Mode Control For Uncertain Systems Research Articles

Event-triggered sliding mode control for uncertain systems with multiple disturbances

ABSTRACT A new event-triggered sliding mode anti-disturbance (ETSMAD) control scheme is presented for the uncertain linear systems encountered by multiple disturbances containing the modelled unmeasurable disturbances and unmodelled disturbances. On the sliding mode reaching stage and sliding stage, different event-triggered programmes are developed to reduce the communication transmission load between the system and controller. The SM control law based on the ET programme is established to achieve the compensation and suppression of the modelled unmeasurable disturbances and unmodelled disturbances, respectively. Meanwhile, the criteria are formed to ensure the robustness of the system. The efficiency of the established ETSMAD control strategy is confirmed by a turbofan system example.

Barrier Function Based Adaptive Sliding Mode Control for Uncertain Systems With Input Saturation

This article aims to present a barrier function based adaptive sliding mode (BFASM) control scheme for a class of uncertain nonlinear systems with actuator saturation. In conventional adaptive sliding mode control for saturated systems, the adaptive gain is often monotonically increasing with respect to the persistent disturbance, which results in aggressive control input with severe chattering that is often giving rise to system instability. In order to solve this problem, this article proposes a BFASM controller with explicit consideration of actuator saturation and uncertainties. The proposed method contains a reaching control input that can adapt to the time-varying disturbances. In addition, the proposed method does not require the upper bound information of disturbance that is commonly requested in conventional sliding mode control and thus removes the conservative assumption on a sufficiently large control gain. Stability analysis proves that the tracking error under the proposed control can asymptotically converge into a prespecified region in the presence of actuator saturation, parameter uncertainties, and external disturbances. The proposed method is also applied to an air-floating positioning system with input saturation, and experimental results demonstrate its efficacy.

Quantization‐based switched second‐order sliding mode control for uncertain systems

AbstractA novel quantization‐based switched second‐order sliding mode control design is considered for nonlinear uncertain systems. A new quantization strategy associated with state‐space partition is utilized to accommodate the control amplitude to different uncertainty levels then the conservatism of the control gain is thus attenuated. Investigating each quantized region, it is obtained that all regions are globally invariant sets which offers a monotonously consecutive decrease of the quantized control amplitude when sliding variable converging to the origin through considered uncertainty levels. To deal with different control objectives, the closed‐loop system performance can be enhanced via adapting the quantization parameters. The finite‐time stability analysis and the effect assessment of quantization parameter on the total convergence time are provided. Simulation shows the efficacy and superiority compared with referenced methods.

Robust adaptive sliding mode control for uncertain systems with unknown time-varying delay input

This article focuses on robust adaptive sliding mode control law for uncertain discrete systems with unknown time-varying delay input, where the uncertainty is assumed unknown. The main results of this paper are divided into three phases. In the first phase, we propose a new sliding surface is derived within the Linear Matrix Inequalities (LMIs). In the second phase, using the new sliding surface, the novel Robust Sliding Mode Control (RSMC) is proposed where the upper bound of uncertainty is supposed known. Finally, the novel approach of Robust Adaptive Sliding ModeControl (RASMC) has been defined for this type of systems, where the upper limit of uncertainty which is assumed unknown. In this new approach, we have estimate the upper limit of uncertainties and we have determined the control law based on a sliding surface that will converge to zero. This novel control laws are been validated in simulation on an uncertain numerical system with good results and comparative study. This efficiency is emphasized through the application of the new controls on the two physical systems which are the process trainer PT326 and hydraulic system two tanks.

LQR Technique based Second Order Sliding Mode Control for Linear Uncertain Systems

ABSTRACT In this paper optimal second order sliding mode controller for uncertain systems by using integral sliding surface is proposed. The optimal controller is designed based on linear quadratic regulator (LQR) method for nominal model of the system. In optimal control method, the LQR is combined with sliding mode control to obtain equivalent control and switching control. The sliding mode controller is designed using integral sliding surface to obtain the value of switching control and to equivalent control values are obtained using LQR technique. It is observed that LQR and integral sliding mode control method are more efficient compare to other conventional techniques. Stabilization of inverted pendulum system is done using the sliding mode control approach. The system of inverted pendulum is used in state space approach. The main advantages of this method is that disturbance rejection, insensitivity to parameter variations and implementation issues are addressed easily using proposed controller stabilization of inverted system. The simulation result conform an advantage of the designed optimal sliding mode control approach in terms of output responses and stabilization of the system.

A new state and perturbation observer based sliding mode controller for uncertain systems

This paper proposes a new continuous sliding mode controller and observer for perturbed systems. The controller, which does not need any knowledge of bounds of any perturbation, is estimated using the uncertainty and disturbance estimation technique and implemented with observer states. The stability of the overall observer-controller combination is proved. The controller-observer combination is validated by implementing the scheme for an actual hardware set-up of serial flexible joint in laboratory.

Discrete-time adaptive sliding mode control for uncertain systems based on multi-rate output measurement

This article presents the design of a discrete-time adaptive sliding mode control (SMC) for uncertain systems using the noisy multi-rate output measurement. It is assumed that the dynamic systems are described by a discrete-time state equation with mismatched uncertainties. The proposed discrete-time adaptive SMC is composed of the equivalent and the nonlinear switching controls, and it is derived based on a new sliding surface. A new least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed without the information of the statistics for the measurement noises and the initial state. In the design of the proposed discrete-time adaptive SMC, the un-measurable states and the uncertainties are, respectively, replaced as their estimates obtained from the proposed LSE, and the sliding coefficient matrices are selected such that the states for the systems are ultimately bounded, and the effect of the external disturbances to give the states is reduced as small as possible. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.

