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Chapter 2 Nominal and robust stability In order to be able to design a robust compensator to control a given pro cess, it is necessary not only to specify a nominal mo del of the process, but also the mo del uncert ainty to whid the control sy stem has to be robust. The compensator is required to make the output follow variations in the reference signal and to attenuate disturbances. Hence, to design the com- ensator, it is also necessary to know the anticipated character of the reference signal and of the disturb ances. Given these, performance specifications can be expressed as requirements of a cert ain level of error reduction in the presence of these input Design of a robust compensator is based on A model of the process a description of the model uncert ainty Knowledge of the character of the inputs(for reference and disturb ances Performance specifications A compensator is said to be robust, if the performance specifications are satisfied both for the nominal model of the process as for any other model cont ained in the admissible set of models as specified by the mo del uncertainty. systems are formulated. For multi variable(MIMO)systems, see Chapter 5 on page A o. In the following sections, a framework for specification of the model, of the mo del uncertain of the character of the inputs and of performance specifications for single variable (S 2.1 A Model of the proces The concepts and met hods used in the sequel are based on linear time invariant models 2.2 Model Uncertainty Model uncert ainty is often specified in the frequency domain. This can lead to a region for each frequency w in the Nyquist plane in which the real'model of the process GaGw) is ! " " # $ % & " $''(% ) $**(% + , -. * / 0 0 1