The closed-loop system was then simulated with the calculated gains to ensure that performance would be satisfactory. The algorithms that calculated the gains of the Kalman filter and FSFB control law assumed that the system is ideal and linear. Besides the nonlinear solenoid current-to-force relationship and the ceiling on the solenoid current, there are other real-life factors that might cause performance to be less-than-optimal once the gains are used in a simulation or in the actual apparatus. These nonideal factors are modeled in the simulation to assess the performance of the calculated gains.

• In the case of the Kalman filter, the recursive algorithm that calculates the gains also assumes the plant is discrete-time. Of course, the motion plant is, in reality, continuous-time.
• The exogenous force might be larger than assumed due to the presence of the two springs. This can be seen in the input force graphs in the Readouts section. They show that the input force does not settle at zero but drifts even when the payload is positioned at its destination and no longer moving.
• The total travel length and the payload mass might have a large tolerance. This has to do with the fact that the travel length and payload mass are so small.
• The solenoids might have deteriorated over time.

Here is a link to a Matlab Simulink file: Simu_Atmpt.slx