Štefan Bucz

PID Controller Design for Specified Performance

„How can proper controller adjustments be quickly determined on any control application?” The question posed by authors of the first published PID tuning method J.G.Ziegler and N.B.Nichols in 1942 is still topical and challenging for control engineering community. The reason is clear: just every fifth controller implemented is tuned properly but in fact:  30% of improper performance is due to inadequate selection of controller design method,  30% of improper performance is due to neglected nonlinearities in the control loop,  20% of improper closed-loop dynamics is due to poorly selected sampling period. Although there are 408 various sources of PID controller tuning methods (O Dwyer, 2006), 30% of controllers permanently operate in manual mode and 25% use factory-tuning without any up-date with respect to the given plant (Yu, 2006). Hence, there is natural need for effective PID controller design algorithms enabling not only to modify the controlled variable but also achieve specified performance (Kozakova et al., 2010), (Osuský et al., 2010). The chapter provides a survey of 51 existing practice-oriented methods of PID controller design for specified performance. Various options for design strategy and controller structure selection are presented along with PID controller design objectives and performance measures. Industrial controllers from ABB, AllenB these methods are based on minimum information about the plant obtained by the well-known relay experiment. Model-based PID controller tuning techniques acquire plant parameters from a step-test; useful tuning formulae are provided for commonly used system models (FOPDT – first-order plus dead time, IPDT – integrator plus dead time, FOLIPDT – first-order lag and integrator plus dead time and SOPDT – second-order plus dead time). Optimization-based PID tuning approaches, tuning methods for unstable plants, and design techniques based on a tuning parameter to continuously modify closed-loop performance are investigated. Finally, a novel advanced design technique based on closed-loop step response shaping is presented and discussed on illustrative examples.

Easy Tuning of PID Controllers for Specified Performance

Abstract The presented method allows achieving maximum overshoot and specified settling time of the closed-loop step response. It provides a simple way to control linear stable SISO systems even if the mathematical model is unknown. Tuning rule parameters are based on one suitably chosen point of the plant frequency response obtained by sine-wave signal with specified excitation frequency, and the required phase margin. The main result provided is construction of empirical charts used to convert time-domain performance specifications (maximum overshoot and settling time) into frequency domain performance measure (phase margin). The method is applicable for systematic shaping of the closed-loop response of the plant. The new approach has been verified on a set of benchmark examples and on a real plant as well.

Robust guaranteed performance PID controller design for non-minimum phase plants

Abstract The paper presents a new original robust PID design method for non-minimum phase plants to achieve closed-loop performance prescribed by the process technologist in terms of settling time and maximum overshoot, respectively. The proposed design procedure has two steps: first, the uncertain system is identified using external harmonic excitation signal with frequency, second, the controller of the nominal system is designed for specified gain margin. A couple of parameters is obtained from the time domain performance specification using quadratic regression curves, the so-called performance Bparabolas so, as to simultaneously satisfy robust closed-loop stability conditions. The main benefits of the proposed method are universal applicability for systems with both fast and slow dominant dynamics as well as performance specification using time domain criteria. The proposed PID design method has been verified on a set of benchmark systems.

A new robust PID controller design methodology for systems with unstable zero

The proposed new method is applicable for control of linear stable single-input-single-output non-minimum phase systems even with unknown mathematical model and unstructured uncertainties. The control objective is to provide required nominal maximum overshoot and settling time of the controlled variable y(t). The proposed new controller design approach guarantees fulfillment of these performance measures specified by the designer for processes with unstable zero. The developed algorithm has been extended to guarantee robustness of the PID controller design for uncertain processes modelled by unstructured uncertainties, and verified on a vast batch of benchmark examples.