M16.4 Performance of Digital Control Systems

The performance of a digital PID controller is rarely significantly different from that of a continuous PID controller, as long as the sample time is relatively short compared with the dominant process time constant and the desired closed-loop response time. A rule of thumb for digital control systems in general is that the sample time should be less than one tenth the dominant time constant. In practice, digital PID controllers have a sample time much shorter than that. Many distributed control systems have a sample rate that is several times per second, so the sample time is less than 1 second. This makes sense for flow control loops but is much shorter than necessary for other loops. The main disadvantages to sampling too fast are that (i) more frequent computations than necessary are being performed, (ii) numerical round-off could be a problem if only small control moves are being made at each sample time, and (iii) there could be increased measurement noise sensitivity.

Example M16.2: Effect of Sample Time on PI Control Performance

Consider the first-order + time-delay process

where the output is temperature (°C), the manipulated input is valve position (%), and the time unit is minutes. In Module 6 we used this example to compare the robustness of different tuning procedures for PID-type controllers. The IMC-based "improved PI"parameters (see Chapter 9), with l = 7.5 minutes, yields k_c = 1.67%/°C and t_I = 12.5 minutes for an analog PI controller. In Figure M16-2 we compare analog PI control with discrete PI control for two sample times (1 and 4 minutes). Clearly, the control performance degrades as the sample time increases.

Problem M16.2 (see the SIMULINK .mdl file in Appendix M16.1)

Perform simulations with different sample times and compare the performance of the digital controller with the continuous controller while keeping the PID tuning parameters the same as shown in the example.