This paper investigates the controllability and reachability of switched linear control systems. It is proven that both the controllable and reachable sets are subspaces of the total space. Complete geometric characterization for both sets is presented. The switching control design problem is also addressed.

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An enhanced automatic tuning procedure developed for process control of PI and PID controllers addresses several potential problems present in current standard autotuners. The proposed enhanced autotuner uses a novel technique based on relay feedback to estimate the process frequency response at two specified phase lags on the Nyquist curve automatically. An iterative procedure then uses these two points to obtain a transfer--function model of the process. Based on this model and a controller-selection scheme, an appropriate controller (PI or PID) is applied to the process automatically. The controller is tuned so that the Nyquist curve of the compensated system is appropriately shaped to satisfy a combined gain and phase-margin type of specGcation. The effectiveness of this enhanced autotuner is demonstrated both in simulations and in real-time experiments for level control of a coupled-tanks system. frequency can be identified. When the critical point, that is, the ultimate gain and frequency, is known, it is straightforward to apply the classic Ziegler-Nichols tuning rules (1943)

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SUMMARYIn this paper, robust adaptive control is presented for a class of perturbed strict-feedback nonlinear systems with both completely unknown control coefficients and parametric uncertainties. The proposed design method does not require the a priori knowledge of the signs of the unknown control coefficients. For the first time, the key technical Lemma is proven when the Nussbaum function is chosen by N ( ) = 2 cos( ), based on which the proposed robust adaptive scheme can guarantee the global uniform ultimate boundedness of the closed-loop system signals. Simulation results show the validity of the proposed scheme.

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