【作者】 肖玲斐；

【导师】 苏宏业； 褚健；

【作者基本信息】 浙江大学 ， 控制科学与工程， 2008， 博士

【摘要】 滑模控制(SMC)理论从其出现至今已有半个多世纪的时间,然而其研究成果尚还主要集中在连续系统的分析与综合中。随着计算机技术的日益普及和数字控制器、执行器的广泛使用,对离散滑模控制理论与应用的研究越来越受到科研工作者和工程应用人员的关注。本论文针对传统SMC需要较大的控制力驱使状态到达滑模面、系统鲁棒性的强弱依赖于不确定项上界等不足,在离散滑模控制器的设计中引入预测控制(MPC)策略。以一般线性系统及几类典型的非线性系统为对象,考虑系统的镇定问题和跟踪问题,通过借用模型算法控制:和广义预测控制思想,构造不同的滑模预测模型(SMPM),采用合适的滑模参考轨迹,运用反馈校正和滚动优化技术,设计了适用于不同系统的预测滑模控制器。理论分析和仿真研究验证了预测滑模控制相比于传统滑模控制的优越性,直升机高度和水箱液位的预测滑模控制实验结果进一步说明了论文中所提方法的有效性和实用性。本论文的主要研究内容包括:1.针对由CARIMA(Controlled Auto-Regressive Integrated Moving Average)模型所描述的一类系统,提出了一种广义预测滑模控制算法。该算法的设计分四个部分:首先,在给出了期望滑模面之后,建立了一个基于系统伴随矩阵的SMPM,用以预测滑模的未来信息;其次,为了驱使SMPM的输出平滑地到达滑模面,设计了合适的滑模参考轨迹;再次,通过定义一个与SMPM输出相关的函数作为性能指标,并基于滚动优化,得到了增量形式的广义预测滑模控制律;最后,结合参数辨识方法,用以在线辨识CARIMA模型参数。由于基于CARIMA模型的广义预测控制算法能够方便地处理控制时滞,我们的算法也能方便地推广到控制时滞系统。2.针对一般离散线性系统,考虑给定运动轨迹的跟踪问题。为了对匹配和不匹配不确定项都具有强鲁棒性,且得到优化的控制量,把MPC结合到SMC中。借用全程滑模的观点,设计出新颖的SMPM;基于一阶惯性环节,构造了滑模参考轨迹,进而保证良好的趋近模态;使用反馈校正和滚动优化观点,系统的不确定项,无论其是否满足匹配条件,均能及时得到补偿;二次型指标中包含了控制量的惩罚项,可以协调滑模预测跟踪误差和控制输入对性能指标的影响;求解二次型指标得到了非切换型的滑模控制器,因而系统中不存在抖振;严格的理论分析证明了闭环系统的鲁棒稳定性。3.针对过程模型可分离为线性部分和非线性部分的系统,将非线性反馈通道沿着在预测时域内已知的某参考轨迹线性化,得到了系统的时变线性模型。为系统指定了合适的滑模面之后,根据所得时变线性系统的标称模型,设计出SMPM。通过反馈校正和滚动优化,得出了无约束情况下的系统优化控制解。理论分析证明闭环系统对有界变化律的匹配和不匹配不确定项具有强鲁棒性。数值仿真说明相比于传统高氏趋近律DSMC方法,所提算法使得闭环系统具有更强鲁棒性和更快的收敛速度,同时不存在抖振。当解存在时,所提方法适用于带约束系统。由于将系统非线性模型转换成了时变线性模型,系统的优化问题是一个二次规划问题,而不是非线性规划问题,因而大大减少了计算量。4.针对下三角规范型离散非线性系统,考虑SMC设计问题。在保证滑模面具有期望性能之后,通过为系统设计时变SMPM,利用反馈校正修正SMPM以实现对不确定项的及时补偿。使用滚动优化,我们得出了优化的预测滑模控制器。理论证明闭环系统具有鲁棒稳定性,不需要不确定项的上界已知,且在采样时间较小或系统不确定性和外部干扰变化较慢时,准滑模带宽可以很小。数值仿真表明,所提算法相比于传统高氏趋近律DSMC方法,闭环系统具有更强的鲁棒性,状态收敛更快,控制信号峰值更小以及不存在抖振。5.针对一类离散不确定非线性耦合系统,提出了预测滑模控制算法。受递归滑模思想的启发,设计了一种SMPM。考虑到模型失配问题,利用预测滑模输出值和实测滑模值之间的差值来对SMPM进行反馈校正,进而应用滚动优化,导出非切换型的滑模控制器。滑模的可达性通过迫使滑模预测值跟踪期望的滑模参考值来实现。由于滚动优化和反馈校正的引入,及时补偿了不确定项对系统的影响,从而保证了闭环系统具有强鲁棒性。鲁棒分析证明了即使当不确定性和外部干扰的界未知时,闭环系统也可以实现鲁棒稳定。数值和旋转倒立摆的仿真结果验证了所提算法的有效性。最后是全文的总结和展望。更多还原

