Internal model-based control for integrating processes

Internal model-based control (IMC) has been shown to possess many advantages over PID control, particularly in the presence of significant process deadtime. Implementation of IMC is simplified in a large class of industrial applications where the process dynamics can be adequately characterized by a simple first-order model requiring only estimates of process gain, lag time constant, and deadtime for implementing the controller design. Tuning of the controller is easily and intuitively done by adjusting the filter time constant; decreasing the time constant speeds up the closed-loop response, and increasing it yields generally a slower but more stable response. There are problems, however, in applying the IMC approach to an integrating process, i.e., a process with a pole at the origin. First, for a first-order lag filter, the steady-state error due to a process input disturbance is generally non-zero. This error can be reduced to zero with a higher-order lead lag filter with proper choice of filter parameters. This is at a cost, however, of increased design complexity, amplification of noise in the controller signals, and a potential numerical overflow issue due to an integrator within the IMC computation loop. To overcome these problems, an alternative IMC implementation is proposed where the integrator in the model is approximated by a first-order lag with a very large time constant. It is shown analytically and verified by computer simulation that this approach assures zero steady-state error for setpoint (SP) changes and process disturbance inputs. Computer simulation studies also show that the transient response can be satisfactorily tuned by proper choice of the filter time constant and that potential numerical instability issues are essentially eliminated. Further, since the choice of time constant in the lag used to approximate the integrator function in the modified IMC also affects the PV(t) response approach, another degree of freedom in the tuning process is introduced. This modified IMC approach has been used successfully in several real-world applications.