Radek Matusu

Various approaches to control of systems with time-varying delay

The paper is focused on control of single-input single-output (SISO) systems with harmonically time-varying delay. Three different approaches to continuous-time control are presented and compared. The first technique uses a modified PI-PD Smith predictor in combination with standard forms for minimum of integral squared time error (ISTE). The second methodology is also based on modified Smith predictor and on design by coefficient diagram method (CDM). And finally, the third approach to synthesis is grounded in general solutions of Diophantine equations in the ring of proper and Hurwitz-stable rational functions (R PS ) for 1DOF control system. The comparison of methods is performed and illustrated on a simulation example.

Robust control of temperature in hot-air tunnel

This paper is aimed to application of simple continuous-time robust regulators of PI and PID type designed through general solutions of Diophantine equations in the ring of proper and stable rational functions to control of temperature in laboratory model of hot-air tunnel of which mathematical model is supposed to include parametric uncertainty. One of the main advantages of the proposed algebraic approach to control design is the existence of a single positive tuning parameter. The contribution contains both identification and control experiments.

A Class of PID Controllers Tuned in Fractional Representation

Abstract The contribution is focused on design and tuning of simple controllers for continuous-time SISO systems without and with time delays by algebraic methods. The control synthesis is based on general solutions of linear Diophantine equations in the ring of proper and Hurwitz stable rational functions (R PS ). Both, feedback (1DOF) a feedback and feed forward (2DOF) structures of the control system are considered. A scalar positive parameter is introduced for tuning and influencing control responses. In the paper, this parameter is used for aperiodic tuning of PI controllers. The methodology is utilized for autotuning principles and for robust applications. Interval perturbations in controlled systems and robustness of proposed algorithms are outlined through the value set concept, zero exclusion condition and Kharitonov theorem. For both applications user-friendly program packages were developed in the Matlab+Simulink environment with the support of Polynomial Toolbox.

Robust PI controller design for a laboratory time delay process

The paper presents an approach to robust PI controller design for systems with interval parametric uncertainty and time delay. It is supposed that the controlled system is described by a transfer function with parameters lying in certain intervals and with a time delay term. The transfer function of the controlled system is modified by approximation of the time delay term by its Pade expansion. The area of all PI controller parameters kp, ki, that are able to assure the robust stability of the feedback closed loop, is found by the method, which is based on plotting the stability boundary locus in the (kp, ki)-plane. Then the pole-placement method is used to specify those controller parameters from the robust stability area, which assure quality of the control performance prescribed by a choice of closed loop poles or relative damping or natural undamped frequency of the control response. The contribution presents theoretical results confirmed by practical experiments in laboratory conditions. Robust PI controllers are found using designed approach for control of an electronic equipment with varying time delay. Designed robust PI controllers are realized using the PLC SIMATIC S7–300.

Design and Practical Application of Simple Robust Controllers: A Parametric Approach

The contribution is focused on brief description of proposed control design process and primarily on practical application of obtained simple robust control algorithms. The synthesis is based on general solutions of Diophantine equations in the ring of proper and stable rational functions, Youla-Kucera parameterization and divisibility conditions and one of its main advantages can be seen in existence of single scalar tuning parameter. The real-time control behaviour has been tested on laboratory model of hot-air tunnel which has been mathematically described by various transfer functions containing parametric type of uncertainty.

Two approaches to description and robust stability analysis of fractional order uncertain systems

The principal goal of this contribution is to present two different approaches to description and robust stability analysis of continuous-time fractional order uncertain systems. The first approach uses fractional order models with parametric uncertainty and robust stability of corresponding closed-loop control systems is investigated by using the value set concept in combination with the zero exclusion condition. On the other hand, the second approach is based on fractional order models with unstructured multiplicative uncertainty created by choosing a nominal plant and a suitable weight function. In this case, the graphical robust stability test utilizes the envelopes of the Nyquist diagrams. Both methods are illustrated by means of the joint example.