【Abstract】 Half century has passed since the appearance of sliding mode control (SMC), however, most of the research results are about continuous-time systems. With the development of computers technology and the widespread of digital controllers/manipulators, the investigation of SMC for discrete-time systems becomes intensive among researchers and engineers. Considering the shortcomings of the conventional SMC, such as great control signal is required to drive system states arrive sliding mode surface, the robustness depends on the upper bound of uncertainties and so on, predictive control strategy is introduced into the design of SMC in this thesis. For general linear systems and some classes of nonlinear systems, focusing on the stabilization problem and tracking problem, using the principles of General Predictive Control (GPC) and Model Algorithmic Control (MAC), several sliding mode predictive models are constructed. By choosing different kinds of sliding mode reference trajectory, employing feedback correction and receding horizon optimization approaches, discrete-time sliding mode controllers which fit to corresponding systems, are obtained. Theoretical analysis and simulation results indicate the advantages of the presented predictive sliding mode control method over the conventional SMC methods. The height control of helicopter and the level control of tank experiments verify the practical efficiency of the proposed methods.The primary results of this thesis can be described as follows,1. For the systems described by Controlled Auto-Regressive Integrated Moving Average (CARIMA) model, the general predictive sliding mode control algorithm is proposed. The design of this algorithm is comprised of four stages: firstly, after giving the desired sliding surface, the sliding mode prediction model (SMPM) is created based on the adjoint matrix of the system, such that the future information of sliding mode can be used; secondly, in order to force the system states to sliding surface smoothly, a suitable sliding mode reference trajectory (SMRT) is designed; thirdly, by defining a performance index which is relatives to the output of SMPM, and then due to receding horizon optimization, the incremental general predictive sliding mode controller is obtained; fourthly, parameter identification is used to identify the parameters in CARIMA model. Because GPC can deal with control time-delay conveniently, our algorithm can be extended to control time-delay systems.2. For general discrete-time linear systems, the tracking problem for known motion is considered. In order to make systems have robustness to matched /unmatched uncertainties, and have optimal control signals, model predictive control (MPC) strategy is combined with SMC. Due to global sliding mode approach, a novel SMPM is constructed. Based on first-order process, SMRT is created, so to guarantee the desired reaching mode. Due to feedback correction and receding horizon optimization, the uncertainties can be compensated in time, no matter the uncertainties are satisfied matched condition or not. Quadratic form performance index which includes the control penalty term, can adjust the influence of sliding mode predictive error and control input in the index. Solving the index, the non-switching type discrete-time sliding mode controller is obtained, thus the chattering will not appear in the system. Rigor theoretic proof verifies the robust stability of the closed-loop systems.3. For a class of systems which can separate to linear component and nonlinear component, by linearizing the nonlinear feedback loop with respect to a known reference trajectory in prediction horizon , a linear time-vary (LTV) system model is gotten. After assigning a suitable sliding surface which can guarantee the stability of ideal sliding mode, according to the gotten LTV model, a time-vary SMPM is given. By feedback correction and receding horizon optimization, for the case of no constraint, the optimal control signal is obtained. In a numerical example, compared with conventional DSMC, the presented algorithm makes the closed-loop system possess stronger robustness and faster convergence, and no chattering. When the solution of the optimization problem exists, the proposed algorithm fits to systems with constraints. Because the nonlinear model is converted to time-vary linear model, the optimization problem is quadratic programming not nonlinear programming, the computational complexity is reduced.4. The SMC is constructed to deal with Brunowsky-like canonical form nonlinear systems. A sliding surface which possesses desired dynamic, is designed at first. By creating a time-vary SMPM, employing feedback correction to compensate the influence of uncertainties, and using receding horizon optimization, the optimal discrete-time sliding mode controller is obtained. Theoretical analysis shows the closed-loop systems is robust stable, the upper bounds of uncertainties are not required, and the quasi-sliding mode band is tiny when the sampling period is small or the uncertainties have slow change rates. Numerical results indicates the presented algorithm guarantees the closed-loop system has stronger robustness, faster convergence and lower peak value in control signal, compared with the conventional reaching law DSMC method.5. For a class of discrete-time coupled nonlinear uncertain systems, enlighten by recursive sliding mode approach, a special SMPM is presented. Considered model mismatching, the error between the output of SMPM and real switching function value is used to make feedback correction. Due to receding horizon optimization, non-switching type discrete-time sliding mode controller is obtained. Because of feedback correction and receding horizon optimization, the influence of uncertainties is compensated immediately, the closed-loop system possesses strong robustness to matched or unmatched uncertainties as a result. Theoretic analysis proofs that the closed-loop system is robust stable even though the upper bounds of uncertainties and external disturbances are unknown. The results of a numerical example and a two-link rotational inverted pendulum illustrate the efficiency of the presented algorithm.The conclusion and perspective are given at the end of the dissertation.更多还原