On Design Tradeoffs in Feedback Systems in the Presence of Input Constraints

This paper describes the feedback limitations caused by the presence of right half-plane poles and zeros in the plant and compensator when bounds on the size of the plant input are imposed. It is shown that nonminimum phase zeros of the plant and unstable poles of the compensator constrain the magnitude of the closed loop transfer function relating the plant input and exogenous signals. A new result shows the distinct role played by unstable poles of the compensator and nonminimum Phase zeros of the plant. This characterization that is lost when the closed loop feedback properties are expressed solely in terms of the loop transfer function. It is shown that if an unstable compensator is used then constraining the size of the plant input may result in peaks of the sensitivity function.