Continuous-discrete 2D Research Articles

Modified preview repetitive control with equivalent-input-disturbance based on two-dimensional model

This paper deals with the problem of two-dimensional (2D) system-based modified preview repetitive control (MPRC) with equivalent-input-disturbance (EID) for continuous-time systems. First, an EID-based MPRC law is used to improve the tracking performance and disturbance attenuation. Next, by using a new equality constraint, a continuous-discrete 2D system is established and the design problem of the EID-based MPRC law is transformed into the stability problem of the 2D system. Then, we employ the 2D system theory together with the linear matrix inequality (LMI) approach, a sufficient condition is derived to ensure the stability of the closed-loop system. By solving an LMI, the gains of the controller and state observer can be obtained. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the developed controller design technique.

Finite Frequency H∞ Control of Fractional-Order Continuous–Discrete 2-D Roesser Models

The H∞ control problem of fractional-order continuous-discrete 2D Roesser models in the finite frequency is investigated in this paper. Firstly, based on the frequency-partitioning method and generalized Kalman–Yakubovič–Popov lemma, the finite frequency bounded real lemmas in form of linear matrix inequalities (LMIs) are proposed, which can be solved by LMI solvers immediately. Then, the H∞ state feedback controller is designed, and the existence conditions are established in form of bilinear matrix inequalities (BMIs). Moreover, by the provided iterative algorithm, these BMI-based conditions can be solved based on LMIs. Finally, the numerical examples are provided verify the validity of our results.

Design of a preview repetitive control with equivalent-input-disturbance system based on a continuous-discrete 2D model

This paper deals with the problem of two-dimensional (2D) system-based preview repetitive control (PRC) with equivalent-input-disturbance (EID) for uncertain continuous-time systems. First, to use the available values of the reference signal, we construct an equality constraint which includes the output of a basic repetitive controller, preview compensation and tracking error. Next, to compensate the unknown external disturbances, we incorporate an EID estimator into the PRC controller. Then, by employing the 2D system theory together with the linear matrix inequality (LMI) approach, we derive a sufficient condition to ensure the robust stability of the closed-loop system. By solving an LMI, the gains of the controller and state observer can be obtained. The results obtained in this paper generalize and include some results in the existings. literature. Finally, a numerical simulation demonstrates the effectiveness and superiority of the proposed method.

Stability analysis and stabilisation of continuous-discrete fractional-order 2D Fornasini–Marchesini first model

This paper focuses on the structural stability and stabilisation of the continuous-discrete fractional-order two-dimensional Fornasini-Marchesini first model. The sufficient and necessary stability conditions are given in polynomial form at first. Secondly, to make the problem solvable, based on the property of Kronecker product and the Generalized–Kalman–Yakubovich–Popov Lemma, the new sufficient and necessary stability conditions are established in the form of linear matrix inequalities. Thirdly, with the help of the Projection Lemma, the stabilisation conditions are obtained after introducing a state feedback controller, which can be solved with an iterative linear matrix inequality algorithm. In the end, the effectiveness of the proposed results is verified by two numerical examples.

LMI-Based Stability Analysis of Continuous-Discrete Fractional-Order 2D Roesser Model

The manuscript investigates the problem of structural stability of continuous-discrete fractional-order 2D Roesser model. This model includes one continuous fractional-order dimension with fractional-order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in (0,2)$ </tex-math></inline-formula> and one discrete dimension. By the equivalent transform and generalized Kalman–Yakubovič–Popov lemma, the necessary and sufficient stability conditions for structural stability of continuous-discrete fractional-order 2D Roesser model are established. Our results are all in the form of linear matrix inequalities. And compared with the existing results, our results have no conservativeness and can be applied in the cases with fractional-order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in (0,2)$ </tex-math></inline-formula> in the continuous fractional-order dimension. Illustrated examples are provided to verify the effectiveness of our results.

Repetitive Control Based on Multi-Stage PSO Algorithm with Variable Intervals for T–S Fuzzy Systems

This study presents a repetitive control method based on a multi-stage particle swarm optimization (PSO) algorithm with variable intervals to enhance the tracking performance of Takagi–Sugeno (T–S) fuzzy systems. First, a T–S fuzzy model is used to describe a nonlinear system. A modified repetitive control structure with two repetitive loops guarantees the tracking accuracy of periodic signals. Taking advantage of the two-dimensional (2D) property with continuous control and discrete learning, a continuous-discrete 2D model is presented to describe the nonlinear repetitive control system. Next, a multi-stage PSO algorithm with variable intervals searches for the best parameter combination in the linear matrix inequality-based stability condition to regulate the control and learning actions, which avoids a suboptimal solution and guarantees high control accuracy. Finally, an application to control the speed of synchronous motor with a permanent magnet demonstrates the validity of the method, and comparisons with related methods show its superiority.

