含间隙机械系统的混杂模型预测控制器

研究含间隙机械系统的混杂模型预测控制问题.首先,将含间隙机械系统的运行模式分为"间隙模式"和"接触模式".其次,建立了含间隙机械系统的混杂分段仿射 (PWA)模型.然后,利用模型预测控制 (MPC)的方法对约束PWA系统的最优控制进行求解,通过动态规划与多参数二次规划方法,得到了MPC的离线解.最后,通过将分段二次 (PWQ)Lyapunov函数的求解转换成半正定规划,找到了确保闭环控制稳定性的PWQ Lyaplanov函数.跟踪参考速度的实验结果表明,混杂模型预测控制器对含间隙机械系统的跟踪控制具有较好的效果,能够满足小采样时间系统的实时控制要求.

Hybrid model-predictive-control for mechanical system with backlash

The hybrid model-predictive-control for mechanical system with backlash is studied. The operation model of a mechanical system with backlash is distinguished into the "backlash mode" and the "contact mode", and a piecewise affine (PWA) model of the mechanical system with backlash is built. For controlling this constrained PWA system, the optimal control law is derived by using the model predictive control (MPC) method; the offline solution of which is obtained by using the dynamic programming and the multi-parametric quadratic programming method. Finally, a piecewise quadratic (PWQ) Lyapuno function for the stability of the closed-loop system is found by transforming its searching process to a semi-definite programming. Experiments in tracking a reference speed signal demonstrate that the hybrid MFC gives desirable performances for the mechanical system with backlash, satisfying the real-time control requirements for systems with small sampling time.