Integral control of linear systems with actuator nonlinearities: lower bounds for the maximal regulating gain
Integral control of linear systems with actuator nonlinearities: lower bounds for the maximal regulating gain
复制标题
具有执行器非线性的线性系统的积分控制：最大调节增益的下限
DOI：
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发表时间：
1999
影响因子：
6.8
通讯作者：
S. Townley
中科院分区：
文献类型：
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作者：
H. Logemann;E. Ryan;S. Townley
对于一类指数稳定的单输入单输出正则线性系统，当线性系统的稳态增益为正，正的积分器增益足够小，且线性系统的线性部分的稳态增益为零时，闭环控制器可以保证系统渐近跟踪恒定的参考信号。3）参考值在非常自然的意义上是可行的。在这里推导出了各种特殊情况下的最大调节增益的下界，包括系统的非超调阶跃响应和二阶系统的输入或输出中的时滞。下限给出的开环频率/阶跃响应数据和Lipschitz常数的非线性，因此很容易获得。
Closing the loop around an exponentially stable single-input/single-output regular linear system, subject to a globally Lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller, is known to ensure asymptotic tracking of constant reference signals, provided that: 1) the steady-state gain of the linear part of the plant is positive; 2) the positive integrator gain is sufficiently small; and 3) the reference value is feasible in a very natural sense. Here lower bounds are derived for the maximal regulating gain for various special cases including systems with nonovershooting step-response and second-order systems with a time-delay in the input or output. The lower bounds are given in terms of open-loop frequency/step response data and the Lipschitz constant of the nonlinearity, and are hence readily obtainable.