PID tuning rules

This chapter introduces new PID tuning rules, derived from the general PID design method proposed in the previous chapter, for frequently encountered first order plus delay processes and integrating plus delay processes. 

This chapter consists of five sections. Section 7.2 presents the development of the PID controller tuning rules for first order plus delay processes. Sections 7.3 and 7.4 illustrate the new tuning rules using simulation and experimental studies, respectively, and compares the results with those obtained using the IMC-PID tuning rules. Section 7.5 presents the development of the PID tuning rules for integrating plus delay processes. 

Tb derive the PID tuning rules, we write the Y function defined in Equation (6.36) in terms of the scaled variable s (or w = dw)... 

Figure 7.14 Stability margins for PID tuning rules (solid (( — 1 solid with o C = 0.707J. Upper diagram gain margins lower diagram phase margins...

The performance of the interacting controller is almost as good as the noninterac ting controller on most processes, but the tuning rules differ because of the above relationships. With digital PID controllers, the noninteracting version is commonly used. 

The two Ziegler-Niehols PID tuning methods provide a useful rule of thumb empirieal approaeh. The eontrol system design teehniques diseussed in Chapters 5 and 6 however will generally yield better design solutions. 

O Dwyer, A. (2000) A summary of PI and PID controller tuning rules for processes with time delay. IFAC Digital Control Past, Present and Future of PID Control, Terrassa, Spain. 

Although Equations (7.11)-(7.25) give analytical solutions for the PID controller parameters, it would be even more convenient for the user to have tuning rules requiring a minimum number of calculations. In order to present a range of desired closed-loop response speeds, we have chosen six different values for the normalized closed-loop time constant id = 4, 2, 1.33, 1, 0.8 and 0.67. The corresponding value of the parameter a can be simply calculated as a = - and the aw tual desired closed-loop time constant is given by... 

Table 7.1 Normalized PID controller tuning rules (subscript 1 PID margins subscript 2 PI margins)...

Table 7.2 PID controller parameters for Process A using new tuning rules...

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