Nonlinear Control Design Blockset

Actuation Limits vs. State Constraints
(Physical vs. Design Constraints)

To incorporate actuator limits and other physical constraints using the Nonlinear Control Design Blockset, simply use Simulink's Saturation block. You do not need to attach an NCD block and define Nonlinear Control Design Blockset constraints for such signals since the physics of the system guarantees that the signal cannot exceed the limits. For example, consider the pendulum examples and notice the Saturation block after the Klqr gain block. This Saturation block models the actuator limits of the controller. The power electronics of the controller limit the voltage supplied to the motor driving the cart. This voltage limit in turn limits the amount of force applied by the cart to ±1 Newton.

On the other hand, to incorporate design constraints, use the NCD block to constrain a state or signal. In the inverted pendulum example, although the pendulum angle physically can exceed ±0.2 radians, we require that an acceptable controller does not allow the pendulum to exceed such a constraint.

Problem Formulation

Minimizing Integrated Positive Signals (Control Energy)