On compensating long actuator delays in nonlinear control
On compensating long actuator delays in nonlinear control
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DOI：
10.1109/acc.2008.4586939
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发表时间：
2008-06
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通讯作者：
M. Krstić
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作者：
M. Krstić
我们感兴趣的是在没有执行器延迟的情况下全局稳定的有限逃逸开环不稳定对象，但在存在延迟的情况下需要重新设计控制器。最简单的是Z(t) = Z(t)2 + U(t - D)，其中D为任意长度的执行器延迟。对于该系统，我们提出了一种补偿延迟并实现反馈线性化的控制律（整个ODE+延迟无限维级联）。然而，即使实现了指数稳定性，结果也不是全局的，因为在反馈控制“到达”t = D之前，植物可以具有具有初始条件Z(0) ges 1/D的有限逃逸。我们证明了一个稳定性结果，其吸引区域本质上是Z(0) < 1/D，并且我们推导了系统范数Z(t)2 + Jt t -D U(theta)2dtheta的渐近稳定性界。
We are interested in finite-escape open-loop unstable plants that are globally stabilizable in the absence of actuator delay but require controller redesign in the presence of delay. The simplest such plant is Z(t) = Z(t)2 + U(t - D), where D is actuator delay of arbitrary length. For this system we present a control law that compensates the delay and achieves feedback linearization (of the entire ODE+delay infinite-dimensional cascade). However, even though exponential stability is achieved, the result is not global because the plant can have a finite escape with an initial condition Z(0) ges 1/D before the feedback control "reaches" it at t = D. We prove a stability result whose region of attraction is essentially Z(0) < 1/D and for which we derive an asymptotic stability bound in terms of the system norm Z(t)2 + Jt t -D U(thetas)2dthetas.