS in finite time. Then, considering the effects of input nonlinearities, another finite-time controller is introduced to stabilize the uncertain HPS with nonlinear control inputs. The finite-time stability and convergence of the proposed schemes are analytically proved. Two illustrative examples are given to show the robustness and feasibility of the proposed finite-time controllers.

Practical synchronization of second-order nonautonomous systems with parameter mismatch and its applications

This paper is concerned with robust practical synchronization for general second-order nonautonomous systems with parameter mismatch. Some simple yet general algebraic criteria are derived based on practical stability theory of nonautonomous dynamical systems. A distinctive feature of this work is that the parameter mismatch cannot only be existed in system parameters, but also in external excitation ones. Furthermore, the obtained results are applied to a typical horizontal platform system and the representative forced Van der Pol oscillator. Subsequently, numerical simulations demonstrate the effectiveness of the criteria and the robustness of the control technique.

Design and Realization of Two-Axis Horizontal Stabilized Platform Based on Self-Correction Control Method

To enhance the accuracy of stabilization, this paper presents a design of two-axis horizontal stabilization platform system, which is based on the combination of gyroscope and inclinometer sensors. The self-correction control method is put forward to solve the system error caused by gyroscope zero drift in traditional gyro stabilized platform, which works in the way of revising the gyroscope zero coefficient, according to the real-time attitude information feed backed by inclinometer sensors fixed in objective platform.

Design and Synchronization of Master‐Slave Electronic Horizontal Platform System

Horizontal platform system (HPS) is one of the mechanical systems with rich behavior and has extensively been applied in offshore and earthquake engineering. A corresponding electronic HPS is proposed in this paper to reduce the research cost and time when studying dynamics of the mechanical HPS. Furthermore, an output feedback controller is proposed for global synchronization between coupled electronic HPS systems and its stability condition is also derived by employing the Lyapunov stability theory. The experimental simulations verify the dynamics of the proposed electronic HPS and the synchronization effectiveness of the proposed control scheme.

Synchronization of mechanical horizontal platform systems in finite time

The horizontal platform system (HPS) is a mechanical device that exhibits rich and chaotic dynamics. In this paper, the problem of finite-time synchronization of two non-autonomous chaotic HPSs is investigated. It is assumed that both drive and response systems are disturbed by model uncertainties, external disturbances and fully unknown parameters. Appropriate update laws are proposed to undertake the unknown parameters. Using the update laws and finite-time control theory, a robust adaptive controller is derived to synchronize the two uncertain HPSs in a given finite time. Subsequently, the effects of input nonlinearities are taken into account and a robust adaptive controller is introduced to synchronize the two uncertain HPSs within a finite time. The finite-time stability and convergence of the proposed schemes are analytically proved. Two illustrative examples are presented to show the robustness and applicability of the proposed adaptive finite-time control techniques.

Design and implementation of fuzzy sliding mode controllers for generalized projective synchronization of chaos horizontal platform systems

This paper presents robust chattering-free fuzzy sliding mode control (FSMC) as a way to achieve generalized projective synchronization (GPS) of two horizontal chaos platform vibration systems with system uncertainty and external disturbance. An appropriate sliding surface is acquired through an SMC design such that the error state trajectories of a master–slave system will reach such a sliding surface and approaches to the origin. Based on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. As a consequence, the system is simulated and experimented to demonstrate that the error state tends to be stabilized and the chattering problem can be thus resolved, implying that the slave horizontal platform system (HPS) is GPS with the master HPS.

Generalized projective synchronization for a class of chaotic systems with parameter mismatching, unknown external excitation, and uncertain input nonlinearity

In this paper, the concept of the generalized projective synchronization in practical type (GPSPT) is introduced and the GPSPT of uncertain horizontal platform systems with parameter mismatching, unknown external excitation, and uncertain input nonlinearity is investigated. Based on the differential inequality methodology, a tracking control is proposed to realize the GPSPT for the uncertain horizontal platform systems with parameter mismatching, unknown external excitation, and uncertain input nonlinearity. Not only the desired scaling factor, the guaranteed exponential convergence rate, and convergence radius can be pre-specified, but also the parameter mismatching and unknown external excitation can be simultaneously conquered by the proposed control. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result.

Master–slave synchronization criteria for horizontal platform systems using time delay feedback control

This paper is concerned with master–slave synchronization for two identical non-autonomous horizontal platform systems by using time-delay feedback control. Compared with some existing results on synchronization for horizontal platform systems, the effect of the time delay in the feedback control on master–slave synchronization is investigated. Applying a delay decomposition approach, some delay-dependent synchronization criteria are established and formulated in the form of linear matrix inequalities (LMIs). Sufficient conditions about the existence of a time delay feedback controller are derived by employing these newly obtained synchronization criteria. The controller gains can be achieved by solving a set of LMIs. One simulation example is given to illustrate the effectiveness of synchronization criteria and the design method.