基于Tube-RMPC的受扰约束系统输出跟踪
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摘要
针对一类受持续有界扰动且具有多胞型表示的约束线性时变系统,当系统状态不可测且扰动边界未知时,给出了基于线性扩张状态观测器与输出反馈Tube鲁棒模型预测控制策略的最优输出跟踪控制器设计方法。该方法首先应用基于集员滤波的扩张状态观测器对系统状态、扰动及其边界进行联合在线估计;其次根据估计结果将输出跟踪问题转化为对虚拟平衡状态跟踪误差系统的鲁棒镇定问题;最后基于跟踪误差模型结合Tube可达集鲁棒模型预测控制策略,设计系统的最优鲁棒跟踪控制律,确保系统闭环输出鲁棒渐近跟踪期望轨迹。仿真结果表明所提控制算法可以很好地消除扰动设定边界与真实边界失配的影响,保证对期望输出的鲁棒跟踪,验证了其有效性。
With regard to a class of polytopic described constrained time-varying linear systems with persistent bounded disturbances, when the states and the disturbance boundary are not available for direct measurement, the linear extended state observer and output-feedback tube-based robust model predictive control(RMPC) techniques are used to design the optimal output tracking controller. Firstly, an augmented observer, constructed by set-membership filter(SMF), is used to estimate the system states, the disturbances and the boundaries in real time. Secondly, according to the estimated results, the original output tracking problem is transformed into an equivalent regulation problem designed for the error system of tracking the artificial steady state. Finally, based on the tracking error model, the tube-reachable set based RMPC control law for the real uncertain system is presented to ensure that the output of the obtained closed-loop system can asymptotically track the desired output. The simulation results demonstrate that the proposed control algorithm can eliminate the effect of mismatch between real disturbances and its set boundaries well and ensure the robust asymptotic tracking the desired output, which show the effectiveness of the proposed method.
With regard to a class of polytopic described constrained time-varying linear systems with persistent bounded disturbances, when the states and the disturbance boundary are not available for direct measurement, the linear extended state observer and output-feedback tube-based robust model predictive control(RMPC) techniques are used to design the optimal output tracking controller. Firstly, an augmented observer, constructed by set-membership filter(SMF), is used to estimate the system states, the disturbances and the boundaries in real time. Secondly, according to the estimated results, the original output tracking problem is transformed into an equivalent regulation problem designed for the error system of tracking the artificial steady state. Finally, based on the tracking error model, the tube-reachable set based RMPC control law for the real uncertain system is presented to ensure that the output of the obtained closed-loop system can asymptotically track the desired output. The simulation results demonstrate that the proposed control algorithm can eliminate the effect of mismatch between real disturbances and its set boundaries well and ensure the robust asymptotic tracking the desired output, which show the effectiveness of the proposed method.
引文
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[2]Lapierre L,Soetanto D.Nonlinear path-following control of an AUV[J].Ocean Engineering,2007,34(2):1734-1744.
[3]Lenain R,Thuilot B,Cariou C,Martinet P.Adaptive and predictive path tracking control for off-road mobile robots[J].European Journal of Control,2007,13(4):419-439.
[4]席裕庚,李德伟,林姝.模型预测控制-现状与挑战[J].自动化学报,2013,39(3):222-236.Xi Y G,Li D W,Lin S.Model predictive control-status and challenges[J].Acta Automatica Sinica,2013,39(3):222-236.
[5]Limón D,Alvarado I,Alamo T,et al.MPC for tracking piecewise constant references for constrained linear systems[J].Automatica,2008,44(9):2382-2387.
[6]Sang Q,Tao G.Adaptive control of piecewise linear systems:the state tracking case[J].IEEE Transactions on Automatic Control,2012,57(2):522-528.
[7]Ferramosca A,Limon D,González A H,et al.Robust MPC for tracking zone regions based on nominal predictions[J].Journal of Process Control,2012,22(10):1966-1974.
[8]Limon D,Alvarado I,Alamo T,Camacho E F.Robust tube-based on MPC for tracking of constrained linear system with additive disturbances[J].Journal of Process Control,2010,20(3):248-260.
[9]Gonzalez R,Fiacchini M,Guzman J L,et al.Robust tube-based predictive control for mobile robots in off-road conditions[J].Robotics and Autonomous Systems,2011,59(10):711-726.
[10]Baranyi P,Várkonyi-Kóczy A R.TP transformation based dynamic system modeling for nonlinear control[J].IEEE Transactions on Instrumentation and Measurment,2005,54(6):2191-2203.
[11]Chernousko F L.Ellipsoidal state estimation for dynamical systems[J].Nonlinear Analysis:Theory,Methods&Applications,2005,63(5):872-879.
[12]Guo B Z,Zhao Z.On the convergence of an extended state observer for nonlinear systems with uncertainty[J].Systems&Control Letters,2011,60(6):420-430.
[13]秦伟伟,马建军,郑志强,等.采用鲁棒容许集对有约束的不确定系统作鲁棒模型预测控制[J].控制理论与应用,2011,28(6):763-770.Qin W W,Ma J J,Zheng Z Q,et al.Robust model predictive control based on robust admissible set for constrained uncertain systems[J].Control Theory&Applications,2011,28(6):763-770.
[14]席裕庚,朱红林,李德伟.基于多面体不变集的离线鲁棒模型预测控制器综合[J].控制与决策,2009,24(2):302-307.Xi Y G,Zhu H L,Li D W.Synthesis off-line robust model predictive control based on polyhedron invariant set[J].Control and Decisions,2009,24(2):302-307.
[15]秦伟伟,郑志强,刘刚,等.高超声速飞行器的LPV鲁棒变增益控制[J].系统工程与电子技术,2011,6(31):1327-1331.Qin W W,Zheng Z Q,Liu G,et al.Robust variable gain control for hypersonic vehicles based on LPV[J].Systems Engineering and Electronics,2011,6(33):1327-1331.