This test models demonstrates the use of the homotopyType
parameter of the LimPID
model in different situations.
The first control loop is initialized in steady state with a value of the set point which is compatible with the control variable limitations. In this case, the default option can be used, which removes the limitations in the simplified model, making it linear and thus easier to solve
The second control loop is initialized in steady state with a value of the set point that causes the control output to hit
the upper saturation limit. If this is known a priori, then by setting homotopyType = UpperLimit
the simplified model just
assumes the PID output to be yMax, thus making the simplified initialization problem linear.
The third control loop is similar to the second, except that the lower saturation limit is now engaged.
The fourth loop does not use any simplified model of the limiter during homotopy - this can be used when it is not known a priori if the controller is saturated or not, and it is important to enforce the PID output limitations throughout the whole homotopy transformation.