基于Popov定理的输入非线性广义预测控制系统的稳定性分析

摘要

对存在输入饱和约束和输入可逆静态非线性的系统,采用两步法广义预测控制策略.首先用线性广义预测控制策略得到中间变量,代表期望的控制作用,然后用解方程方法补偿可逆静态非线性并用解饱和方法满足饱和约束,得到实际的控制作用.两步法计算简单,特别适用于快速控制的场合.将该控制系统闭环结构转化为静态非线性增益反馈结构,利用Popov定理分析了该系统的闭环稳定性,得到了稳定的充分条件,并具体给出了有效的控制器参数确定算法使得稳定性结论具备实用的价值.给出了算例验证了稳定条件.%For systems with input saturation constraint and invertible static input nonlinearity, a two step generalized predictive control (TSGPC) strategy is adopted. An intermediate variable representing the desired control action is obtained by applying linear GPC (LGPC), then the invertible static nonlinearity is compensated by solving nonlinear algebraic equation (NAE) and the input saturation constraint is satisfied by desaturation. TSGPC has low computational burden and is especially suitable for fast control application. The closed-loop block diagram of this system is turned into a static nonlinear feedback form, and Popov′s theorem is applied to the closed-loop stability analysis. The sufficient stability conditions are obtained. Effective algorithms for determining controller parameters are given to make the stability conclusions applicable and an example is given for illustration.