非线性板球系统的监督分层智能自适应控制算法研究
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摘要
板球系统(Ball and Plate System)是一个典型的多变量不确定非线性控制对象。已经成为控制理论的典型benchmark实验研究平台。针对非线性板球系统的模型不确定性、欠驱动、耦合等非线性特性，许多学者仅考虑非线性板球系统的简化模型设计控制算法。另外，基于操作者的大量实验调试及语言经验知识的智能控制算法能够应用于类似于板球系统的不确定系统，因而针对这类不确定非线性系统，智能控制算法与典型的非线性控制算法的结合具有极其有效性。
通常，影响板球系统运行性能的主要因素包括两方面，即环境与任务约束、小球运动速度。当根据环境与任务要求所确定的小球运动轨迹的曲率变化频繁或曲率较大，以及要求小球运动速度较高时，都将为控制提出更高的要求。因此，设计一种可以随时监督系统稳定性和状态变量变化的监督分层控制器具有重要意义。本文将控制器分成两层：上层为监督与优化层；下层是结合自适应规则和滑模理论、智能算法的优点设计的控制器。
主要研究内容包含几个方面：
1、针对忽略两个方向轴耦合与小球平板摩擦力的非线性板球系统，提出了两层控制器：将基本控制器设计成基于神经网络的比率、微分、积分控制器(PID)，作为底层控制器；将补助控制器设计成基于粒子群-差分进化(PSO-DE)算法的控制器作为上层控制器。此两层控制器利用PSO-DE算法研究了基于神经网络PID控制器加权因子在线学习机构的自适应控制器。由PID控制器的基本控制规则与人类经验，给出了神经网络PID的层数目、各层的神经元数目、每个神经元之间的连接方法，从且使得神经网络PID具有在线学习能力、记忆能力和对任何函数的近似能力。此外，非线性板球闭环系统，通过上层控制器的PSO-DE优化过程调整了神经网络PID (NN-PID)控制器的每个连接线加权值，保证了板球系统的稳定性与收敛性。本文提出的方法克服了反向传播算法(BP)的缺点（即，容易落在局部优化点），同时使得了控制器具有PID控制器的优点：简化机构、良好的动态性和稳定性。
2、针对小球在高速运动时非线性板球系统明显的不确定性和干扰变动等情况，提出了基于稳定性监督的监督分层模糊自适应直接型滑模控制器设计方法。基于Lyapunov稳定性理论与状态变量变化范围监督，此控制器采用模糊自适应规则的上层监督补助控制器设计方法，提出了以直接型滑模控制器为底层控制器的算法。本文将两个方向轴之间耦合项与摩擦力项等外部干扰相加，得到多种干扰项之和d(t)，并分别研究了两个轴的小球运动而将板球系统分解成四个子系统。同时，分别对每个子系统定义了滑模面，利用耦合系数将滑模面结合构建了直接型滑模控制器。构造了以滑模表面与滑模表面微分函数为模糊输入变量的模糊自适应规则，基于Lyapunov稳定性理论和状态变量变化范围监督策略，设计了调节滑模耦合系数的自适应规则，从而实现了板球系统的稳定控制并避免了复杂的计算。本文对所提出的控制方法进行了仿真实验验证。仿真结果表明，此方法能够较好地实现非线性不确定系统的镇定控制和轨迹跟踪问题。
3、针对不确定多变量非线性板球系统，提出了一种具有监督控制与自适应补偿功能的监督分层间接型模糊自适应控制算法。近几十年来，模糊自适应控制方法经常被应用于不确定SISO非线性系统，可对于实际工程中常见的多变量、控制矩阵不可逆的非线性系统却缺乏一定的适用性。在不确定非线性板球系统的运行过程中，当控制增益矩阵的行列式等于零的时刻，即控制矩阵不可逆的时刻，则球处在失控状态。因此，针对控制增益矩阵不可逆的多变量不确定系统，设计模糊自适应控制是有意义的。本文研究了能够克服上述难题的方法，通过与第五章相似的设计过程推导出了以上层的算法为监督分层模糊自适应控制算法和基于函数误差与状态变量误差的误差自适应补偿控制，底层控制器由间接型模糊控制律构成。该方法不要求控制对象的增益矩阵可逆性。因此，针对典型的不确定非线性MIMO系统即不确定非线性板球控制系统，在不要求控制增益矩阵可逆的条件下提出了一种具有监督控制项的间接模糊自适应控制方法。而且基于Lyapunov稳定性理论设计了自适应控制规则和自适应补偿控制律的参数，以能够保证闭环系统的稳定性和跟踪误差趋于零的小领域内的收敛性。
在板球系统实验平台BPVS-JLU-II上，上述的控制算法完成了板球系统的大范围变动镇定仿真实验和各种轨迹（圆形、方形和8字形等）跟踪控制仿真实验。
综上所述，本文针对不确定非线性板球系统，设计了监督分层智能自适应控制器，并且进行了深入的理论和实验研究，所设计的控制方案的有效性、可行性、稳定性和收敛性可以很好地保证。
The ball and plate system is a typical multivariable, uncertain and nonlinear controlobject. It has become a typical benchmark experimental research platform of control theory.In order to consider nonlinear characteristics such as underactuation and coupling, modeluncertainty, much attention have been paid to design control strategies based on a simplifiedmodel of the non-linear ball and plate system. In addition, intelligent control algorithmsbased on a large number of trial and error and language experiential knowledge can beapplied to uncertain systems such as the ball and plate system, therefore the combination ofintelligent control and nonlinear control approaches is extremely effective for the uncertainnonlinear systems.
In general, the main factors which affect the control performance of the BPS includetwo aspects: environment and task constraint, and the movement speed of the ball. Whenmotion trajectory of the ball which is determined by environment and task requirements hasa frequent curvature change or a big curvature, and a high movement speed of the ball isrequired, it has put forward higher demands for control system.
