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Chapter 6 Robust Design for Multivariable Systems Above, analysis for multivariable control systems with resp ect to nominal and robust st ability as well as nominal and robust performance has been assessed. It was assumed that the spec ifications for robust ness were given in terms of weight matrices Wul(s)and Wu2(s), and that the performance specifications similarly were given by weight matrices WpI(s) and wp2( s) How to derive weight matrices leading to good compensators is to some extent still an open question and possibly the most difficult in robust control. In the following, two approaches to weight matrix selection will be proposed. These approaches, though, can not be considered to be final answers to the weight selection problem in any sense 6.1 Loop Shaping The idea behind loop shap ing is to find a compensator K(s) which shapes the open loop system o(L(w)), such that cert ain requirements for robustness and performance are satisfied Natural requirements for performance would be a good dist urb ance attenuation, resulting in a small tracking error. As seen above, the tracking error can be determined as e(8s)=S(s)(T(8)-d(8s)+T(8)n(s) 6.1) Sometimes it can be reasonable to neglect the measurement noise n(s), so the most significant requirement for performance is the output sensitivity o(Solu)) to be small in the frequency range where the most dominant disturb an ces o As most disturbances are low frequent this leads to a requirement for the output sensitivity to be small at frequencies up to a cert ain an evaluation of the domina disturbances. This can be achieved by specifiy ing pl (6.3) here Wp(s)is a scalar transfer function with low pass characteristics. A requirement of this ! ! " #$%& ' " #$(& #$)& $)