**1. Introduction**

"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:


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 illustrative examples.

PID Controller Design for Specified Performance 5

Consider the FOPDT (j=1) and FOLIPDT (j=3) plant models given as GFOPDT=K1e-D1s/[T1s+1]

lim ( )

*c c*

*G j*

where Kc and c are critical gain and frequency of the plant, respectively. Normed time delay j and parameter j can be used to select appropriate PID control strategy. According to Tab. 1 (Xue et al., 2007), the derivative part is not used in presence of intense noise and a

() 2 *s cc*

;

*sG s TK K*

High noise  

2 3

(3)

1

Low measurement noise

<sup>3</sup> <sup>2</sup>

 

Precise control needed

1 1 () 1 <sup>1</sup> *R d*

*G s K Ts*

*i f*

*Ts T s* 

(4)

Low saturation

3

<sup>2</sup> <sup>1</sup>

*arctg*

 ; 0 3 3

**2.1.3 PID controller structure selection based on plant parametres** 

3 *D T*

PID controller is not appropriate for plants with large time delays.

No precise control necessary

Table 1. Controller structure selection with respect to plant model parameters:

<sup>1</sup> () 1

*T s Gs K*

In practical cases N8;16 (Visoli, 2006). The PID controller design objectives are:

2. rejection of disturbance d(t) and noise n(t) influence on the controlled variable y(t). The first objective called also "servo-tuning" is frequent in motion systems (e.g. tracking required speed); techniques to guarantee the second objective are called "regulator-tuning".

1>1; 1<1,5 I I+B+C PI+B+C PI+B+C 0,6<1<1; 1,5<1<2,25 I or PI I+A PI+A (PI or PID)+A+C 0,15<1<0,6; 2,25<1<15 PI PI PI or PID PID 1<0,15; 1>15 or 3>0,3; 3<2 P or PI PI PI or PID PI or PID 3<0,3; 3>2 PD+E F PD+E PD+E

A: forward compensation suggested, B: forward compensation necessary, C: dead-time compensation suggested, D: dead-time compensation necessary, E: set-point weighing

Consider the following most frequently used PID controller types: ideal PID (4a), real interaction PID with derivative filtering (4b) and ideal PID in series with a first order filter

> 1 *d*

*T s T*

Performance measures indicating satisfactory quality of setpoint tracking (Fig. 2a) and disturbance rejection (Fig. 2b) are small maximum overshoot and small decay ratio,

*i d*

*s N*

;

and GFOLIPDT=K3e-D3s/{s[T3s+1]} with following parameters

1 1 *K Kc* ; <sup>3</sup> 3

1

1 *D T*

Ranges for and

necessary, F: pole-placement

<sup>1</sup> () 1 *R d*

*G s K Ts T s* 

respectively, given as

*i*

;

*R*

1. tracking of setpoint or reference variable w(t) by y(t),

**2.3 Performance measures in the time domain** 

(4c)

**2.2 PID controller design objectives** 

1

;