Adaptive integral higher order sliding mode controller for uncertain systems

This paper proposes an adaptive integral higher order sliding mode (HOSM) controller for uncertain systems. Instead of a regular control input, the derivative of the control input is used in the proposed control law. The discontinuous sign function in the controller is made to act on the time derivative of the control input. The actual control signal obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used in the proposed controller eliminates the need of prior knowledge about the upper bound of the system uncertainties. Stability and robustness of the proposed controller are proved by using the classical Lyapunov criterion. Simulation results demonstrate the advantages of the proposed control scheme.

Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems

In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlinear feedback (CNF) method is proposed. The aim of the controller is to improve the transient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feedback control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller.

Discrete-time sliding mode control for uncertain systems with state and input delays

This article presents a discrete-time sliding mode control method for the robust stabilisation of linear uncertain multi-input discrete-time systems with state and input delays. The systems are assumed to have structured mismatched time-varying parameter uncertainties. A specified switching surface is proposed and a sliding mode controller is derived to ensure the existence of the quasi-sliding mode. Based on the improved Lyapunov function and linear matrix inequality technique, delay-independent sufficient conditions for the design of a stable switching surface are given and the stability of the overall closed-loop system is guaranteed. Neither chattering phenomenon will occur nor the knowledge of upper bound of uncertainties is required. Finally, simulation results demonstrate the efficacy of the proposed control methodology.

Robust integral sliding mode control for uncertain systems with multiple time delays

This paper proposes a robust integral sliding mode (RISM) manifold and the corresponding stabilization control law for uncertain systems with multiple time-varying time delays based on the techniques of linear matrix inequalities (LMI). The sufficient condition for the existence of the RISM manifold is given in terms of LMI, and then, the sliding mode control (SMC) law that can keep the system state on the RISM manifold from the initial time moment is developed. The efficiency and feasibility of the results are illustrated by a numerical example.

Output Feedback Integral Sliding Mode Control for Uncertain Systems with Bounded L2 Performance

This paper presents an output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties along with disturbances and matched nonlinear perturbations. A scheme of the output-dependent integral sliding surface is proposed and a control law is then designed to satisfy the reaching and sliding condition. Through utilizing H∞ control analytical technique, once the system is in the sliding mode, the proposed algorithm can guarantee robust stabilization and sustain the nature of performing disturbance attenuation in terms of an algebraic Riccati equation. Finally, the feasibility of our proposed algorithm is illustrated using a numerical example.

Robust discrete-time sliding mode control for uncertain systems with time-varying state delay

A robust discrete-time sliding mode control (DT-SMC) for uncertain linear systems with unknown time-varying state delay is analysed, in which uncertainties consist of mismatched uncertain parameters and unknown bounded nonlinear function. By using the linear matrix inequality approach, a sufficient condition for the existence of stable sliding surfaces depending on the lower and upper delay bounds is established. On the basis of this existence condition, the synthesised DT-SMC can guarantee the sliding mode reaching condition of the specified discrete-time sliding surface. Two examples verify the effectiveness of the proposed method.

A sliding mode control approach for systems subjected to a norm‐bounded uncertainty

AbstractThis paper proposes a design approach of continuous sliding mode control of uncertain systems, the uncertainty being norm bounded. The two steps of the design methodology are investigated. The existence step, in which we choose the sliding surface that gives good behaviour during the sliding mode, is formulated as a pole assignment of linear uncertain system in a sector through convex optimization. The solution to this problem is therefore numerically tractable via linear matrix inequalities (LMI) optimization. In the reaching step, we propose a continuous nonlinear control strategy ensuring a bounded motion about the ideal sliding mode, thus approximating the ideal dynamic behaviour in the presence of uncertainty. Finally, the validity and the applicability of this approach are illustrated by a flight stabilization benchmark example. Copyright © 2006 John Wiley & Sons, Ltd.

Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.

Sliding mode control of uncertain systems: a singular perturbation approach

In this paper we consider a nonlinear control system affected by deterministic uncertainty and described by a system of ordinary differential equations. The uncertainty is modelled by a multivalued map whose t -measurable and x-Lipschitz selections represent the possible system dynamics of the uncertain system. We propose a dynamical feedback control design, based on the singular perturbation theory, which allows all the possible system trajectories corresponding to the system dynamics to have the same prescribed behaviour. Specifically, given a manifold K of the state space, defined as the zeros of a smooth map, the proposed control steers and then holds, during finite or infinite time intervals, any possible system trajectory to any prescribed neighbourhood of K .A result ensuring the exact attainability of K is also provided. Some examples illustrating the obtained results are presented.

Robust control of delay systems: a sliding mode control design via LMI

This paper considers the sliding mode control of uncertain systems with single or multiple, constant or time-varying state-delays, submitted to additive perturbations. The sliding surface is designed so to maximize the calculable set of admissible delays. The conditions for the existence of the sliding regime are studied by using Lyapunov–Krasovskii functionals and Lyapunov-Razumikhin functions. LMIs are used for the optimization procedure. Two examples illustrate the proposed method.

Robust Control of Linear System with a Time-Varying Delay : A Sliding Mode Control Design via LMI.

This paper considers the sliding mode control of uncertain systems with single, time-varying state-delay, submitted to additive perturbations (possibly non-vanishing). The sliding surface is designed so to maximize the calculable set of admissible delays (this means, those which don't destabilize the relay-delay system). The conditions for the existence of the sliding regime are studied by using a Liapunov-Razumikhin function. LMIs are used for the optimization procedure. An example illustrates the proposed method.