MPC Designer produces controller with overshoot response, given Min Rate constraint

Hi,

I'm designing a nonlinear controller which does not respond to positive decreasing voltage.

I used MPC Designer to come out with an initial design, where the minimum rate is not constrained (thus responds linearly to positive decreasing voltage). I then set the Min Rate constraint from -Inf to zero. These are my observations (blue line is predicted input, red line is predicted output, sampling time is 0.5 s, prediction horizon is 5, control horizon is 1):

1. Original controller (without min rate constraint): It can be seen that at the first sequence (t=1 s, that is when step input is applied), the MPC is already targeting a displacement of ~1.2 cm. Then, at the next sampling instance (t=1.5s), it targets 1.138cm. It’s not until the fourth samples (t=2.5s) that it starts to target something close to 1 (1.04cm).

2. Modified controller (with min rate constraint of 0): It can be seen that it tries to follow the same strategy as before, targeting a displacement of ~1.2 cm at the first instance. Then at the next instance (t=1.5), it couldn’t bring down the input as it can in the original scenario, because the min rate is constrained, even though it knows that the predicted displacement would be 1.3092. Therefore, overshoot happens.

My question is, why did it target 1.2cm at the very first instance even though I instructed it to strictly target minimum error (by setting the only parameter in the cost function to be Manipulated Output (MO))? And why did it still target 1.2cm at the second scenario even though it knew it cannot bring the output down?