One goal of the paper is to prove that a control strategy with unknown disturbance rejection reduces the control effort to a minimum. A similar statement appeared in the literature, but without proof. The disturbance to be rejected is completely unknown except for a sectorial bound. The control unit is endowed with a state observer which includes a disturbance dynamics whose state tracks the unknown disturbance to be rejected. Observers of this kind are commonly referred to as extended state observers. The novel contributions of the paper are the following. First, we derive a robust stability condition for the proposed control scheme, holding for all the nonlinearities that are bounded by an estimated maximum slope. Second, we compute bounds on the closed-loop bandwidth of the extended state predictor and of the state feedback. Third we propose a novel approach for designing observer and state feedback gains, which guarantee robust closed-loop stability. Fourth, we show that the designed control system yields, with a minimum control effort, the same control performance as a robust state feedback control, which on the contrary may require a larger command activity. A simulated multivariate case study is presented.
The problem of using approximate, reduced order, models for control systems design is investigated. Assuming that both plant and simplified model are driven by the same feedback controller, the plant output uncertainty range with respect to the output of the simplified model is analysed and expressed in terms of the given openloop modelling uncertainty and of the frequency-domain response of the designed cout.rollcr. The analysis met-hod is based on evaluation of Q suitable set of charactceist.ic functions on a standard Nyquist D contour. Therefore it leads to the formulation of addir.ioual requirements to be directly included in the set of specifications for tho control problem when it, is approached by means of frequency-domain design techniques. In the case where the control design is developed by using time-domain techniques, it is shown that tho well-known separation theorem may also allow treatment of the uncertainty reducibility problem in two stages.
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