一类对称非线性系统及其约束广义预测控制

摘要

针对随机广义Hammerstein模型的“不对称性”和控制问题,分析了其不能描述“对称非线性系统”的原因,在模型中加入控制输入的符号函数,提出可描述“对称非线性系统”的改进模型.对超二次型目标函数的不合理性,在其中加入控制输入的符号函数,提出一个合理的超二次型目标函数.从而给出约束广义预测控制算法,适用于开环不稳定的“非最小相位”系统.对一些控制算法有稳态偏差和控制输入不收敛于以原点为中心的变化域内的问题,采用目标函数形式的切换,提出了相应的控制策略.采用投影梯度算法和变尺度算法求解目标函数的最优解.仿真研究表明了上述研究的合理性和有效性.%The unsymmetrical and control problem of Generalized Hammerstein Model (GMM) which can not be applied to the symmetric nonlinear systems was analyzed in this paper, and a Modified Generalized Hammerstein Model (MGHM) was developed by adding a symbolic function with control input GMM. The reasonable object func-tion of hyper - quadratic forms was developed by adding a symbolic function with control input into an unreasonable hyper - quadratic form object function. So a constraint generalized predictive control algorithm applicable to the non - minimum phase systems with open - loop unstable characterization was developed. Using the transformation of the object function, one control policy was suggested, which can guarantee the simulative results without steady state deviation and the control input being converged to a variation region centered in the zero - point. The projection gradient algorithm and the variable metric algorithm were used for obtaining the optimal solution of the object function. Validation of the constraint generalized predictive control algorithm was proved by the simulated results.