**Part 1**

**The Theory of PID Controllers and Their Design Methods** 

**1** 

*Slovak Republic* 

**PID Controller Design for** 

*Institute of Control and Industrial Informatics,* 

*Slovak University of Technology, Bratislava* 

*Faculty of Electrical Engineering and Information Technology,* 

"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

30% of improper performance is due to inadequate selection of controller design

 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 (Kozáková 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, Allen&Bradley, Yokogawa, Fischer-Rosemont commonly implement built-in model-free design techniques applicable for various types of plants; 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

**1. Introduction** 

but in fact:

method,

illustrative examples.

**Specified Performance** 

Štefan Bucz and Alena Kozáková
