不确定系统的终端滑模变结构控制
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摘要
滑模变结构控制作为控制系统的一种综合方法,适用于线性系统、非线性系统、时变系统、不确定系统,是一种有效的鲁棒控制方法。滑模变结构控制中,通过选择滑模面,设计滑模控制器,使得系统到达滑模面后,在满足一定匹配条件下,系统在滑模面上的运动即滑动模态对参数摄动和外部扰动影响具有完全的鲁棒性或不变性,表现出比普通鲁棒控制更为优越的特性,正是这种独特的优点,使得滑模变结构在解决不确定系统的鲁棒控制中受到重视。
本文在掌握滑模变结构控制理论的国内外研究现状的基础上,深入研究了匹配或不匹配不确定系统终端滑模变结构控制,论文的主要工作如下：
研究不确定多变量线性系统的快速终端滑模控制。终端滑模是一种新型的非线性滑模面,具有比线性滑模更快的收敛速度和更高的稳态精度。线性滑模很容易应用到多变量线性系统的设计中,终端滑模适用于二阶系统,但不能简单地推广到多变量线性系统中。针对一类不确定多变量线性系统,应用全局快速终端滑模、指数型快速终端滑模和对数型快速终端滑模分别设计变结构鲁棒控制律,内容有：非线性终端滑模超曲面的构造、滑模面参数矩阵的选取、变结构控制算法,并证明系统状态在有限时间内收敛到终端滑模面上,随后系统滑模按相应的快速终端滑模规律运动,以较普通终端滑模更快的速度在有限时间内收敛到平衡点。
研究二阶不确定系统的非奇异终端滑模控制。将非奇异终端滑模控制方法应用到控制通道参数摄动的二阶不确定系统,导出了相应的滑模变结构控制律。进一步提出基于非奇异终端滑模的二阶不确定系统的模型跟踪变结构控制方案,并将其应用于BTT导弹滚转通道的自动驾驶仪设计。该方案除克服普通终端滑模控制的奇异问题外,还能够确保系统跟踪误差在有限时间内收敛至平衡点,有效改善控制精度。且控制算法简单,工程实现方便。仿真结果表明,应用该方案设计的BTT导弹滚动通道自动驾驶仪能够克服气动参数大范围摄动及外界干扰影响,具有良好的指令跟踪性能和较强的鲁棒性。
研究不确定多变量线性系统的积分非奇异终端滑模控制。提出一种新的状态变换矩阵,通过线性变换将不确定多变量线性系统分解为两个子系统：非匹配的内部稳定子系统和匹配的输入输出子系统,对输入输出子系统应用积分非奇异终端滑模设计变结构控制律,使该子系统的状态在有限时间内到达零点。而内部稳定子系统的状态则随之收敛到平衡点的某一有限临域内,达到全局一致最终有界稳定。积分滑模的使用可以削弱滑动模态的抖动,并减少系统的稳态误差。
研究不确定多变量线性系统的动态非奇异终端滑模控制。为了消除滑模控制固有的抖振问题,同时避免普通终端滑模的奇异性,针对不确定多变量线性系统,提出一种动态非奇异终端滑模控制方法。同积分非奇异终端滑模控制时采用的方‘法一样,也是通过一种新的状态转换将不确定多变量线性系统分解为两个子系统：非匹配的内部稳定子系统和匹配的输入输出子系统,对输入输出子系统应用动态非奇异终端滑模设计变结构控制律,使该子系统的状态在有限时间内到达零点。而内部稳定子系统的状态则随之收敛到平衡点的某一有限临域内,达到全局一致最终有界稳定。动态滑模的使用消除了滑动模态的抖动,平滑了控制输入。
As one kind of control system design approaches, variable structure control with sliding mode is a powerful method for robust control, which is suitable to linear systems, nonlinear systems, time-varying systems and uncertain systems. The sliding mode controller, which is designed by selecting sliding mode surface, can drive the system states to reach the sliding hypersurface. Under certain matching conditions, the movement of system on the sliding hypersurface, i.e. the sliding mode, is completely insensitive to parametric uncertainty and external disturbance, which exhibits more superior characteristics than ordinary conventional robust control. Owing to this special feature, sliding mode control is attractive in solving the robust control problems for uncertain systems.
After knowing well the development of variable structure control with sliding mode, variable structure control with terminal sliding mode for matched or unmatched uncertain systems is deeply studied. Main results are as follows.
