Roman Prokop

Graphical analysis of robust stability for systems with parametric uncertainty: an overview

Systems with parametric uncertainty play an important role in both the theory and practical applications of robust control. They are described by the mathematical model containing parameters that are not precisely known, but the values thereof lie within given intervals. This type of uncertainty can arise during the control of real processes, eg, as a consequence of modelling effort, imprecise measuring or the influence of certain external conditions. The number of robust stability analysis techniques has been developed during the previous years of research interest. However, many of them are highly specialized only for specific types of uncertainty structure. This paper offers an overview of illustrative examples aimed at usage of a universal graphical approach to robust stability analysis for systems with parametric uncertainty. The investigation method is based mainly on the combination of the value set concept and the zero exclusion condition, which is greatly advantageous especially for more complicated problems.

SIMPLE ROBUST CONTROLLERS: DESIGN, TUNING AND ANALYSIS

Abstract The contribution is focused on robust design and analysis of continuous-time controllers for SISO systems without and with time delays. Controllers are obtained via solutions of diophantine equations in the ring of proper and stable rational functions by Youla-Kucera parameterization. Uncertainty is studied through the infinity norm H ∞ . A scalar parameter was proposed as a tuning knob for minimization of the sensitivity function and uncertainty conditions. Both, feedback a feedback and feedforward structures of the controlled system are considered. Disturbance rejection and attenuation can be also easily solved by the proposed methodology.

Single-Parameter Tuning of PI Controllers: From Theory to Practice

The paper deals with influence of a single scalar positive tuning parameter on performance properties of the closed control loop which contains algebraically designed PI controller while the response quality is evaluated by the size of first under- or overshoots. The controller coefficients are calculated from general solutions of diophantine equations in the ring of proper and Hurwitz stable rational functions. Subsequently, these controllers can be tuned by the only parameter. The contribution brings simple tuning rules and, moreover, it presents their possible practical application during control of real laboratory model assumed as system with parametric uncertainty.

DESIGN OF ROBUST PI CONTROLLERS AND THEIR APPLICATION TO A NONLINEAR ELECTRONIC SYSTEM

Design of Robust PI Controllers and their Application to a Nonlinear Electronic System The principal aim of the paper is to present a possible approach to the design of simple Proportional-Integral (PI) robust controllers and subsequently to demonstrate their applicability during control of a laboratory model with uncertain parameters through the Programmable Logic Controller (PLC) SIMATIC S7-300 by Siemens Company. The proposed and utilized synthesis consists of two steps. The former one is determination of controller parameters area, which ensures the robustly stable control loop and is based on computing/plotting the stability boundary locus while the latter one lies in the final choice of the controller itself relying on algebraic techniques. The basic theoretical parts are followed by laboratory experiments in which the 3rd order nonlinear electronic model has been successfully controlled in various working points.

Robust Control of a Two Tank System Using Algebraic Approach

The paper deals with design of a robust controller via algebraic μ-synthesis for a two tank system, which is a well known benchmark problem. The controller is obtained by decoupling two-input two-output system into two identical SISO (Single-Input Single-Output) plants. The task of robust controller design is then performed by finding a suitable pole placement for the SISO systems. The robustness is measured by the structured singular value denoted μ. The final controller is verified through simulation for plants perturbed by worst case perturbations.

Single-parameter tuning of PI controllers: Theory and application

Abstract The paper deals with the influence of a single tuning parameter on performance properties of the closed control loop which contains algebraically designed continuous-time PI controller while the response quality is evaluated by the size of first under- or overshoots. The controllers are obtained from general solutions of Diophantine equations in the ring of proper and stable rational functions and can be subsequently tuned via the only parameter. This article brings simple tuning rules, verifies their validity by means of simulation example and, moreover, it presents their possible practical application during control of real laboratory model assumed as system with parametric uncertainty.

Autotuning for delay systems using meromorphic functions

Abstract The paper presents an autotuning method for time delay systems. The novelty in principles is a new combination of biased-relay feedback identification and an algebraic control design method for time-delay systems. The estimation of the controlled process is based on an asymmetrical limit cycle data experiment. Then, a stable transfer function with a dead-time term is identified. The controller is designed through solutions of Diophantine equations in the ring of stable and proper retarded quasipolynomial meromorphic functions. Controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. First and second order identification gives Smith-like feedback controllers with the realistic PI and PID structure. The design principle also offers a scalar tuning parameter m0 > 0 which can be adjusted by a suitable principle or an optimization method. The developed approach is illustrated by examples in the Matlab + Simulink environment.

Robust Proportional-Integral Control of a Laboratory Model Using Programmable Logic Controller SIMATIC S7-300

Abstract The main aim of the contribution is to present a possible approach to design of simple Proportional-Integral (PI) robust controllers and subsequently to demonstrate their applicability during control of a laboratory model with uncertain parameters through the Programmable Logic Controller (PLC) SIMATIC S7–300 by Siemens Company. The proposed and utilized synthesis consists of two steps – the former one is a determination of controller parameters area, which ensures the robustly stable control loop and which is based on the computing/plotting the stability boundary locus while the latter one lies in the final choice of the controller itself relying on algebraic techniques. The basic theoretical parts are followed by laboratory experiments in which the 3rd order nonlinear electronic model has been successfully controlled in various working points.

PI autotuners based on biased relay identification

Abstract The paper describes an automatic tuning procedure for a wide class of continuous-time systems without and with time delays. Every auto-tuning method has two basic steps. The first one is experimental and yields an estimated model. The second step consists in a design procedure of controllers. The developed auto-tuning procedure identifies a first order estimation model obtained by a biased relay feedback test. The consecutive design is based on a general solution of Diophantine equations and results in a PI-like controller. Moreover, the Diophantine equation approach gives a scalar tuning parameter which is adjusted according to the equalization of weighted moments.

Robust Stability of Fractional Order Time-Delay Control Systems: A Graphical Approach

The paper deals with a graphical approach to investigation of robust stability for a feedback control loop with an uncertain fractional order time-delay plant and integer order or fractional order controller. Robust stability analysis is based on plotting the value sets for a suitable range of frequencies and subsequent verification of the zero exclusion condition fulfillment. The computational examples present the typical shapes of the value sets of a family of closed-loop characteristic quasipolynomials for a fractional order plant with uncertain gain, time constant, or time-delay term, respectively, and also for combined cases. Moreover, the practically oriented example focused on robust stability analysis of main irrigation canal pool controlled by either classical integer order PID or fractional order PI controller is included as well.