Smith Predictor
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The Smith predictor (invented by Otto_J._M._Smith|O. J. M. Smith in 1957) is a type of predictive Controller_(control_theory)|controller for systems with pure time delay. The idea can be illustrated as follows.Suppose the plant consists of G(z) followed by a pure time delay z^{-k}. As a first step, suppose we only consider G(z) (the plant without a delay) and design a controller C(z) with a closed-loop transfer function H(z)=\frac{C(z) G(z)}{1+C(z)G(z)} that we consider satisfactory. Next, our objective is to design a controller \bar{C}(z) for the plant G(z) z^{-k} so that the closed loop transfer function \bar{H}(z) equals H(z) z^{-k}. Solving \frac{\bar{C} G z^{-k}}{1+\bar{C}G z^{-k}} = z^{-k} \frac{C G }{1 + C G}, we obtain\bar{C} = \frac{C}{1+CG(1-z^{-k})}. The controller is implemented as shown in the following figure, where G(z) has been changed to \hat{G}(z) to indicate that it is a model used by the controller. Note that there are two feedback loops. The outer control loop...
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