摘要
模型预测控制自上世纪70年代问世以来,被认为是能够显式地处理约束的有效先进过程控制策略。在实际应用中,由于不可避免地存在外界扰动以及系统不确定性,鲁棒模型预测控制(RMPC)作为模型预测控制(MPC)的重要分支,近年来越来越受到各界的广泛关注。针对一个控制器如何使其闭环系统保持稳定性和具有满意的系统性能是现代预测控制综合理论的一个重要问题。
在鲁棒预测控制的研究领域中,分别以H_2和H∞为指标的鲁棒预测控制的稳定性和性能已得到了较好的解决,但对于同时能处理性能和扰动的混合H_2 /H∞指标的鲁棒预测控制,针对不同的系统,在系统性能、鲁棒性、可行域和在线计算量之间如何得到一个很好的权衡仍有待解决。本文以此为出发点,分别针对不同的系统,研究了混合H_2 /H∞指标的鲁棒预测控制,分析了闭环系统的性能、鲁棒性、可行域和在线计算量,得到了下列结果:
针对以往混合H_2 /H∞指标鲁棒预测控制设计不能确保递归可行性的问题,通过附加新的系统约束,使系统具有稳定性保证,并有较好的控制性能。进一步采用离线设计在线综合的策略,减少在线计算量。
针对多胞不确定系统和结构不确定系统,提出了混合H_2 /H∞多步鲁棒预测控制算法,该算法减少了设计反馈控制律的保守性,扩大了初始可行域,并获得了更好的系统性能。进一步采用了离线设计椭圆不变集,在线优化组合系数的方法,以降低在线计算量并获得更好的系统性能。其中针对结构不确定系统的混合H_2 /H∞鲁棒预测控制算法,引入输入状态稳定的方法证明其稳定性。
针对系统执行器饱和问题,本文针对原执行器饱和预测控制算法的不足,提出了新的算法,从而改进了系统性能。进一步为了满足多目标控制的需求,针对带有执行器饱和的不确定系统,考虑了执行器饱和的混合H_2 /H∞鲁棒预测保性能控制问题,提出了执行器饱和的混合H_2 /H∞的鲁棒预测控制算法。
针对时滞不确定系统的鲁棒预测控制问题,提出针对时滞系统的混合H_2 /H∞鲁棒预测控制算法,同时针对时滞问题的混合H_2 /H∞鲁棒预测控制进行了可行性分析。最后将时滞系统的混合H_2 /H∞鲁棒预测控制算法推广至不确定系统。
Model Predictive Control (MPC) has been developed since 1970s. It has been recognized as an efficient advanced process control strategy that can explicitly deal with various engineering constrains. Among them, Robust MPC (RMPC) has received particular attention when dealing with ubiquitous external disturbances and model uncertainties in practical applications. It is important to design controllers to stabilize the closed-loop system yet to achieve a satisfactory control performance in the MPC synthesis.
In RMPC research, the closed-loop stability and control performance of RMPC with H_2 or H∞performance index have been widely investigated. However, the design approach of employing mixed H_2 /H∞performance indices, which can handle closed-loop stability and conrol performance simultaneously, remains a fundamental question on how to design RMPC algorithms for different systems to tradeoff among system performance, robustness, initial feasible regions and online computational butden. This is also the key issue that this dissertation is focusing on. The detailed research topics are listed as follows:
To remedy the drawbacks of traditional MPC algorithm, we firstly apply mixed H_2 /H∞design method to ensure the recursive feasibility of RMPC problem. We propose a control design strategy to reduce the conservativeness of the single feedback control law as well as the online computational loads.
We study the synthesis methods to design RMPC for the systems with parameter and structural uncertainties. We introduce a multi-step control strategy to reduce the conservativeness and expand the initial feasible region and then analyze the recursive feasibilities. We further design an ellipsoid invariant set offline and later optimize a combination of coefficients online to mitigate the real time computational burden and achieve better performance. Meanwhile, we apply the method of input to state stability(ISS) to analyse the stabibility of closed-loop system with structural uncertainties.
We develop an RMPC design method to deal with actuator saturations and also to meet the requirements of multi-objective control. The closed-loop system performance and robustness have been carefully studied.
For the system with time delay, a RMPC synthesis method is proposed to use mixed H_2 /H∞design approach. We analyze its feasibility and then apply it to uncertain system.
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