AN EXTENDED NICHOLS CHART WITH CONSTANT MAGNITUDE LOCI OF SENSITIVITY AND COMPLEMENTARY SENSITIVITY FUNCTIONS FOR LOOP-SHAPING DESIGN

Gain and phase margins are widely used stability indices of feedback control systems; although they are both considered explicitly only from the analysis point of view, the phase margin alone is usually considered in the design stage. That is quite restrictive since even if a large phase margin is guaranteed, the feedback control system may show poor robust stability performances. A more general approach consists of bounding the value of the maximum resonance peaks of both the complementary sensitivity and sensitivity functions. In order to handle such resonance peak specifications, it is crucial to set out effective graphical tools which provide explicit reading of closed loop properties from the open loop frequency behaviour. To this end, an Extended Nichols Chart (ENC) which displays constant magnitude loci of the sensitivity function along with the well assessed constant magnitude loci of the complementary sensitivity is introduced in this paper. The advantages of using the ENC in an educational context will be shown in the control design of an unstable laboratory process.