比例–积分控制加广义预测控制算法及其应用

针对比例–积分(proportional-integral, PI)控制因不能预测未来输出而提前改变控制量使其用于光电稳定伺服系统时往往响应剧烈的问题,研究了光电稳定伺服系统的广义预测控制(generalized predictive control, GPC).首先通过证明受控自回归积分滑动平均(controlled auto-regressive integral moving-average, CARIMA)模型的直接递推预测与Diophantine方程预测等价,提出了预测较快的模型等价预测GPC算法,其预测复杂度比原GPC降低了一个阶次.其次通过对PI和GPC的特点进行分析,综合考虑两者的优缺点,提出了一种新型的基于PI增量和GPC增量加权的比例积分控制加广义预测控制(proportional-integral control plus generalized predictive control, PI+GPC)算法,实现了基于历史、当前和未来偏差计算控制量,并给出了算法设计流程和参数选取规则.最后通过仿真并在某光电稳定伺服平台上验证后得出, PI+GPC和PI相比稳定精度有所提高,且平稳性和快速性大为改善.

Proportional-integral control plus generalized predictive control algorithm and its application

The PI control of the photoelectric stabilized servo system tends to respond violently, for it cannot predict the future output of the controlled plant and change the control variable earlier. So generalized predictive control (GPC) of the photoelectric stabilized servo system is studied as well as the controlled auto-regressive integral moving-average (CARIMA) model prediction. The prediction by direct recursion of CARIMA model is proved mathematically equivalent to the prediction obtained by Diophantine equation, its prediction complexity is reduced by one order. And then the characteristics of PI and GPC are analyzed in the paper. Comprehensively considered the advantages and disadvantages of PI and GPC, an increment proportional-integral control plus generalized predictive control (PI+GPC) algorithm with its parameter selection rule is put forward. Based on the weighted sum of PI increment and GPC increment, it is realized that the control variable is calculated by historical, current and future deviations. When used on a photoelectric stabilized servo platform, PI+GPC get better steady precision than PI, and shows higher rapidity and stability.