Ind. Eng. Chem. Res. 1987,26, 2163
2163
Response to Comments on “Internal Model Control. 4. PID Controller Design” Sir: Just like other optimal control techniques, unconstrained IMC (Garcia and Morari, 1982) allows the designer to obtain the best closed-loop performance for a particular system limited only by process inherent characteristics like time delays ana R H P zeros. It is evident from the derivation that the complexity of an IMC controller increases with the complexity of the process model. Rivera et al. (1986) state the following: “The goal of this article is to show that for the objectives and simple models common to chemical process control, the IMC procedure leads naturally to PID-type controllers...”. They prove that even in ideal circumstances (no constraints, no model uncertainty), more complex models than those currently used in the process industries are necessary to justify using anything but PID controllers for SISO systems. Specifically, the value of a Smith Predictor for systems with time delay is questioned. “For the particular case of a first-order lag with dead-time process, the improvement of the ISE for a step set point/disturbance by the Smith Predictor over a PID controller is a t most 10% regardless of O / T . ” In their correspondence, Harris and Tyreus (1987) state that “these performance claims are misleading since they require excessive control action.” As always, we value their opinion. We insist, however, on the correctness of our original statements and cannot find any evidence to the contrary in their arguments. We are well aware of the importance of constraints. Indeed, the issue is discussed in the first part of this series of papers (Garcia and Morari, 1982). The comparison (PID vs. the Smith Predictor and PI) is between two unconstrained controllers. It is true that depending on the chosen tuning parameters, the PID controller might require excessive control action as demonstrated by Harris and Tyreus (1987). Under these conditions, however, the Smith Predictor and PI configuration will require even more excessive control action to lead to improvement over the PID controller. Thus, there is no possibility to realize the gains offered by this more complex controller structure and the PID controller is completely adequate. The effect of input constraints on the control performance of SISO systems is self-evident and understood by any engineer. Clearly, the tighter the constraints chosen, the smaller is the opportunity to affect control performance by clever design and tuning. To illustrate this, consider the input and output trajectories given by the ISE optimal controller for the plant g(s) = ke-8s/(m+ 1)and a step set point change, of magnitude ysp,in the presence of the input constraint lu(t)l IumaX: u(t) =
K=
t > t*
&
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