Kwan Ho Lee

Robust decentralized stabilization of a class of linear discrete-time systems with non-linear interactions

This paper deals with robust stabilization of a class of linear discrete-time systems under non-linear perturbations via output feedback. A bound on the non-linear perturbations is maximized in the design. It is shown that degree of freedoms by the introduction of instrumental variables employed in this paper lead to much flexibility in obtaining both a robust output feedback controller and a maximal allowable bound of the non-linear perturbations. An improved method involving linear matrix inequalities are suggested to solve the matrix inequalities characterizing a solution of the robust stabilization problem. Consequently, the proposed method can yield a much less conservative result than that of earlier methods. Of major interest is an extension to a class of interconnected systems composed of linear subsystems with non-linear interactions. A robust decentralized controller is presented such that the closed-loop systems are maximally tolerant to interconnected non-linear couplings. Numerical examples illustrate the validity of the proposed approach.

Stiction Estimation Using Constrained Optimisation and Contour Map

A closed-loop method for valve-stiction detection and quantification based on Hammerstein modelling is discussed. A suitable model structure of valve stiction is chosen prior to conducting valve-stiction detection and quantification. Given the stiction-model structure, a bounded search space of a stiction model is defined and a constrained optimisation problem is performed. The best unknown stiction-model parameters are found by satisfying a mean-squared error criterion within a space of valve stiction model parameters. For this purpose, a multi-start adaptive random search is used. The proposed strategy not only detects but also quantifies valve stiction. The validity of the proposed method is illustrated through industrial examples. Also, the closed-loop identifiability issue is addressed.

H∞ structured model reduction algorithms for linear discrete systems via LMI-based optimisation

In this article, H ∞ structured model reduction is addressed for linear discrete systems. Two important classes of systems are considered for structured model reduction, i.e. Markov jump systems and uncertain systems. The problem we deal with is the development of algorithms with the flexibility to allow any structure in the reduced-order system design, such as the structure of an original system, decentralisation of a networked system, pole assignment of the reduced system, etc. The algorithms are derived such that an associated model reduction error guarantees to satisfy a prescribed H ∞ norm-bound constraint. A new condition for the existence of desired reduced-order models preserving a certain structure is presented in a set of linear matrix inequalities (LMI) and non-convex equality constraints. Effective computational algorithms involving LMI are suggested to solve the matrix inequalities characterising a solution of the structured model reduction problem. Numerical examples demonstrate the advantages of the proposed model reduction method.

Implementation of FIR control for H ∞ output feedback stabilization of linear systems

In this paper, finite impulse response (FIR) control is addressed for H ∞ output feedback stabilization of linear systems. The problem we deal with is the construction of an output feedback controller with a certain finite impulse response structure such that the resulting closed-loop system is asymptotically stable and a prescribed H ∞ norm bound constraint is guaranteed. Some solvability conditions are suggested in this paper. Sufficient conditions are derived to obtain a suboptimal solution of the H ∞ FIR control problem via convex optimization. Also, an equivalent condition for the existence of H ∞ FIR control is presented in the set of linear matrix inequalities and a reciprocal matrices equality constraint. An effective computational algorithm involving linear matrix inequalities is suggested to solve a concave minimization problem characterizing a local optimal solution of the H ∞ FIR control problem. Numerical examples demonstrate the validity of the proposed H ∞ FIR control and the numerical efficiency of the proposed algorithm for FIR control.

Implementation of FIR control for H ∞ output feedback stabilisation of linear systems

In this paper, finite impulse response (FIR) control is addressed for H∞ output feedback stabilization of linear systems. The problem we deal with is the construction of an output feedback controller with a certain finite impulse response structure such that the resulting closed-loop system is asymptotically stable and a prescribed H∞ norm bound constraint is guaranteed. Some solvability conditions are suggested in this paper. Sufficient conditions are derived to obtain a suboptimal solution of the H∞ FIR control problem via convex optimization. Also, an equivalent condition for the existence of H∞ FIR control is presented in the set of linear matrix inequalities and a reciprocal matrices equality constraint. An effective computational algorithm involving linear matrix inequalities is suggested to solve a concave minimization problem characterizing a local optimal solution of the H∞ FIR control problem. Numerical examples demonstrate the validity of the proposed H∞ FIR control and the numerical efficiency of the proposed algorithm for FIR control.

Controller Performance Analysis Technology for Industry: Implementation and Case Studies ⋆

Abstract In this paper, an industrial MPC performance monitoring technology is introduced with a focus on the industrial implementation. A plant-oriented framework for APC performance monitoring is proposed on the basis of industrial computer control systems background. A software package integrating this technology, which is called Performance Analysis Toolbox and Solutions (PATS), is introduced. The major components of PATS are discussed including process data collection, data preprocessing, process model identification, similarity clustering, control valve stiction detection, multivariate controller performance assessment, and APC economic performance assessment using linear matrix inequality optimization. An industrial case study of a hydrogen unit is illustrated. A limited trial version of the software package can be downloaded from the web http://www.ualberta.ca/~bhuang/research/research.htm