Nonlinear Control Design Blockset

Minimizing Integrated Positive Signals (Control Energy)

Again, such signals can be considered design constraints. If the signal does not exist naturally in the system, you can model it using the Abs and Integrator blocks in Simulink. Even though we do not typically view such constraints as point-by-point constraints (i.e., intermediate time values of the signal are of no interest), the design constraint analogy still holds because over time, the integral increases. Thus you know that the signal can never have a value at its final time smaller than at any intermediate time. Also, although many problems concerning the minimization of integrated signals extend to an infinite time horizon (the Nonlinear Control Design Blockset is practical only over shorter time horizons), the signals typically begin converging to their infinite time horizon limit in a finite time (over which the Nonlinear Control Design Blockset can practically be applied).

Before using the Nonlinear Control Design Blockset to minimize integrated signals, consider whether such a design goal really makes sense to you. Much modern control theory considers the minimization of integrated positive signals, partly because such signals possess some relation to the real world and partly because such problems possess well known closed-form solutions. For something such as simple motor actuation, you may instead want to incorporate actuator saturation using a Saturation or Limited Integrator block. On the other hand, for something such as jet engine control, minimizing total fuel consumption (an integrated positive signal) may be necessary.

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

Noise Inputs