一类非线性系统的逼近逆模型及趋近律控制

Integrated Control Method Based on Approximate Inverse Model and Tendency Rate for a Class of Nonlinear System

提出基于逼近逆模型及趋近律的综合控制方法来综合一类非线性系统的控制律。首先对与控制量没有显现关系的子系统，按二次型性能指标来设计逼近逆模型的拟控制律，然后，由拟控制律，构成滑动面，并按趋近律来综合控制律。最后，将其应用于飞行控制，作了仿真研究，验证其可行性，得到了满意的结果。

An integrated control method based on approximate inverse model and tendency rate for a class of nonlinear system is presented. In order to solve the tracking problem for a class of nonlinear system, many methods have been proposed, such as feedback linearizable , inverse model, predictive method . They depend on that the control number, m 1, is equal to the output number, m 2. But, in fact, there are many systems in which the control number is less then output number. In this paper, three different cases (m 1=m 2, m 1>m 2, and m 1<m 2) are discussed. When m 1=m 2 and m 1>m 2 the control rules are very easy to derive with our method (eq.6). When m 1<m 2, we use an index performance J , a quadratic function of predicted value H i , Which is a combination of tracking error, its derivative, and its integral. Let  J / Z =0, We get a new pseudo control rule given by eqs.(8) through (12). Then, we use the concept of tendency in VSC (variable structure control) to derive the control rule given by eq.(18). As in Ref., we use the flight control system problem given in Ref. as numerical example. New control results obtained with our method are shown in Figs.1.2 and 3. These new results are better than those in Ref..