约束不确定系统的误差有界无偏跟踪

Error-bounded and offset-free tracking for constrained uncertain systems

为使精密制造设备中定位机构实现在容许的误差带内对时变轨迹的精准无偏跟踪,针对约束不确定系统提出一种基于鲁棒控制不变(RCI)集的误差有界且无偏模型预测控制(EOMPC)方法.首先,为了消除由扰动引起的稳态误差,构建包含可测输出、估计状态和估计扰动的增广系统作为EOMPC的预测模型以提高预测精度;其次,基于增广系统和轨迹模型,使用可以在有限步内终止的迭代方法求解RCI集,并将其作为最优控制问题(OCP)中的状态约束以实现误差有界的跟踪;然后,为保障OCP的实时性,给出一种可在线执行的数值优化方案;最后,在磁悬浮定位系统上验证了所提出方法的有效性.

In order to achieve the precise and offset-free tracking of the positioning mechanism in precision manufacturing for the time-varying trajectories within the allowed error bound, an error-bounded and offset-free model predictive control(EOMPC), based on robust control invariant(RCI) sets, is proposed for constrained uncertain systems. Firstly, for the purpose of removing the steady-state errors caused by the disturbances, an augmented system that contains the system output, estimated state, and estimated disturbance, is constructed and used as the prediction model to improve the prediction accuracy. Then, on the basis of the augmented system and trajectory model, an iterative procedure that can be terminated in finite steps is presented to obtain the RCI set, which is used as the state constraints in an optimal control problem(OCP) to promise the error-bounded tracking. A numerical optimization scheme that can be executed online is then given for the real-time performance of the OCP. Finally, the effectiveness of the method is illustrated on the maglev positioning system.