Saulat S. Chughtai

Identification of spatially interconnected systems

This paper presents a method for the identification of spatially interconnected system in rational form, using input-output data. Unlike previously proposed approaches, this method does not rely on a separability condition. The motivation for this approach is to identify a spatially interconnected model in Roesser form for which efficient control synthesis approaches have been recently proposed. The algorithm explicitly takes into consideration boundary conditions, which makes it suitable for boundary value problems such as conduction of heat through metal or vibration in fixed, simply supported or cantilever beams. The approach is illustrated by applying it to a beam element with various boundary conditions. The effectiveness of the method is demonstrated by a controller synthesis based on the identified model.

Distributed Control for a Class of Spatially Interconnected Discrete-time Systems

Abstract This paper considers the analysis and synthesis of a spatially distributed controller for discrete-time spatially interconnected parameter-varying system. The system under consideration has both discrete time and space dynamics. The concept of quadratic separators (Iwasaki and Shibata, 2001), (Chughtai and Werner, 2007) has been extended to compute a measure of worst-case performance for such systems by solving an LMI problem. The use of quadratic separator allows a systematic search for a parameter dependent Lyapunov function, thus resulting in less conservative controllers. The problem of synthesizing controllers leads to a nonlinear matrix inequality, and a hybrid evolutionary-LMI approach to solving this problem, based on LMI solvers and genetic algorithms, is proposed in this paper. A design example illustrates the efficiency of the proposed method.

Consistent identification of two-dimensional systems

This paper presents an identification technique to consistently identify two-dimensional (2-D) systems with additive output noise in transfer function representation. The method is an extension of a one-dimensional instrumental variable (IV) method to two-dimensional systems. In this paper we consider a general two-dimensional (2-D) systems, which may be separable or non-separable, causal, semi-causal (spatially interconnected systems) or non-causal. Furthermore the algorithm can handle boundary conditions. The effectiveness of the method is shown with application to simulation examples.

Consistent identification of spatially interconnected systems

This paper presents an identification technique to consistently identify multi-dimensional systems with additive output colored noise in transfer function representation. The method is an extension of a one-dimensional refined instrumental variable method to multi-dimensional systems. It can be used to identify models for multi-dimensional systems with Box-Jenkins structure; the method may give estimates with minimum bias and variance. In this paper we consider a general multi-dimensional system, which may be separable or non-separable, causal, semi-causal (spatially interconnected systems) or non-causal. Furthermore the algorithm can handle boundary conditions. The effectiveness of the method is shown with application to simulation examples.

Transition control of plane Poiseuille flow - a spatially interconnected model

This paper proposes a new mathematical model for the transition control problem in plane Poiseuille flow. Most of the previously proposed models are based on pseudospectral approaches and are valid only for a single spatial wave number. In this work we propose a new model which is based on a finite difference approach in streamwise direction and a spectral approach in wall normal direction. The model obtained is valid for all spatial frequencies and can be used for the synthesis of controllers for flow control problems, using some recently developed ideas for spatially interconnected systems. Since these controllers are designed in physical domain they are simple to implement using MEMS arrays. The model is compared with results obtained with previously proposed models and is found to be in good agreement with them. To illustrate its usefulness, a stabilizing dynamic output feedback controller is designed for a Reynolds number of 6000.

Modeling and Distributed Control of Transition in Plane Poiseuille Flow

Recently a mathematical model for flow transition control in 2-D channels has been proposed that is in interconnected systems representation. The model is valid for all spatial frequencies and can be used for the synthesis of controllers for flow transition control problems in channels of infinite length. In this brief the model is validated against known features of plane Poiseuille flow and against the response of a nonlinear simulation at Reynolds number 2000. Based on this model a distributed control scheme is then synthesized for Reynolds number 10 000 using a recently proposed approach for interconnected systems. The controller is designed to stabilize the otherwise spatially unstable flow. This instability causes the transition from laminar to turbulence. Furthermore, a desired closed loop frequency response is obtained by tuning the weighting filters. The designed controller is then tested in a nonlinear simulation and closed-loop results are presented. The approach proposed here does not make any assumption on the periodicity of the channel, as is the case in most of previously published work. The control scheme can be implemented on microelectro-mechanical systems (MEMS)-based control systems. Such systems are spatially discrete in nature which is taken into consideration in the controller synthesis phase.

A Hybrid Gradient-LMI Algorithm for Solving BMIs in Control Design Problems

Abstract This paper presents an algorithm for solving optimization problems with bilinear matrix inequality constraints. The algorithm is based on a combination of gradient-based optimization and LMIs, which makes it fast and enables it to handle a large number of decision variables. It is applied to two controller synthesis problems: static output feedback controller synthesis and robust controller synthesis for linear parameter varying (LPV) systems using the idea of quadratic separation. Since the second problem has large number of decision variables, a hybrid approach is applied, in which LMI solvers are used for the evaluation of the cost function. The algorithm is applied to two examples, and results are compared with some existing approaches.

Synthesis of Low-Order Controllers for LPV Systems Using LMIs and Evolutionary Search

A procedure for designing robust and gain-scheduled controllers for linear parameter-varying (LPV) systems is proposed that exploits known bounds on the rate of parameter variation to reduce conservatism. Recent results on stability analysis of LPV systems with known bounds on the rate of parameter change, using the concept of quadratic separators have been extended to compute a measure of worst-case performance of an LPV system by solving an LMI problem. The problem of synthesizing robust and gain-scheduled controllers leads to a bilinear matrix inequality, and a hybrid approach to solving this problem based on LMI solvers and genetic algorithms is proposed in this paper. Two design examples illustrate the efficiency of the proposed method

Identification of LPV models for spatially varying interconnected systems

This paper presents a method for system identification of two dimensional parameter varying systems. The idea of linear parameter varying (LPV) identification for one dimensional causal systems in input-output form is extended to identify two dimensional (2-D) parameter varying systems in input-output form which may be causal, semi-causal or non-causal. The identification method is general in the sense that it can be used to identify systems which may be separable or non-separable. Furthermore, the algorithm explicitly takes boundary conditions into consideration. The effectiveness of the approach is demonstrated by applying it to identify a spatially varying model for a non-uniform beam.

New Dilated LMIs to Synthesize Controllers for a Class of Spatially Interconnected Systems

This paper presents sufficient conditions based on dilated LMIs to analyze and synthesize controllers that minimize the L2-norm of the the closed-loop system for spatially varying interconnected polytopic systems. The approach presented here searches for a parameter dependent Lyapunov function (PDLF) by dilating the original LMIs. This dilation not only helps in the search for a PDLF but also introduces extra degrees of freedom which may result in further reduction of conservatism. Approaches to synthesize full-order polytopic controllers and reduced-order, reduced-structure controllers are also presented here.