In this paper, the specific research content is as follows:
1. In the condition of the nonlinear ball and plate system to ignore the shaft coupling oftwo direction and the friction of small ball plate, the controller of two layers is proposed. Thebasic controller is composed of the ratio, differential and integral controller (PID) based onneural network as the underlayer controller. The complement controller is designed by thecontroller using the particle swarm-differential evolution (PSO-DE) algorithm as theupperlayer controller that is the adaptive controller for online learning structure of theweighted factor of PID neural network controller using the PSO-DE algorithm. From thebasic rules of PID controller and human experience, gave out the layer number of PID neuralnetwork, the number of neurons in each layer and the connection methods between eachneuron. Thus the PID neural network has the ability of online learning, remembering andapproximation for any function. Moreover, for closed-loop system of the nonlinear ball andplate, each connecting weighted value of PID neural network (PIDNN) controller is adjustedby the PSO-DE optimization process of the upperlayer controller, therefore the stability andconvergence of the ball and plate system was assured. The proposed approach overcame thepropagation algorithm (BP) disadvantage easy falling in local optimum, at the same time,make the controller has the advantages of PID controller: the simplification mechanism,good dynamic characteristics and stability.
2. The design method of the hierarchical supervisory direct adaptive fuzzy slidingmode controller based on the stability supervision is proposed for the uncertainty andinterference of the nonlinear ball and plate system when the small ball is moved with the high speed. Based on the Lyapunov stability theory and supervision of state variables, theupper supervision-complement controller was researched, and the underlying controlleralgorithm is proposed as a direct sliding mode controller. The external interference based onthe coupling between the two axis direction and the friction term etc is behaved as sum h(t)of a variety of disturbance terms, and ball movement of two axes is respectively studied. Andthe ball and plate system is decomposed into four subsystems, each subsystem definesrespectively the sliding surface, two sliding surfaces is combined to one sliding surface bythe coupling coefficient, thereby a direct fuzzy sliding mode controller is constituted. Thefuzzy adaptive rule was constructed by the fuzzy input variables: the sliding surface anddifferential function of the sliding mode surface. Based on Lyapunov stability theory and thesuroervition of state variables, the adaptive rule of the coupling coefficient of sliding modesurface is designed, so the stability control of the ball and plate system is achieved, and thecomplex calculation was avoided. The experiment result shows that this proposed controlmethod can realize better the stabilization control and trajectory tracking problems ofnonlinear uncertain systems.