Fast terminal sliding control for uncertain multivariable linear systems is studied. As a novel nonlinear sliding mode surface, compared with linear sliding mode, the terminal sliding mode possesses faster convergence speed and higher steady-state precision. Unlike linear sliding mode being easily applied to the design of multivariable linear systems, terminal sliding mode is suitable to second-order system, which can not be easily extended to multivariable linear systems. For a class of uncertain multivariable linear systems, by using global fast terminal sliding mode, exponential fast terminal sliding mode and logarithmic fast terminal sliding mode, the robust control laws are derived respectively. The content contains structure of nonlinear terminal sliding hypersurface, selection of its parameter matrix, and algorithm of variable structure control law. It is proved that the system state variables can be driven to reach the sliding hypersurface in finite time, then retain on the sliding hypersurface and converge to the equilibrium point with higher speed than ordinary fast terminal sliding mode in finite time according to the motion law of the corresponding fast terminal sliding mode law.
Nonsingular terminal sliding mode control for second-order uncertain system is studied. It is extended to the second-order uncertain system with parameter perturbation in control channel, and the corresponding sliding mode control law is gained. A model tracing variable structure control methodology based on nonsingular terminal mode for second-order uncertain systems is proposed. Using this method, BTT roll channel autopilot is designed. This method overcomes singular problem in ordinary terminal sliding mode control, and guarantees system tracking errors converge to equilibrium point in finite time. Simulation results prove the roll channel autopilot of BTT missile has fine instruction following performance and strong robustness.
An integral nonsingular terminal sliding mode control for uncertain multivariable linear systems is studied. A new state transformation matrix is presented. By using this transformation, uncertain multivariable linear system is decomposed into two subsystems:an unmatched stable internal subsystem and a matched input-output subsystem. Then, integral nonsingular terminal sliding mode control law is applied to the input-output subsystem so that this subsystem states converge to the equilibrium points in finite time. Meanwhile, the states of the internal stability subsystem converge to the neighborhood of the equilibrium points and guarantee global uniform ultimate bounded stability. Integral sliding mode reduces the chattering phenomenon and steady-state error.
A dynamic nonsingular terminal sliding mode control for uncertain linear multivariable systems is studied.In order to eliminate the inherent chattering problem in sliding mode control, and avoid the singularity in conventional terminal sliding mode control, a dynamic nonsingular terminal sliding mode control for uncertain linear multivariable systems is proposed. Just as the integral nonsingular terminal sliding mode control mentioned above, uncertain multivariable linear system is decomposed into two subsystems through a special transformation:an unmatched stable internal subsystem and a matched input-output subsystem. A nonsingular terminal sliding mode manifold is used for the input-output subsystem to design the control law. The states of this subsystem converge to the equilibrium points. Meanwhile, the states of the internal subsystem converge to the neighborhood of the equilibrium points. This realizes the global uniform ultimate bounded stability. Dynamic sliding mode can be used to eliminate the sliding mode chattering, and smooth control input.
本文在掌握滑模变结构控制理论的国内外研究现状的基础上,深入研究了匹配或不匹配不确定系统终端滑模变结构控制,论文的主要工作如下：
研究不确定多变量线性系统的快速终端滑模控制。终端滑模是一种新型的非线性滑模面,具有比线性滑模更快的收敛速度和更高的稳态精度。线性滑模很容易应用到多变量线性系统的设计中,终端滑模适用于二阶系统,但不能简单地推广到多变量线性系统中。针对一类不确定多变量线性系统,应用全局快速终端滑模、指数型快速终端滑模和对数型快速终端滑模分别设计变结构鲁棒控制律,内容有：非线性终端滑模超曲面的构造、滑模面参数矩阵的选取、变结构控制算法,并证明系统状态在有限时间内收敛到终端滑模面上,随后系统滑模按相应的快速终端滑模规律运动,以较普通终端滑模更快的速度在有限时间内收敛到平衡点。
研究二阶不确定系统的非奇异终端滑模控制。将非奇异终端滑模控制方法应用到控制通道参数摄动的二阶不确定系统,导出了相应的滑模变结构控制律。进一步提出基于非奇异终端滑模的二阶不确定系统的模型跟踪变结构控制方案,并将其应用于BTT导弹滚转通道的自动驾驶仪设计。该方案除克服普通终端滑模控制的奇异问题外,还能够确保系统跟踪误差在有限时间内收敛至平衡点,有效改善控制精度。且控制算法简单,工程实现方便。仿真结果表明,应用该方案设计的BTT导弹滚动通道自动驾驶仪能够克服气动参数大范围摄动及外界干扰影响,具有良好的指令跟踪性能和较强的鲁棒性。
研究不确定多变量线性系统的积分非奇异终端滑模控制。提出一种新的状态变换矩阵,通过线性变换将不确定多变量线性系统分解为两个子系统：非匹配的内部稳定子系统和匹配的输入输出子系统,对输入输出子系统应用积分非奇异终端滑模设计变结构控制律,使该子系统的状态在有限时间内到达零点。而内部稳定子系统的状态则随之收敛到平衡点的某一有限临域内,达到全局一致最终有界稳定。积分滑模的使用可以削弱滑动模态的抖动,并减少系统的稳态误差。
研究不确定多变量线性系统的动态非奇异终端滑模控制。为了消除滑模控制固有的抖振问题,同时避免普通终端滑模的奇异性,针对不确定多变量线性系统,提出一种动态非奇异终端滑模控制方法。同积分非奇异终端滑模控制时采用的方‘法一样,也是通过一种新的状态转换将不确定多变量线性系统分解为两个子系统：非匹配的内部稳定子系统和匹配的输入输出子系统,对输入输出子系统应用动态非奇异终端滑模设计变结构控制律,使该子系统的状态在有限时间内到达零点。而内部稳定子系统的状态则随之收敛到平衡点的某一有限临域内,达到全局一致最终有界稳定。动态滑模的使用消除了滑动模态的抖动,平滑了控制输入。
