桥式吊车系统的伪谱最优控制设计

对于桥式吊车系统的最优控制问题,根据实际的工况要求,性能指标有时不一定是标准的二次形式.同时,在实际的控制问题中,状态和控制输入往往会受到一些边界条件和路径过程中的约束.针对这一问题,本文应用Chebyshev伪谱优化算法来处理,它可以处理状态和控制约束的非线性最优化问题以及一个非标准的目标函数.首先对桥式吊车系统模型进行一系列的坐标变换,将其转变为上三角系统形式的误差模型.然后将桥式吊车最优控制问题转化成具有一系列代数约束的参数优化问题,即非线性规划问题.通过求解离散化后的参数优化问题,得到桥式吊车的最优控制律.本文还给出了Chebyshev伪谱最优解的可行性和一致性分析.最后,在仿真研究中验证该控制器的有效性.

Optimal control design for an overhead crane system using pseudospectral method

In the optimal control for an overhead crane system, the performance index is not necessarily in a quadratic form. It depends on actual requirements of the application. In some cases, states and control are usually constrained due to boundary conditions and track conditions. To deal with this problem, we employ the Chebyshev pseudospectral algorithm to solve the nonlinear optimal control problem with states and/or control in constrain and the cost function in nonstandard quadratic form. Firstly, the model of the overhead crane system is transformed to an error model in upper triangular form. Next, the optimal control problem of the overhead crane system is transformed into a sequence of parametric optimization problems with algebraic constrains, i.e., a nonlinear programming problem. By solving the discretized optimization problems, we obtain the optimal control law for the overhead crane system. The feasibility and the uniformity of the Chebyshev pseudospectral optimal solution are also analyzed. Simulations are performed to show the effectiveness in applying the pseudospectral optimal design method to an overhead crane system.