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Chapter 3 Nominal and robust performance This chapter presents approaches to formulate performance specifications for a control sy stem. d(8) rs e(s) K(8) s) G(s) Figure 3. 1: Standard feedback configuration Figure 3. 1 shows a st andard sy stem with feedback control. The controlled sy stem has an input reference r and a dist urb ance signal d. Since the two input s have the same transfer function to the error signal e(except for the sign difference), they are treated collectively, denoted by the signal u A compensator is traditionally designed for a specific input. This is true for classical design methods, where the design often aims at achieving cert ain characteristics for the closed loop resp onse to a step or ramp input as mentioned in Chapter 1. Likewise, linear quadratic control aims at minimizing the error for a given input signal In practice, it is often more relevant to design the compensator for a class of related inputs with the same characteristics. The exposition below aims at assessing the input error for ferent compensators exp osed to exogenous signals of the same 'size interpreted in a norr 3.1 Signal norms To measure the 'size' of a time domain signal, a norm will be applied. Predominantly, the 2 norm will be applied, which is defined by: !" " # " $ %" & ' ( " )') )') " * " "