3. For the strong coupling and the uncertain friction of the multivariable nonlinearsystem-ball and plate system, the hierarchical supervisory fuzzy adaptive indirect controlalgorithm which has the supervisory control and adaptive compensation function has beenproposed. In fact, in recent decades, the fuzzy adaptive control method is proposed for theuncertain SISO nonlinear system. But, in the practical engineering, a kind of commonsystems are all the multivariable nonlinear system are easy to encounter. Also, in manypractical engineering, control gain matrix is irreversible nonlinear. When the ball is movedon the laboratory plate, the moment that the control gain matrix determinant equal to zero isexist, exactly is appear the moment which the control matrix is irreversible, this time the balleasily exist in the out of control state. Therefore, for the multivariable uncertain systemswhich the control gain matrix is irreversible, the fuzzy adaptive controller design ismeaningful. In this paper, the method that can overcome the above problems is researched.Through as same design algorithm of previous chapter, the upperlayer controller is designedas the hierarchical supervisory fuzzy adaptive controller and the error adaptive compensationcontroller based on tracking function error and state variable error, and that the underlyingcontroller is composed of the indirect type fuzzy control law. This method does not requirethe invertibility of the control gain matrix of the objects. In this paper, for the typicaluncertain nonlinear MIMO system-uncertain nonlinear ball and plate control system, underthe condition that does not require the reversible control gain matrix, a kind of indirect fuzzyadaptive control method with the supervisory control term is proposed. The Adaptive controlrule and the adaptive compensation control law parameters is induced by Lyapunov stabilitytheory, so can guarantee the stability of the closed-loop system and the convergence of thetracking error to zero within a small territory.
On the ball and plate experimental platform BPVS-JLU-II, With the proposed controlalgorithm, completed stable simulation experiment of a wide change of variables and various trajectory tracking control simulation experiment (circular, square and curve eight, etc.) withthe proposed control algorithm.
In conclusion, in this paper, the hierarchical supervisory intelligent adaptive controllerfor the uncertain nonlinear ball and plate systems is designed, had in-depth theoretical andexperimental research. Through the simulation experiment research of the uncertainnonlinear ball and plate system BPVS JLU–II, the research results clearly show that theeffectiveness of the proposed control scheme, feasibility, stable and convergence.
