Iterative LMI Approach Research Articles

Weighted sensitivity design of multivariable PID controllers via a new iterative LMI approach

This paper addresses the weighted sensitivity design of multivariable proportional–integral–derivative (PID) controllers for multi-input multi-output (MIMO) processes. First, the PID reference tracking problem is formulated into an H∞ PID control problem by using the weighted sensitivity synthesis, and the problem is further casted into an H∞ SOF control problem. Second, based on the idea of T–K iteration, a new iterative LMI algorithm has been developed to locally solve the optimal H∞ SOF control problem. Then, a design procedure is presented for weighted sensitivity design of multivariable PID Controllers for MIMO processes. Finally, three application examples are provided to show the effectiveness and good performance of our method for practical industrial processes.

Iterative LMI Approach to Robust Hierarchical Control of Homogenous Linear Multi-Agent Systems Subject to Polytopic Uncertainty and External Disturbance

This paper investigates design of robust hierarchical control for linear multi-agent systems (MAS) subject to polytopic uncertainty and external disturbance. Each agent of MAS is described by a homogeneous linear time-invariant dynamic model. The control structure has two layers, namely, an upper layer and a lower layer. Local actions are executed in the lower layer. Each agent shares information through an undirected graph with neighboring agents in the upper layer to achieve the global stabilization and disturbance attenuation. We employ a parameter-dependent Lyapunov function to formulate the robust control design of the local and global feedback in terms of bilinear matrix inequalities and incorporate constraints on disturbance attenuation. We propose the sufficient condition, where system matrices and Lyapunov variables are separated. The parameterization of the controller depends on a common slack variable instead of the Lyapunov matrices. We develop an iterative approach based on the coordinated optimization to solve sub-problems over linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed robust control designs. It is shown that our proposed robust control designs outperform other robust control designs in terms of achievable disturbance attenuation and maximum admissible uncertainty bound.

Iterative LMI approach to robust static output feedback control of uncertain polynomial systems with bounded actuators

This paper presents a novel static output feedback stabilization of polynomial systems with bounded actuators. We propose a new sufficient condition for static output feedback design for nominal polynomial systems with constraints on input magnitudes. In the proposed stabilization condition, the system matrices and the Lyapunov matrices are separated, and hence parameterization of the controller is independent of the Lyapunov matrices. The main result is the novel parameter-dependent Lyapunov functions that are readily applied to robust static output feedback design of polynomial systems subject to parametric uncertainty. The proposed design conditions are bilinear in the decision variables. Hence, we provide iterative algorithms to solve the design problems. At each iteration, the design condition is cast as parameter-dependent linear matrix inequalities using the sum-of-squares technique and can be efficiently solved. The proposed approach leads to enhanced static output feedback design with computationally tractable formulation. Effectiveness of the proposed approach is demonstrated by numerical examples.

Iterative LMI Approach to Robust State-feedback Control of Polynomial Systems with Bounded Actuators

This paper presents a novel approach to state-feedback stabilization of polynomial systems with bounded actuators. To overcome limitation of the existing approaches, we introduce additional variables that separate the system matrices and the Lyapunov matrices. Therefore, parameterization of the state-feedback controllers is independent of the Lyapunov matrices. The proposed design condition is bilinear in the decision variables, and hence we provide an iterative algorithm to solve the design problem. At each iteration, the design condition is cast as convex optimization using the sum-of-squares technique and can be efficiently solved. In addition, the novel parameter-dependent Lyapunov functions are readily applied to robust state-feedback stabilization of polynomial systems subject to parametric uncertainty. Effectiveness of the proposed approach is demonstrated by numerical examples.

Controller Design and Sparse Measurement Selection in Self-optimizing control

Self-optimizing control focuses on minimizing loss for processes in the presence of disturbances by holding selected controlled variables at constant set-points. A measurement combination can be found, using the Null-space method, which further reduces the loss. Since self-optimizing control focuses on the steady-state operation, little attention has been put on the dynamic performance when selecting measurement combinations. In this work, an iterative LMI approach is combined with the sparsity promoting weighted l1-norm, to find a measurement subset together with PI controllers for the Null-space method. The measurement combination and the controllers are designed such that, the dynamic response is improved when the process is facing disturbances. The proposed method is illustrated on a Petlyuk column case study.

Mean Square Stability Based on H∞ Control for Uncertain Networked Control Systems with Random Data Loss

This paper studies the design of uncertain linear discrete-time Networked Control Systems over imperfect communication channels with time-varying data loss. This leakage is modeled as stochastic parameter and norm-bounded uncertainties. In addition, this paper defines the necessary conditions for the design of the dynamic output feedback controller; subsequently, an iterative LMI approach is specified to compute the controller state parameters. The simulation results show that the designed controller improves the H∞ disturbance attenuation performance of the concerned uncertain system.

Iterative LMI approach to design robust state-feedback controllers for Lur’e systems with time-invariant delays

In this paper, we present a design of robust state-feedback stabilization and a design of robust state-feedback H∞ control for Lur’e systems with time-invariant delays and norm-bounded uncertainties. The criteria of state-feedback stabilization and state-feedback H∞ control are developed using Lyapunov-Krasovskii Theorem with a delay-partitioning Lyapunov-Krasovskii functional and an integral of sector-bounded nonlinearities. The design criteria are given in terms of bilinear matrix inequality, which is non-convex optimization. We develop algorithms based on coordinate optimization, which alternate between two LMI optimization problems, to solve for the robust state-feedback controllers. The proposed iterative LMI algorithm for H∞ control design is a local optimization procedure, but it can return satisfactory state-feedback controllers depending on the initialization. Numerical examples show that the proposed LMI algorithms can provide robust state-feedback stabilization to guarantee the closed-loop stability of LSTD and yield robust state-feedback control to guarantee the worstcase H∞ performance of the closed-loop LSTD.

An iterative LMI approach to H<SUB align=right>∞ networked control with random communication delays

In this paper, an iterative LMI approach is proposed to deal with the control problem for Networked Control Systems (NCSs) with random communication delays. Both random measurement and control delays are simultaneously considered due to limited communication capacity. The NCSs with both measurement and control delays are modelled as a stochastic parameter system which contains two independent Bernoulli distributed white sequence. A dynamic output controller is designed to exponentially stabilise the networked system in the sense of mean square, and also achieve the prescribed H∞ disturbance attenuation level. An iterative algorithm is developed to compute the optimal H∞ disturbance attenuation and the controller parameters. An illustrative example is provided to show the applicability of the proposed method.

An improvement on multivariable PID controller design via iterative LMI approach

This note improves the results of Zheng, Wang, and Lee (Automatica 38 (2002) 517) on the design of multivariable PID controllers via LMI approach. The idea of the improvement is to transform the problem of PID controller design to that of static output feedback (SOF) controller design for a system in descriptor form. The merits of the present result are: (1) The present condition removes the invertibility constraint on the controllers in Zheng et al. (2002) and incorporates it to the matrix inequality to be solved. (2) Once the SOF matrix is obtained, the PID gains are ready in hand and no additional computation is needed. (3) The present approach can deal with the case of some system parameters subject to perturbations.