Synthesis of a Minimum-Energy Controller Subject to an Average Power Constraint

The synthesis of controllers, optimum in the sense of Min∫u2(t)dt, u(t) u the control function, and Subject to the constraint T = ∫0Tu2(t)dt is given for a plant with constant coefficients and distinct characteristic roots. Several variations in the synthesis are considered if the plant has numerator dynamics. The computation involves solving a single transcendental equation for the response time T. Results for several particular plants are given, and these are fimilar to time optimal control.