Empirical study of robust/developed PID control for nonlinear time-delayed dynamical system in discrete time domain

International audience

Robust fault detection for a class of nonlinear time-delay systems

This paper reviews the development of fuzzy systems and the problem of time delay control in nonlinear systems. Based on this review, a fuzzy Lyapunov method defined in fuzzy blending quadratic Lyapunov functions is proposed from which to derive stability conditions. In the controller procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller (FLC) by blending all linear local state feedback controllers. Furthermore, the multiple time-delay interconnected systems are considered in the nonlinear fuzzy systems. Key words: Interconnected systems, fuzzy Lyapunov method, linear matrix inequality.

A novel theorem for prescribed-time control of nonlinear uncertain time-delay systems

The optimal control problem for nonlinear time-delay large-scale systems with persistent disturbances is considered. By using the successive approximation approach, the high order, coupled, nonlinear two-point boundary value (TPBV) problem with both time-delay and time-advance terms, which is derived from the necessary condition of the original optimal control problem, is transformed into a sequence of linear decoupled differential equations. By iteratively solving the sequence of linear differential equations, an optimal control law is obtained, which consists of analytic linear feedforward, feedback terms and a dynamic compensator. The feedforward term is used for persistent disturbance attenuation and the compensator is for the purpose of compensating nonlinearities and time delays. A suboptimal control law is obtained by truncating a finite term of the adjoint vector sequence as its compensator. An iterative algorithm to obtain the suboptimal control law is proposed. A simulation example illustrates the validity of the algorithm.

Robust model predictive control of discrete nonlinear systems with time delays and disturbances via T–S fuzzy approach

Systems with time delays are present in many applications and considerable research efforts have been made for design and analysis of controllers for this class of systems. Since time delay itself is nonlinear in nature, various approximation techniques have been developed based on restrictive assumptions. A common approximation technique for time delay is by using the Pade rational polynomials which expresses time delay transfer function e/sup -ts/ in the form of numerator and denominator in s. In this paper, systems with time delay are investigated directly in discrete time domain. The time delay is modeled accurately without linear assumption and an augmented state space model is obtained. Control law is developed and closed loop stability is proven. An example is given to demonstrate the technique.

Linear stabilization of the programmed motions of non-linear controlled dynamical systems under parametric perturbations

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

A new recurrent neural-network predictive feedback control structure for a class of uncertain nonlinear dynamic time-delay systems in canonical form is developed and analyzed. The dynamic system has constant input and feedback time delays due to a communications channel. The proposed control structure consists of a linearized subsystem local to the controlled plant and a remote predictive controller located at the master command station. In the local linearized subsystem, a recurrent neural network with on-line weight tuning algorithm is employed to approximate the dynamics of the time-delay-free nonlinear plant. No linearity in the unknown parameters is required. No preliminary off-line weight learning is needed. The remote controller is a modified Smith predictor that provides prediction and maintains the desired tracking performance; an extra robustifying term is needed to guarantee stability. Rigorous stability proofs are given using Lyapunov analysis. The result is an adaptive neural net compensation scheme for unknown nonlinear systems with time delays. A simulation example is provided to demonstrate the effectiveness of the proposed control strategy.

This paper proposes an indirect adaptive fuzzy neural network (FNN) controller with state observer and supervisory controller for a class of uncertain nonlinear dynamic time delay systems. First, the approximate function of unknown time delay system is inferred by the adaptive time delay FNN system. Next, a state observer is designed to estimate the unknown system states and the indirect adaptive fuzzy controller is constructed. Finally, the closed loop controller is obtained by incorporating the supervisory controller with the indirect adaptive fuzzy controller. Therefore, if the system tends to unstable, i.e., error dynamics is larger than a prescribed constraint which is determined by designer, the supervisory controller will activate to force the state to be stable. The free parameters of the indirect adaptive FNN controller can be tuned online by observer-based output feedback control law and adaptive laws by means of Lyapunov stability criterion. The resulting simulation example shows that the performance of nonlinear time delay chaotic system is fully tracking the reference trajectory. Meanwhile, simulation results show that the adaptive control effort of the proposed control scheme is much less due to the assist of the supervisory controller.

This article addresses fault detection, estimation, and compensation problem in a class of disturbance driven time delay nonlinear systems. The proposed approach relies on an iterative learning observer (ILO) for fault detection, estimation, and compensation. When there are no faults in the system, the ILO supplies accurate disturbance estimation to the control system where the effect of disturbances on estimation error dynamics is attenuated. At the same time, the proposed ILO can detect sudden changes in the nonlinear system due to faults. As a result upon the detection of a fault, the same ILO is used to excite an adaptive control law in order to offset the effect of faults on the system. Further, the proposed ILO-based adaptive fault compensation strategy can handle multiple faults. The overall fault detection and compensation strategy proposed in the paper is finally demonstrated in simulation on an automotive engine example to illustrate the effectiveness of this approach. Copyright © 2005 John Wiley & Sons, Ltd.

This paper presents a discrete time adaptive sliding control law for SISO nonlinear systems with mismatched uncertainties. The systems are assumed to have no zero dynamics, i.e. the relative degree is the same as the system order. Control objective is for the output to track a sufficiently smooth desired trajectory. The control law utilizes the idea of the multiple sliding surface. The developed discrete time adaptation laws differ from those of conventional sliding control, and aim at adaptation on time varying parameters such as disturbances or unstructured unmodeled dynamics. The close loop stability is checked in the discrete time domain, and exponential decay of the adaptation error can be guaranteed by proper placement of the discrete time closed loop poles.

Distributed adaptive output feedback containment control for time-delay nonlinear multiagent systems

An adaptive system for linear systems with unknown parameters is a nonlinear system. The analysis of such adaptive systems requires similar techniques to analyse nonlinear systems. Therefore it is natural to treat adaptive control as a part of nonlinear control systems. Nonlinear and Adaptive Control Systems treats nonlinear control and adaptive control in a unified framework, presenting the major results at a moderate mathematical level, suitable for MSc students and engineers with undergraduate degrees. Topics covered include introduction to nonlinear systems; state space models; describing functions for common nonlinear components; stability theory; feedback linearization; adaptive control; nonlinear observer design; backstepping design; disturbance rejection and output regulation; and control applications, including harmonic estimation and rejection in power distribution systems, observer and control design for circadian rhythms, and discrete-time implementation of continuous-time nonlinear control laws.