PID Control for Electric Vehicles Subject to Control and Speed Signal Constraints

Algorithm 1

1: Convert the continuous system into a state space system, where the states are the errors and the input is the

control action, according to equation (11);

2: Compute the maximal contractive controlled invariant set contained in the set of constraints, which must

be reexplained in terms of the new state representation;

3: Solve the mp-LP problem described in equation (2);

4: Compute the integral of error, error, and derivative of error;

5: Identify which polyhedral region the computed state belongs to.

6: Use the affine control law to control the system with and being the mp_PID parameters,

corresponding to the j-th polyhedral region;

7: If the control routine is not interrupted, return to step 4.