通常，影响板球系统运行性能的主要因素包括两方面，即环境与任务约束、小球运动速度。当根据环境与任务要求所确定的小球运动轨迹的曲率变化频繁或曲率较大，以及要求小球运动速度较高时，都将为控制提出更高的要求。因此，设计一种可以随时监督系统稳定性和状态变量变化的监督分层控制器具有重要意义。本文将控制器分成两层：上层为监督与优化层；下层是结合自适应规则和滑模理论、智能算法的优点设计的控制器。
主要研究内容包含几个方面：
1、针对忽略两个方向轴耦合与小球平板摩擦力的非线性板球系统，提出了两层控制器：将基本控制器设计成基于神经网络的比率、微分、积分控制器(PID)，作为底层控制器；将补助控制器设计成基于粒子群-差分进化(PSO-DE)算法的控制器作为上层控制器。此两层控制器利用PSO-DE算法研究了基于神经网络PID控制器加权因子在线学习机构的自适应控制器。由PID控制器的基本控制规则与人类经验，给出了神经网络PID的层数目、各层的神经元数目、每个神经元之间的连接方法，从且使得神经网络PID具有在线学习能力、记忆能力和对任何函数的近似能力。此外，非线性板球闭环系统，通过上层控制器的PSO-DE优化过程调整了神经网络PID (NN-PID)控制器的每个连接线加权值，保证了板球系统的稳定性与收敛性。本文提出的方法克服了反向传播算法(BP)的缺点（即，容易落在局部优化点），同时使得了控制器具有PID控制器的优点：简化机构、良好的动态性和稳定性。
2、针对小球在高速运动时非线性板球系统明显的不确定性和干扰变动等情况，提出了基于稳定性监督的监督分层模糊自适应直接型滑模控制器设计方法。基于Lyapunov稳定性理论与状态变量变化范围监督，此控制器采用模糊自适应规则的上层监督补助控制器设计方法，提出了以直接型滑模控制器为底层控制器的算法。本文将两个方向轴之间耦合项与摩擦力项等外部干扰相加，得到多种干扰项之和d(t)，并分别研究了两个轴的小球运动而将板球系统分解成四个子系统。同时，分别对每个子系统定义了滑模面，利用耦合系数将滑模面结合构建了直接型滑模控制器。构造了以滑模表面与滑模表面微分函数为模糊输入变量的模糊自适应规则，基于Lyapunov稳定性理论和状态变量变化范围监督策略，设计了调节滑模耦合系数的自适应规则，从而实现了板球系统的稳定控制并避免了复杂的计算。本文对所提出的控制方法进行了仿真实验验证。仿真结果表明，此方法能够较好地实现非线性不确定系统的镇定控制和轨迹跟踪问题。
3、针对不确定多变量非线性板球系统，提出了一种具有监督控制与自适应补偿功能的监督分层间接型模糊自适应控制算法。近几十年来，模糊自适应控制方法经常被应用于不确定SISO非线性系统，可对于实际工程中常见的多变量、控制矩阵不可逆的非线性系统却缺乏一定的适用性。在不确定非线性板球系统的运行过程中，当控制增益矩阵的行列式等于零的时刻，即控制矩阵不可逆的时刻，则球处在失控状态。因此，针对控制增益矩阵不可逆的多变量不确定系统，设计模糊自适应控制是有意义的。本文研究了能够克服上述难题的方法，通过与第五章相似的设计过程推导出了以上层的算法为监督分层模糊自适应控制算法和基于函数误差与状态变量误差的误差自适应补偿控制，底层控制器由间接型模糊控制律构成。该方法不要求控制对象的增益矩阵可逆性。因此，针对典型的不确定非线性MIMO系统即不确定非线性板球控制系统，在不要求控制增益矩阵可逆的条件下提出了一种具有监督控制项的间接模糊自适应控制方法。而且基于Lyapunov稳定性理论设计了自适应控制规则和自适应补偿控制律的参数，以能够保证闭环系统的稳定性和跟踪误差趋于零的小领域内的收敛性。
在板球系统实验平台BPVS-JLU-II上，上述的控制算法完成了板球系统的大范围变动镇定仿真实验和各种轨迹（圆形、方形和8字形等）跟踪控制仿真实验。
综上所述，本文针对不确定非线性板球系统，设计了监督分层智能自适应控制器，并且进行了深入的理论和实验研究，所设计的控制方案的有效性、可行性、稳定性和收敛性可以很好地保证。
The ball and plate system is a typical multivariable, uncertain and nonlinear controlobject. It has become a typical benchmark experimental research platform of control theory.In order to consider nonlinear characteristics such as underactuation and coupling, modeluncertainty, much attention have been paid to design control strategies based on a simplifiedmodel of the non-linear ball and plate system. In addition, intelligent control algorithmsbased on a large number of trial and error and language experiential knowledge can beapplied to uncertain systems such as the ball and plate system, therefore the combination ofintelligent control and nonlinear control approaches is extremely effective for the uncertainnonlinear systems.
In general, the main factors which affect the control performance of the BPS includetwo aspects: environment and task constraint, and the movement speed of the ball. Whenmotion trajectory of the ball which is determined by environment and task requirements hasa frequent curvature change or a big curvature, and a high movement speed of the ball isrequired, it has put forward higher demands for control system.
