Vojtech Vesely

Design of robust decentralised controllers using the M-Δ structure robust stability conditions

This article proposes a new frequency domain approach to the design of robust decentralised controllers (DC) for continuous-time systems described by a set of transfer function matrices. Nominal stability, required nominal performance and robust stability (RS) are guaranteed using the independent design approach applied for nominal system, adapted so as to satisfy the M−Δ structure-based RS conditions modified for the closed-loop system under a decentralised controller. The proposed design technique enables us to include nominal interactions in the nominal model thus relaxing the conservatism of the RS conditions.

Decentralized Digital PID Controller Design for Performance

Abstract The paper deals with the frequency domain decentralized discrete-time controller design methodology to guarantee specified performance of the overall system. The underlying theory evolves from the stability conditions developed in the “Equivalent Subsystems Method” approach and applies closed-loop performance specification based on the relationship between phase margins of equivalent subsystems and maximum overshoot of the full system. To design local PI controllers for specified phase margin, Bode plots of discrete equivalent subsystems are used. Designed local continuous controllers are then converted to their discrete versions and implemented for the controlled plant. The design procedure is illustrated on the case study.

Robust Controller Design: New Approaches in the Time and the Frequency Domains

Robust stability and robust control belong to fundamental problems in control theory and practice; various approaches have been proposed to cope with uncertainties that always appear in real plants as a result of identification /modelling errors, e.g. due to linearization and approximation, etc. A control system is robust if it is insensitive to differences between the actual plant and its model used to design the controller. To deal with an uncertain plant a suitable uncertainty model is to be selected and instead of a single model, behaviour of a whole class of models is to be considered. Robust control theory provides analysis and design approaches based upon an incomplete description of the controlled process applicable in the areas of non-linear and time-varying processes, including multi input – multi output (MIMO) dynamic systems. MIMO systems usually arise as interconnection of a finite number of subsystems, and in general, multivariable centralized controllers are used to control them. However, practical reasons often make restrictions on controller structure necessary or reasonable. In an extreme case, the controller is split into several local feedbacks and becomes a decentralized controller. Compared to centralized full-controller systems such a control structure brings about certain performance deterioration; however, this drawback is weighted against important benefits, e.g. hardware, operation and design simplicity, and reliability improvement. Robust approach is one of useful ways to address the decentralized control problem (Boyd et al., 1994; Henrion et al., 2002; de Oliveira et al., 1999; Gyurkovics & Takacs, 2000; Ming Ge et al., 2002; Skogestad & Postlethwaite, 2005; Kozakova and Veselý, 2008; Kozakova et al., 2009a). In this chapter two robust controller design approaches are presented: in the time domain the approach based on Linear (Bilinear) matrix inequality (LMI, BMI), and in the frequency domain the recently developed Equivalent Subsystem Method (ESM) (Kozakova et al., 2009b). As proportional-integral-derivative (PID) controllers are the most widely used in industrial control systems, this chapter focuses on the timeand frequency domain PID controller design techniques resulting from both approaches. The development of Linear Matrix Inequality (LMI) computational techniques has provided an efficient tool to solve a large set of convex problems in polynomial time (e.g. Boyd et al., 1994). Significant effort has been therefore made to formulate crucial control problems in

Design of robust controller with input constraints

A novel approach to robust controller design with input hard constraints is presented. The proposed design procedure contains robust stability condition based on the M-delta structure and it is used for system with additive uncertainty. The obtained results, illustrated on example, show the applicability of the designed robust controller and its ability to cope with model uncertainties.

PID robust gain-scheduled controller design

A novel methodology is proposed for robust gain-scheduled PID controller design for uncertain LPV systems. The proposed design procedure is based on the parameter-dependent quadratic stability approach. A new uncertain LPV system model has been introduced in this paper. To access the performance quality the notion of a parameter varying guaranteed cost is used. Numerical examples show the benefit of the proposed method.

Robust output feedback controllers for MIMO systems, BMI and LMI approach

The paper presents two methods of robust output feedback controller design for MIMO systems. First is based on solving bilinear matrix inequalities (BMI) and second uses linearisation to transform problem into linear matrix inequality (LMI). Both methods can be applied to continuous or discrete time systems. In order to test the applicability, a set of randomly generated unstable systems was created. Then the number of successfully solved systems and time required to solve the problem is compared. Although the LMI method is only heuristic experiments showed that it has better results and can be used with higher order systems.

Robust controller design for nonlinear Lipschitz systems: Gain scheduling approach

The Paper is devoted to the design of robust PID controllers for the case of nonlinear Lipschitz systems using the gain scheduling plant model approach. The proposed method is based on an uncertain gain scheduled plant model, H2 performance (guaranteed cost) and the Bellman Lyapunov equation.

Robust LPV-based infinite horizon LQR design

In this paper, the problem of robust infinite horizon linear quadratic regulator (LQR) design is addressed for uncertain affine linear parameter-varying (LPV) systems. The proposed method extends the standard infinite horizon LQR design to LPV-based static output-feedback (SOF), dynamic output-feedback (DOF) and to a well known proportional, integral and derivative (PID) controller design for uncertain affine LPV systems. The optimal (suboptimal) controller design is formulated as an optimization problem subject to some linear/bilinear matrix inequality (LMI/BMI) constraints. As the main result, the suggested performance and stability conditions, without any restriction on the controller and system structure, are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples.

Engine speed control using gain scheduling method

This paper presents a gain scheduled controller design for SISO systems applied on laboratory engine. Presented frequency domain method is based on the M-delta structure of closed loop systems. The small gain theory is exploited to obtain the stability condition. The gain scheduling control is applied on laboratory engine with variable load and compared with classic robust control.

Robust decentralized controller design in frequency domain

The paper presents control system design based on robust decentralized control. Controller design will be done in the frequency domain for nominal model with time delay. Robust condition ensuring stability also by delay change, based on M-delta structure is included in controller design. In controller design for multivariable systems equivalent subsystem method is used. For subsystems of equivalent model, frequency method ensuring desired phase margin and crossover frequency is applied. Design procedure is illustrated on example and compare conservativism by using of different characteristic functions.