Implementation of Control Design Methods into Matlab Environment

Computer-aided tools for analysis and synthesis of control systems are widely employed by many users from a range of researchers, control engineers or students. The reason is obvious. Such toolboxes represent comfortable and effective way of dealing with an array of complex control problems, sometimes even without deeper knowledge of the specific method. For example, Control System Toolbox, Robust Control Toolbox or Polynomial Toolbox (PolyX, 2011) for Matlab belong among the most popular ones in the control field. The main aim of this chapter is to present two simple and freely downloadable Matlab programs which allow user-friendly work for two selected specific control design issues by means of Graphical User Interface (GUI). First of the packages (Matusů, 2010; Matusů & Prokop, 2011a) is focused on algebraic design of continuous-time controllers under assumption of interval plants. The program takes advantage of Matlab + Simulink + Polynomial Toolbox (PolyX, 2011) environment and it represents an easy but effective and user-friendly way to control synthesis, robust stability analysis and simulation. The second of the presented programs (Matusů & Prokop, 2010, 2011b, 2011c) deals with control of time-delay systems using three various modifications of Smith predictor. The software implementation includes the modification for unstable and integrating processes, PI-PD modification for systems with long dead time, and modification applying control design by Coefficient Diagram Method (CDM). The described software products, which can be used both for research and educational purposes, are freely available on the Internet (Matusů & Prokop, 2011a, 2011b). Their application potential is going to be illustrated on several control examples. The chapter is organized as follows. The Section 2 focuses on algebraic design of controllers for interval plants. It is divided into three partial subsections dealing with brief outline of basic theoretical background, description of the developed program itself and demonstration of its capabilities by means of an illustrative example, respectively. Analogically, the Section 3 has the very same structure but it presents the control of time-delay systems using three modifications of Smith predictor. Finally, Section 4 offers some conclusion remarks. The partial versions of this work have been already presented in (Matusů & Prokop, 2010, 2011c; Matusů 2010).

A software tool for algebraic design of interval systems control

This paper intends to describe a software tool for algebraic design of continuous-time control under assumption of interval plants. The program takes advantage of the MATLAB + Simulink + Polynomial Toolbox environment and it represents an easy but effective and user-friendly way to control synthesis, robust stability analysis and simulation. The product, which can be used both for research and educational purposes, is freely available on the internet.

Software Implementation of Self-Tuning Controllers

Real control of industrial processes is almost always burden with various perturbations, disturbances and changes in process parameters or dynamics due to varying operational conditions, plant properties themselves, etc. Furthermore, an acceptable a priori mathematical model does not have to be known. In spite of it, such processes have to be controlled. A possible solution to this task represents an area of control theory known as adaptive control or more specifically usage of self-tuning controllers (Astrom & Wittenmark, 1973); (Astrom et al., 1977); (Clarke & Gawthrop, 1979); (Astrom & Wittenmark, 1989); (Wellstead & Zarrop, 1991); (Isermann et al. 1992); (Hang et al., 1993); (Bobal et al., 1999); (Bobal et al., 2005). Main idea consists in modification of control law according to the changing plant parameters obtained via recursive identification. Their advantage is some kind of “intelligent” behaviour, but on the other hand these regulators are quite complex and not easily applicable. This chapter deals mainly with software implementation of selected digital self-tuning control algorithms into the Matlab and Pascal environment for the purpose of possible industrial utilization. The work was motivated by co-operation with a manufacturer of aluminium-based rolled products and packaging materials. His project has supposed primarily the application of discrete-time adaptive compensator to control of a metal smelting furnace. Other requirements were the plant model with “a2b3” structure and final implementation in Borland Pascal (because of integration into the existing system). However the paper presents not only derived relations applicable to Pascal environment but also program for simulative purposes and testing created under Matlab and some preliminary simulation results. In the first stage, the applied methods have included a polynomial approach to discrete-time control design and recursive least-squares identification algorithm LDDIF, but subsequently also two alternative techniques, namely control using continuous-time regulator with fixed parameters and use of delta approach in self-tuning control, have been verified. Although all the tasks were motivated by our

Description And Analysis Of Interval Systems.

Control of real industrial processes is almost always burden with an uncertainty. The reasons of that unfavorable fact are mainly an imprecise modelling and measuring or an influence of some external conditions. A convenient tool for dealing with such class of issues represents the application of models with parametric uncertainty. The mathematical model is then supposed to contain parameters which are not precisely known, but the values thereof lie within given intervals. If individual uncertain coefficients (in polynomial, in transfer function etc.) are mutually independent, the uncertainty has a simple interval structure. This contribution offers several possibilities of utilization of interval uncertainty for systems description and presents the tools for robust stability analysis, emphasizing advantages and limitations connected with the use of this simple structure, even for more complicated problems.