基于LMI的随动系统PID控制下的多指标相容性

Multi-objective consistency for servo system with PID controller based on LMI technique

针对PID控制下的随动系统,把PID调节器的设计问题转化为不完全状态反馈问题,以线性矩阵不等式(LM I)和双线性矩阵不等式(BM I)为工具,研究了系统PID控制可稳的判据,可稳时系统的最大衰减度,与给定稳态误差系数和稳态输出方差相容的最大衰减度,与给定稳态误差系数、控制器增益约束和稳态输出方差相容的最大衰减度。给出了求解与给定指标相容的衰减度的求解算法,并通过算例说明了文中算法的有效性。

For the PID controlled servo systems, the PID controller design was transformed to the partial state feedback problem, then by using linear matrix inequality （LMI） and bilinear matrix inequality （BMI）, a stabilization criterion of PID controller, maximum attenuation degree for the systems stabilized by PID, maximum degree consistent with the given steady-state output covariance, steady error coefficients, and controller gain constrains. The proposed algorithm for the solution of attenuation degree agreed with the given performance was presented and the validity of the algorithm was proved with the illustrated examples.