Optimisation of control and learning actions for a repetitive-control system based on Takagi–Sugeno fuzzy model

This paper deals with the problem of designing a two-dimensional (2D) modified repetitive-control system based on a Takagi–Sugeno (T-S) fuzzy model to achieve high tracking performance for a nonlinear plant. First, a nonlinear plant is represented by a T-S fuzzy model, and a modified repetitive controller with two repetitive loops is used to increases design flexibility. Next, a continuous-discrete 2D model is established to make use of the 2D characteristics in the modified repetitive-control system. Then, a sufficient stability condition is derived in terms of linear matrix inequalities. Three parameters are used to balance continuous control and discrete learning actions: one in a repetitive loop and two in a Lyapunov–Krasovskii functional. A particle swarm optimisation algorithm yields optimal parameters and the gains of the modified repetitive and state-feedback controllers. Finally, simulation and comparison results demonstrate the effectiveness of our method.

On H∞ and H2 Performance of 2D Systems

In this paper we consider parameterized Lyapunov inequalities arising in H∞ and H2 performance evaluation for continuous-discrete 2D systems. A way of transforming these problems is presented that significantly reduces computational complexity compared to known methods. The H∞ performance evaluation method can have varying degrees of conservativeness, while H2 performance evaluation is exact. Numerical examples are provided.

Necessary Conditions for 2D Systems' Stability

In this paper we consider parameterized Lyapunov inequalities arising in stability analysis of discrete-discrete and continuous-discrete 2D systems. A necessary condition for their feasibility is presented. This condition is based on an optimization method published earlier by the author. Its properties include being reasonably easy to check, and its coverage being adjustable via the algorithm's settings.

Robust $$H_\infty $$ H ∞ Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay

This paper investigates the problem of robust $$H_\infty $$H? repetitive control for a class of linear stochastic switched systems with time delay. Based on the lifting technique, a continuous-discrete stochastic 2D (two-dimensional) delayed model is firstly proposed to describe the control and learning actions of the repetitive control system. Then a sufficient condition for the asymptotical stability with $$H_\infty $$H? performance of the 2D model is derived by choosing an appropriate common Lyapunov functional. The feedback controller gains are then obtained by solving a set of linear matrix inequalities. One example is given to illustrate the effectiveness of the proposed method.

Design of Robust Modified Repetitive-Control System for Linear Periodic Plants

This paper concerns a linear-matrix-inequality (LMI)-based method of designing a robust modified repetitive-control system (MRCS) for a class of strictly proper plants with periodic uncertainties. It exploits the nature of control and learning and the periodicity and continuity of repetitive control to convert the design problem into a robust stabilization problem for a continuous-discrete 2D system. The LMI technique and Lyapunov stability theory are used to derive an LMI-based asymptotic stability condition that can be used directly in the design of the gains of the repetitive controller. Two tuning parameters in the condition enable preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.

New stability conditions for positive continuous-discrete 2D linear systems

New stability conditions for positive continuous-discrete 2D linear systemsNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

Feedback iterative learning control for time-delay systems based on 2D analysis approach

This paper deals with the iterative learning control (ILC) design for multiple-input multiple-output (MIMO), time-delay systems (TDS). Two feedback ILC schemes are considered using the so-called two-dimensional (2D) analysis approach. It shows that continuous-discrete 2D Roesser systems can be developed to describe the entire learning dynamics of both ILC schemes, based on which necessary and sufficient conditions for their stability can be provided. A numerical example is included to validate the theoretical analysis.

Guaranteed Cost Design of Modified Repetitive Control Systems Based on 2D Hybrid Model

摘要: 针对一类具有参数不确定性的线性系统, 基于连续/离散二维混合模型进行改进型重复控制系统的保性能设计. 首先给出一种具有反馈作用的改进型重复控制系统结构, 通过独立地考虑重复控制系统的连续控制行为与离散学习行为, 建立重复控制系统的连续/离散二维混合模型, 并将重复控制的设计问题转化为一类连续/离散二维系统的状态反馈控制问题. 然后, 应用二维Lyapunov泛函导出保性能改进型重复控制器存在的充分条件, 进而证明该条件等价于一个线性矩阵不等式可解性问题. 最后通过求解对应的凸优化问题, 给出了最优保性能控制器的具体形式. 数值仿真验证了所提出方法的有效性. 关键词: 参数不确定性 / 线性系统 / 改进型重复控制 / 保性能设计 / 二维系统 / 线性矩阵不等式

Optimal Control of Non-stationary Differential Linear Repetitive Processes

Differential repetitive processes are a distinct class of continuousdiscrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics.

A delay systems approach to linear differential repetitive processes: Controllability and optimization

Differential linear repetitive processes are a class of continuous-discrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle. In this paper, we investigate further the structural links between differential linear repetitive processes and a special class of time delay systems. This leads to some significant new controllability and optimal control results for these processes.