The modulus optimum (MO) criterion can be used for analytical design of the PID controller for linear systems with dominant dead time. However, although the method usually gives fast and non-oscillating closed-loop responses, in the case of large dead time the stability margin gets reduced and even non-stable behavior can be observed. In this case a correction of the settings is needed to preserve the stability margin. We describe and compare two methods of design of the PID controller based on the MO criterion that for the stable first-order systems with dead time preserve the stability margin, trying to keep maximum of the performance of the original MO settings.
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Computer-based control applications, especially if they run under general-purpose opera\-ting systems, often exhibit variance of the scan period of processing inputs and outputs. Although this phenomenon is usually neglected when discrete control algorithms are used, it can cause worse performance of the control loop in comparison to theoretical case. In this paper we describe a modified discrete LQG control algorithm that takes disturbances of the scan period into account and partially compensates their effect. This modification concerns both the state estimation and generating the control output. We also show that such a controller can be implemented even on relatively simple hardware platforms if the system dynamics is time-invariant.
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The paper describes a way of determination of quadratic-optimal regulator for linear continuous and discrete systems with constraints. The method is based on direct numerical minimization of the quadratic criterion expressing the quality of control. Constant regulator matrix, independent on the starting state, is obtained as a result. Due to the constraints the optimal regulator however depends on initial state. Therefore, the problem formulation was modified by using an extended criterion of optimality that guarantees quality behavior for any initial state within a given set.
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