In this paper, the specific research content is as follows:
1. In the condition of the nonlinear ball and plate system to ignore the shaft coupling oftwo direction and the friction of small ball plate, the controller of two layers is proposed. Thebasic controller is composed of the ratio, differential and integral controller (PID) based onneural network as the underlayer controller. The complement controller is designed by thecontroller using the particle swarm-differential evolution (PSO-DE) algorithm as theupperlayer controller that is the adaptive controller for online learning structure of theweighted factor of PID neural network controller using the PSO-DE algorithm. From thebasic rules of PID controller and human experience, gave out the layer number of PID neuralnetwork, the number of neurons in each layer and the connection methods between eachneuron. Thus the PID neural network has the ability of online learning, remembering andapproximation for any function. Moreover, for closed-loop system of the nonlinear ball andplate, each connecting weighted value of PID neural network (PIDNN) controller is adjustedby the PSO-DE optimization process of the upperlayer controller, therefore the stability andconvergence of the ball and plate system was assured. The proposed approach overcame thepropagation algorithm (BP) disadvantage easy falling in local optimum, at the same time,make the controller has the advantages of PID controller: the simplification mechanism,good dynamic characteristics and stability.
2. The design method of the hierarchical supervisory direct adaptive fuzzy slidingmode controller based on the stability supervision is proposed for the uncertainty andinterference of the nonlinear ball and plate system when the small ball is moved with the high speed. Based on the Lyapunov stability theory and supervision of state variables, theupper supervision-complement controller was researched, and the underlying controlleralgorithm is proposed as a direct sliding mode controller. The external interference based onthe coupling between the two axis direction and the friction term etc is behaved as sum h(t)of a variety of disturbance terms, and ball movement of two axes is respectively studied. Andthe ball and plate system is decomposed into four subsystems, each subsystem definesrespectively the sliding surface, two sliding surfaces is combined to one sliding surface bythe coupling coefficient, thereby a direct fuzzy sliding mode controller is constituted. Thefuzzy adaptive rule was constructed by the fuzzy input variables: the sliding surface anddifferential function of the sliding mode surface. Based on Lyapunov stability theory and thesuroervition of state variables, the adaptive rule of the coupling coefficient of sliding modesurface is designed, so the stability control of the ball and plate system is achieved, and thecomplex calculation was avoided. The experiment result shows that this proposed controlmethod can realize better the stabilization control and trajectory tracking problems ofnonlinear uncertain systems.
3. For the strong coupling and the uncertain friction of the multivariable nonlinearsystem-ball and plate system, the hierarchical supervisory fuzzy adaptive indirect controlalgorithm which has the supervisory control and adaptive compensation function has beenproposed. In fact, in recent decades, the fuzzy adaptive control method is proposed for theuncertain SISO nonlinear system. But, in the practical engineering, a kind of commonsystems are all the multivariable nonlinear system are easy to encounter. Also, in manypractical engineering, control gain matrix is irreversible nonlinear. When the ball is movedon the laboratory plate, the moment that the control gain matrix determinant equal to zero isexist, exactly is appear the moment which the control matrix is irreversible, this time the balleasily exist in the out of control state. Therefore, for the multivariable uncertain systemswhich the control gain matrix is irreversible, the fuzzy adaptive controller design ismeaningful. In this paper, the method that can overcome the above problems is researched.Through as same design algorithm of previous chapter, the upperlayer controller is designedas the hierarchical supervisory fuzzy adaptive controller and the error adaptive compensationcontroller based on tracking function error and state variable error, and that the underlyingcontroller is composed of the indirect type fuzzy control law. This method does not requirethe invertibility of the control gain matrix of the objects. In this paper, for the typicaluncertain nonlinear MIMO system-uncertain nonlinear ball and plate control system, underthe condition that does not require the reversible control gain matrix, a kind of indirect fuzzyadaptive control method with the supervisory control term is proposed. The Adaptive controlrule and the adaptive compensation control law parameters is induced by Lyapunov stabilitytheory, so can guarantee the stability of the closed-loop system and the convergence of thetracking error to zero within a small territory.
On the ball and plate experimental platform BPVS-JLU-II, With the proposed controlalgorithm, completed stable simulation experiment of a wide change of variables and various trajectory tracking control simulation experiment (circular, square and curve eight, etc.) withthe proposed control algorithm.
In conclusion, in this paper, the hierarchical supervisory intelligent adaptive controllerfor the uncertain nonlinear ball and plate systems is designed, had in-depth theoretical andexperimental research. Through the simulation experiment research of the uncertainnonlinear ball and plate system BPVS JLU–II, the research results clearly show that theeffectiveness of the proposed control scheme, feasibility, stable and convergence.
引文
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