PID control for MIMO processes

Real industrial processes are almost all of multi-input and multi-output (MIMO) nature, and any change or disturbance occurring in one loop will affect the other loops through the cross-couplings between loops, which is the most important features of a MIMO system, and which implies that the control engineer cannot design each loop independently as they do for SISO systems. Therefore, the requirements for high performance in MIMO control are known to be much more difficult than in the SISO control. Despite great advances in modern control theory, the PID controller is still the most popular controller type used in process industries due to its simplicity and reliability. There are rich theories and designs for the SISO PID control, but little has been done for MIMO PID control while much is demanded for the latter to reach the same maturity and popularity as the single-loop PID case. In this chapter, we first introduce some fundamentals for MIMO systems such as transfer function matrices, poles, zeros, and feedback system stability. Then, we present a graphical method for the design of a multiloop PI controller to achieve the desired gain and phase margins for each loop. Finally, we define the loop gain margins and compute them for multivariable feedback systems. In this way, the stability and robustness of an multivariable feedback system can be really achieved and guaranteed.