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Top2. Principle Of Optimal Design
The preconditions of autopilot optimization are that the rise time, overshoot, transient time and steady state error should satisfy the performance indexes (Wang, 2007; Wang, 2006; Shen, 2007). Therefore, we should ascertain the ranges of overshoot and steady state error by empirical values firstly. The optimization objective is minimizing the rise time. And then the optimization design could be regard as solve the optimization problem with multiple constraints and single target.
Suppose overshoot is a percent of steady state value, steady state error is ±b percent of steady state value, transient time is t1, simulation time is T, simulation step size is h, and steady state value is g. Then the sketch of system response with constraint conditions could be shown as Figure 1.
Constraints have been set in every simulation node of system response curve. As shown in Figure 1, there is one constraint in every simulation node from 0s to t1s, and the simulation value should lesser than the constraint value; there are two constraints in every simulation node from t1s to Ts, and the simulation value should between the constraint values. Therefore, the number of constraints is t1/h+2(T- t1) /h.
The simulation time, when the simulation value is rise to 80 percent of steady state value firstly, is defined as the rise time. This rise time is the optimization objective. Then we should find out the control parameters which have the minimum rise time and satisfy the constraint conditions. Thus, the optimal design of missile autopilot is translated to the optimal design of nonlinear system with multiple constraints.
Figure 1. Sketch of system response and constraints
Top3. Realization Of Optimal Design
There are many optimum design methods in modern control theory, such as LOG reaction control system optimum design method, 
synthetic optimum design method. But these methods are difficulty to calculate and realize. So the idea of exhaustion method in classical control theory has been considered in this paper, and one optimization method has been put forward for the design of missile autopilot.