Mingxuan Sun

Digital Control Strategies With Attractiveness and Invariance Specifications

This paper presents a control design approach for discrete-time input–output systems on the basis of attracting law (AL) with attractiveness and invariance specifications. A measure of disturbance rejection is embedded in the AL, by which a control law is derived. The steady-state error band, absolute attractive layer, and the monotone decreasing region of the error dynamics are defined, and the bounds are derived in detail, in order to characterize the closed-loop performance with respect to control parameter values. It is shown that the chattering can be alleviated by replacing the sign function, involved in the conventional attractive law, with the saturation function. Such an alternative approach is of the equally important feature of the reaching-law approach, namely, the ease of obtaining the control law, the simplicity and efficiency in the implementation, and the resultant robust characteristic to parametric uncertainties and external disturbances. Numerical simulation and experiments are carried out for performance evaluation of the presented control strategies.

Learning control for systems subject to fractional uncertainties

This paper presents a Lyapunov-based design of repetitive learning controllers for uncertain systems. The controller design is unified due to the use of the parametrization and norm-bounding technique, and the novelty lies in the less requirement for the knowledge about the system undertaken. In addition, this design can handle fractional uncertainties involved in the dynamics effectively. The estimation for the fractional uncertainties is performed to facilitate the controller design and property analysis. Unsaturated- and saturated-learning algorithms are characterized, through rigorous analysis, for the establishment of the boundednesss of the variables in the closed-loop system and the the asymptotical convergence of the tracking error. Numerical examples are provided to verify effectiveness of the proposed learning control scheme.

Feedback-aided PD-type iterative learning control using LMI

This paper presents feedback-aided PD-type iterative learning control strategies for discrete-time linear time-invariant systems, where the 2-D Roesser model is derived for the closed-loop system. With the aid of the bounded real lemma, the issue of convergence of the learning algorithm is converted to the problem whether a linear matrix inequality(LMI) is solvable or not. The specific design of the feedback-aided PD-type iterative learning controller can be given by solving the LMI. The design method of a feedback-aided D-type iterative learning controller is also presented. Effectiveness of the learning control strategies of this paper is verified through the numerical results.

Barrier Lyapunov function-based fuzzy adaptive iterative learning control

In this paper, the problem of error-constrained adaptive iterative learning control is presented for a class of nonlinear systems which performs a given task over a finite time interval repeatedly, where the fuzzy system is used to approximate the unknown nonlinearity. Different from the output tracking control, the error tracking approach is used to deal with arbitrary initial conditions. An improved logarithmic barrier Lyapunov function is given to design an adaptive iterative learning controller, by applying the error tracking approach. It is shown that the practical tracking error trajectory is ensured to converge to the desired error trajectory as the iteration increases, and kept in the pre-specified region all the time. An illustrative example is presented to demonstrate the effectiveness of the proposed method.

Characteristic models and AILC design of time-varying nonlinear systems

This paper presents a characteristic modeling method for continuous/discrete time-varying nonlinear systems, where the model, the first-order time-varying differential equation, is a unified one. Learning identification algorithms are suggested for the purpose of parameter estimation, and the adaptive iterative learning control strategy is proposed for achieving the perfect tracking of the desired trajectory over a pre-specified finite-time interval. The proposed control scheme is applied on a permanent-magnet synchronous motor, where the least squares/gradient learning algorithms with a forgetting factor are applied, respectively, and the experimental results are presented to demonstrate the effectiveness of the learning control schemes.

Feedback-aided iterative learning control

This paper presents feedback-aided iterative learning control strategies for linear time-invariant systems. Sufficient conditions of convergence of the feedback-aided PD-type learning algorithm are derived, and the converged output trajectory is given. The initial rectifying action is applied to eliminate the effect of initial shifts. It is shown that the system output converges to the desired one over the pre-scribed finite interval, whatever value the initial error takes but fixed. Numerical results are presented to demonstrate effectiveness of the proposed learning control schemes.

Finite-time iterative learning control: Feedback-aided strategies

This paper presents an iterative learning control scheme for linear systems in the presence of a fixed initial state shift between iterative initial state and the desired one. The finite-time control strategies are adopted in the design of iterative learning controllers, and feedback-aided strategies are applied as well. The sufficient conditions for convergence of the learning control algorithms are derived, and the limit trajectories by applying the learning algorithms are given, which are of finite-time convergence. Numerical simulation is carried out to verify effectiveness of the proposed feedback-aided learning control strategies.

Piecewise-reaching-law based discrete variable structure repetitive control

This paper presents a piecewise-reaching variable structure repetitive control method for uncertain discrete-time linear system. As for the reaching law approach, one needs to modify the original reaching law, as the resultant error dynamics depend on the system uncertainties, By embedding the performance measure of uncertainty rejection into the reaching law to form the ideal switching dynamics, the design of repetitive control can eliminate the periodic disturbances effectively. The control performance will mainly depend on the non-periodic uncertainties. In order to establish stability and convergence of the closed-loop system, the monotone convergence layer, absolute convergence layer and quasi-sliding mode are discussed, and the detailed derivations are given. Numerical simulations are presented to verify the effectiveness of the proposed repetitive control scheme.

Ideal error dynamics based design of discrete-time repetitive controllers

This paper deals with the problem of repetitive control for single-input single-output discrete-time systems. An ideal error dynamics is formed by using a discrete attracting law, and the repetitive control law is derived based on the ideal error dynamics. The compensation for periodic disturbances is involved, and tracking performance could be improved so that the periodic disturbances are rejected completely. The steady-state error band, absolute attractive layer and the monotone decreasing region of the error dynamics are derived theoretically, in order to characterize the closed-loop performance with respect to control parameter values. Numerical simulation is conducted to verify the validity of the proposed method.

Ideal integral error dynamics based design of linear servo systems

In this paper, an ideal integral error dynamics based control design method is proposed for linear servo systems. Two cases are detailed, which in one case dose not use any disturbance compensation, while other case the compensation is involved. The control performance for both cases is analyzed, respectively. Numerical simulation and practical experiment are carried out, and the obtained results are presented to demonstrate effectiveness of the proposed ideal integral error dynamics based control method.