As one kind of control system design approaches, variable structure control with sliding mode is a powerful method for robust control, which is suitable to linear systems, nonlinear systems, time-varying systems and uncertain systems. The sliding mode controller, which is designed by selecting sliding mode surface, can drive the system states to reach the sliding hypersurface. Under certain matching conditions, the movement of system on the sliding hypersurface, i.e. the sliding mode, is completely insensitive to parametric uncertainty and external disturbance, which exhibits more superior characteristics than ordinary conventional robust control. Owing to this special feature, sliding mode control is attractive in solving the robust control problems for uncertain systems.
After knowing well the development of variable structure control with sliding mode, variable structure control with terminal sliding mode for matched or unmatched uncertain systems is deeply studied. Main results are as follows.
Fast terminal sliding control for uncertain multivariable linear systems is studied. As a novel nonlinear sliding mode surface, compared with linear sliding mode, the terminal sliding mode possesses faster convergence speed and higher steady-state precision. Unlike linear sliding mode being easily applied to the design of multivariable linear systems, terminal sliding mode is suitable to second-order system, which can not be easily extended to multivariable linear systems. For a class of uncertain multivariable linear systems, by using global fast terminal sliding mode, exponential fast terminal sliding mode and logarithmic fast terminal sliding mode, the robust control laws are derived respectively. The content contains structure of nonlinear terminal sliding hypersurface, selection of its parameter matrix, and algorithm of variable structure control law. It is proved that the system state variables can be driven to reach the sliding hypersurface in finite time, then retain on the sliding hypersurface and converge to the equilibrium point with higher speed than ordinary fast terminal sliding mode in finite time according to the motion law of the corresponding fast terminal sliding mode law.
Nonsingular terminal sliding mode control for second-order uncertain system is studied. It is extended to the second-order uncertain system with parameter perturbation in control channel, and the corresponding sliding mode control law is gained. A model tracing variable structure control methodology based on nonsingular terminal mode for second-order uncertain systems is proposed. Using this method, BTT roll channel autopilot is designed. This method overcomes singular problem in ordinary terminal sliding mode control, and guarantees system tracking errors converge to equilibrium point in finite time. Simulation results prove the roll channel autopilot of BTT missile has fine instruction following performance and strong robustness.
An integral nonsingular terminal sliding mode control for uncertain multivariable linear systems is studied. A new state transformation matrix is presented. By using this transformation, uncertain multivariable linear system is decomposed into two subsystems:an unmatched stable internal subsystem and a matched input-output subsystem. Then, integral nonsingular terminal sliding mode control law is applied to the input-output subsystem so that this subsystem states converge to the equilibrium points in finite time. Meanwhile, the states of the internal stability subsystem converge to the neighborhood of the equilibrium points and guarantee global uniform ultimate bounded stability. Integral sliding mode reduces the chattering phenomenon and steady-state error.
A dynamic nonsingular terminal sliding mode control for uncertain linear multivariable systems is studied.In order to eliminate the inherent chattering problem in sliding mode control, and avoid the singularity in conventional terminal sliding mode control, a dynamic nonsingular terminal sliding mode control for uncertain linear multivariable systems is proposed. Just as the integral nonsingular terminal sliding mode control mentioned above, uncertain multivariable linear system is decomposed into two subsystems through a special transformation:an unmatched stable internal subsystem and a matched input-output subsystem. A nonsingular terminal sliding mode manifold is used for the input-output subsystem to design the control law. The states of this subsystem converge to the equilibrium points. Meanwhile, the states of the internal subsystem converge to the neighborhood of the equilibrium points. This realizes the global uniform ultimate bounded stability. Dynamic sliding mode can be used to eliminate the sliding mode chattering, and smooth control input.
引文
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