一类MISO对称非线性系统及其约束自校正控制器

A Class of MISO Symmetric Nonlinear Systems and Self-tuning Controllers

针对MISO随机广义Hammerstein模型,从实际工程对象的物理意义出发,分析了其不能描述"对称非线性系统"的问题。在模型中加入控制输入的符号函数,提出一可描述"对称非线性系统"的MISO随机广义Hammerstein模型。在目标函数中加入控制输入的高次项和其符号函数提出一超二次型目标函数。对控制输入加入饱和限幅,给出了改进的MISO随机广义Hammerstein模型的约束自校正控制器算法,适用于开环不稳定的"非最小相位"系统。提出一控制策略使算法无稳态偏差,且控制输入收敛于以原点为中心的变化域内。采用约束最优化的投影梯度法和无约束最优化的变尺度算法对目标函数寻优,证明了可行域内所有点均可作为投影梯度算法的初始可行点,并证明了线性不等式约束的任意紧约束组合时其可行域即为正则域。仿真研究表明了合理性和有效性。

Based on physical meaning of the practical objective,the problems of MISO Random Generalized Hammerstein Model（MISO RGHM）being not applied to the symmetric nonlinear systems were analyzed,and a modified MISO RGHM was developed by adding a symbolic function with control input into the model.A hyper-quadratic object function was put up by adding highest order control input term with a symbolic function into the object function,and an algorithm for the constrained self-tuning controller being suitable for the non-minimum phase systems with open-loop unstable characterization was established by forcing the control input with saturated limitation.The algorithm with one control policy can guarantee the simulative results without steady state deviation and the control input being converged to a varying region centered in the zero-point.Optimization results of the object function using the projection gradient algorithm for the constrained optimization and the variable metric algorithm for the un-constrained optimization are indicated that any point in the feasible region can be employed as the initial feasible point for the projection gradient algorithm and the feasible region consisted of any closely-constraints combination is a regular domain.Validation of the control algorithm is demonstrated by the simulated results.