Design of discrete-time repetitive control system based on two-dimensionalmodel

A new design method of the repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented, which can design a low-pass filter of the repetitive controller and a stabilizing controller simultaneously in the repetitive control system. Using a Lyapunov functional for the repetitive control system, sufficient conditions are derived in terms of a linear matrix inequality (LMI), which ensure robust stability of the repetitive control system and achieve the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance. Based on derived conditions, the problem of designing a stabilizing controller and finding the cut-off frequency of a low-pass filter is reformulated as an optimization problem with an LMI constraint of the free parameter. Then, an iterative algorithm is presented to calculate the largest cut-off frequency of a low-pass filter and design the corresponding state-feedback controller simultaneously. A numerical example is presented to illustrate the validity of the proposed method.

In this paper, first, the design method of the discrete-time position control system of a body supported elastically is showed. In the design of the discrete-time position control system, the pulse transfer function of the body supported elastically and driven by a linear DC motor is derived by the z-transform, and the discrete-time control voltage of the linear DC motor is obtained by applying the inverse dynamics or the neuro-adaptive control in consideration of the delay time due to the computation time of the control digital computer. Then, from the experimental results, the usefulness of the present design method of the discrete-time position control system is confirmed, and the control performance of both control methods in regard to disturbance is compared. Furthermore, from the numerical simulation results, the effects of the sampling time on the control performance of the neuro-adaptive control is demonstrated.

A Design of Repetitive Control Systems – high Accuracy Servomechanisms for Periodic Inputs

Repetitive control, a distinctive control method with a human-like learning capability, is of both theoretical and practical importance. This paper deals with the problem of designing a robust observer-based repetitive-control system that provides a given H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> steady-state disturbance-attenuation performance for a class of plants with time-varying structured uncertainties. A continuous-discrete two-dimensional hybrid model is built that accurately describes the features of repetitive control so as to enable independent adjustment of the control and learning actions. A sufficient condition for the repetitive-control system to have a steady-state disturbance-attenuation bound in the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sub> setting is given in terms of a linear matrix inequality. The condition is then used to obtain the parameters of the repetitive controller and the state observer. Finally, a numerical example demonstrates the effectiveness of the method.

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

This paper investigates the problem of designing a robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> repetitive control system with periodic time-delay. Firstly, a continuous-discrete two-dimensional (2D) model with time-delay is constructed to describe the control and learning actions of the system. Then, by choosing an appropriate Lyapunov functional, LMI-based sufficient stability conditions for asymptotic stability and satisfactory H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> tracking performance of the 2D model is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

The problem of designing output error controllers to track periodic reference signals for a class of uncertain linear time-delay systems subject to periodic disturbances is addressed. A repetitive controller, which is a type of output error controller, is developed for these systems and a sufficient condition for stability of the closed-loop system is derived by applying the Lyapunov–Krasovskii functional and linear matrix inequalities (LMIs). In order to relax the stability condition, the theory of the modified repetitive control (RC) system is extended to the systems represented by irrational transfer functions. Based on the extended theory of the modified RC system, a modified repetitive controller, another type of output error controller, is developed for these systems and sufficient conditions for stability of the closed-loop system are derived in terms of a frequency-domain criterion and LMI. Numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model

A repetitive controller contains a pure-delay positive-feedback loop that makes it difficult to stabilize a strictly proper system. A low-pass filter is inserted in a repetitive controller to relax the stability condition of the modified repetitive-control system at the cost of degrading the tracking performance. In this study, a modified repetitive-control approach is developed, which reaches a balance between the stability and tracking performance for a class of affine nonlinear systems based on the Takagi–Sugeno fuzzy model. First, a 2D model is established to adjust continuous control and discrete learning actions preferentially induced by exploiting the 2D property in a repetitive-control process. Then, the Lyapunov stability theory and 2D system theory are used to derive a sufficient stability condition in the form of linear matrix inequalities to design parallel-distributed-compensation-based state-feedback controllers. Finally, an application-oriented example is used, and a comparison is performed to show that an extra variable is introduced such that the developed method has a better tracking performance.

Automatica Prize Paper Awards 2014

This paper deals with the problem of two‐dimensional (2D) system‐based preview repetitive control (PRC) with external periodic disturbance for a class of continuous‐time linear systems. First, a repetitive learning‐based estimator (RLE) is incorporated into the controller block to compensate for the periodic disturbance. Next, the PRC law with repetitive learning compensation disturbance is obtained by combining the observer and RLE. Then, we combine the 2D system theory with the linear matrix inequality (LMI) method to derive sufficient conditions to ensure the robustness and stability of the closed‐loop system. Finally, numerical simulations verify the superiority of the proposed method.

This paper presents an approach of modeling and controller design for cloud control system (CCS), which considers both network and controller uncertainties. Firstly, we establish a generalized state space model with network time delay, and design a cloud controller model with uncertain parameters including state observer and control law. Then, by means of Lyapunov stability theorem and linear matrix inequality (LMI) method, the stability criteria are given for obtaining the parameters of the cloud controller. The simulation results show the effectiveness of the proposed method to CCS with uncertainties.

This paper discusses the issues of robust control law design for fault-tolerant systems. Based on the assumption that the effects of faults can be expressed in linear-fractional-transformation (LFT) forms, a fault-tolerant control systems design problem is formulated and solved via a linear matrix inequality (LMI)-based synthesis approach. In order to recover the convexity of the design problem whilst considering the robust performance and robust stability against faults and uncertainties simultaneously, a constrained optimisation approach is used. The simulation results of a design example (a longitudinal motion flight control problem for an unmanned aircraft in the case of suffering battle damage on its wing ) show that robust stability and satisfactory performance have been achieved.

Nonlinear active disturbance rejection control is much more effective than linear active disturbance rejection control in tolerance to uncertainties and disturbances. However, it brings a great challenge for theoretical analysis, especially the stability analysis. This article proposes a linear matrix inequality method to analyze the absolute stability of generalized nonlinear active disturbance rejection control form which contains multiple nonlinearities with different parameters in both extended state observer and control law for single-input single-output systems. The generalized nonlinear active disturbance rejection control algorithm and the single-input single-output system are transformed into a direct multiple-input multiple-output Lurie system. A sufficient condition to determine its absolute stability based on linear matrix inequality method is given. The Lyapunov function of the Lurie system exists when the group of linear matrix inequalities is feasible. The free parameters and coefficients in Lyapunov function are given by the solution of these linear matrix inequalities. The electromagnetic valve actuator system in camless engine is presented as an application to illustrate how to perform the proposed method for absolute stability analysis and the stable region of parameter perturbations is obtained via the method. Simulation results show that the linear matrix inequality–based method is convenient and effective to determine whether the closed-loop system is absolutely stable.

The problem of mean square bounded-input bounded-output(BIBO) stability is investigated for a class of discrete-time stochastic control systems with time delays and non-linear perturbations. In this paper, a special point δ in the time delay's variation interval is introduced, and the variation interval is divided into two subintervals. Then, by defining a special Lyapunov-Krasovskii functional and checking its variation in the two subintervals, respectively, some novel delay-dependent stability criteria for the discrete-time stochastic control systems are derived. These conditions are expressed in the forms of linear matrix inequalities(LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Meanwhile, this paper provides a new method for studying discrete-time stochastic mean square BIBO stability. Finally, a numerical example is given to illustrate the validity of the main results.