基于先进辨识的控制策略研究及其应用
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摘要
在控制系统设计与分析中，建模、控制和状态估计构成了其三大重要组成部分。在经典控制理论中，由于涉及到的控制对象一般为单输入单输出系统，所以传递函数便成为描述控制对象运动规律最适用的模型之一。系统辨识的主要工作集中于发展基于最小二乘法、曲线拟合和极大似然估计等点估计理论的辨识算法。系统辨识作为控制理论中的重要组成部分，为控制设计提供模型基础，同时系统辨识理论可渗透于先进控制理论中，仅根据观测数据直接进行控制器设计。因此，本课题在系统辨识理论的基础上，从系统辨识的角度研究先进控制方法，针对精密伺服控制系统和无人机航迹规划，展开对系统辨识和先进控制理论在其中的应用研究。
针对精密伺服控制系统中的典型产品—转台，研究利用系统辨识的方法对转台控制系统中的三环传递函数进行辨识估计。在开环条件下转台速度环传递函数的递推辨识中，引入递推辨识奇异值分解算法，可获得较好的数值特性，能提高系统参数实时辨识的精度；对于输入和输出观测信号中都带有外界干扰的白噪声时，采用非线性可分离的最小二乘法可获得模型参数的一致性估计。而当输出观测噪声为有色噪声时，在辅助变量算法的基础上结合偏差补偿算法进行推广得到偏差补偿辅助变量辨识算法；对转台位置闭环系统的辨识，联合自回归滑动平均模型辨识的辅助变量法和用于状态空间模型的子空间辨识方法，得到闭环子空间最优辅助变量辨识法。
针对精密伺服控制中被控对象的数学模型未知时控制器的设计问题，研究一种模型参考自适应控制—基于数据驱动的虚拟参考反馈校正控制。该方法有效地解决闭环系统中未知对象模型下参数化控制器的设计，将控制器设计问题转化为参数辨识优化过程；针对闭环非线性系统中的控制器为一非线性函数，采用虚拟参考反馈校正控制的设计思想，根据此时控制器的输入输出观测数据构造一基于输出数据的线性仿射函数，通过最小化逼近误差，利用系统辨识的参数估计方法求取线性仿射函数中可调参数权值。研究虚拟参考反馈校正控制在转台位置环跟踪回路中的应用，由虚拟参考反馈校正控制得到的PID参数可使得PID控制系统的动态性能得到改进，具有跟踪不同频率信号的能力；针对转台中的非线性摩擦力矩，采用非线性函数的线性仿射函数逼近，便于控制之前的建模。
针对精密伺服控制对外部干扰的抑制问题，考虑闭环系统中对象模型存在不确定性因素，从系统辨识的角度研究内模控制中的内部模型参数的递推辨识，并对内模控制系统中的闭环试验信号进行设计；在考虑外部干扰作用下，引入内模H无穷控制达到抑制外部干扰的目的。根据对转台机理的分析，采用内模H无穷控制策略对其速率回路的校正器进行设计，表明该方法可用于同时对稳定系统和不稳定系统进行控制器设计，达到预先指定的控制性能指标。
针对滚动时域控制的优化目标函数中，需要使用到输出预测值的显式表达式。根据系统辨识中的子空间辨识理论，利用状态空间形式下过去和现在的输入输出数据构造将来时刻的输出预测值，为联合系统辨识和控制器设计，在子空间辨识的基础上，研究了一种新颖的滚动时域子空间预测控制。该控制方法可自动校正模型预测控制中的系统参数，克服了传统的线性二次高斯最优控制中繁琐的设计过程，且不依赖于任何控制器的先验信息。在考虑带有约束条件时，利用椭球优化算法来迭代地产生一系列体积逐渐减小的椭球序列，该序列最终能收敛到一个最优解，在算法的基础上推导了椭球优化算法达到收敛时所需要迭代次数的一个上界，可以用于颤振的主动抑制；从优化问题解存在的最优性角度考虑非线性系统的滚动时域控制，分别从有或无集合约束条件下，利用凸优化理论中的可分离定理推导出该优化问题是否存在全局最优解的充要条件。针对无人机航迹规划中的数学优化问题，使用滚动时域控制和椭球迭代算法进行求解最优控制输入序列。
上述研究内容的完成，既为解决各种先进控制问题提供了一种新的方法，又为实现精密伺服系统的控制和无人机航迹规划提供了一种结合系统辨识与先进控制方法的有效控制手段，有利于提高控制性能。
In control system design and analysis, model, control and state estimation are the three main bodies.And in the classical control theoty, because the considered control objects are always single inputsingle output systems, then the transfer function is the most suitable model to describe the controlobject’s law of motion. The main work of system identification is to develop some identificationalgorithms based on some point estimation theory such as least square algorithm, maximum likelihoodtechnique and curve fitting. The system identification theory is the main part in the whole controltheory, because it can provide the mdel for the control design. The most important is that the systemidentification theory can penetrate in the advanced control theory and directly design a controller basedon input-output measurement datas. Therefore, we consider three advanced control methods from thepoint of the system identification theory. For the precision servo control system and UAV’s pathplanning, researches on system identification and advanced control theory are carried out in this paper.
For the precision servo control system’s typical product such an turnplate, the three kinds of transferfunctions exist in turnplate systems are identified and estimated using system identification methods.When considered the recursive identification of the turnplate veloocity loop’s transfer function underopen loop condition, we introduce a realize form in the recursive identification methods based onsingular value decomposition. The proposed method can not only obtain good nunerical property butalso improve the precision in real time identify system parameters. When the observed input-outputdatas are all corrupted with the white noise, the nonlinear separable least square algorithm is adopted toobtain the consistent estimations about eh model parameters. When the output noise is modeled as thecoloured noise, we extend the biased compensated method and instrumental variable methos to get thebias compensaten insturmental variable method. When identified the turnplate’s position closed loop,we combine the instrumental variable method in ARMA identification and subspace identification instate space model to propose a new closed loop subspace optimal instrumental variable method.
For the problem of the controller designed about the unknown model in the precision servo controlsystem, we diccuss a model reference adaptive control-virtual reference feedback tuning controlVRFT only based on data deriven. This control design method can effectively solve how to design theparametric controller about the unknown object’s model in closed loop system. It regulates th problemof designing controller into a procedure of parameters optimization. As the controllere’s expression inthe nonlinear closed loop is a nonlinear function, by using the idea of the VRFT, we construct a linearaffine function of the output datas, based on the parameter estimation iterative method. Through mixmizing the approximation error, we can seek the adjunct weights in the linear affine function.When applied the VRFT into the turnplate position tracking loop, the dynamic property of the PIDcontroller which is given from the VRFT has been improved and the tracking loop has the ability oftracking different frequency signal. For the nonlinear friction moment, we can also model thenonlinear nonlinear friction moment as a linear affine function, so as to be benefit to control.
For the problem of how to suppress the external disturbance, we study the model parametersrecursive identification for inteernal model control, When considering some uncertainty factors of theobject model in the closed loop. The optimal closed loop input signal for the internal model control isalso designed. Under the effect of the external disturbance, we introduce a internal model H infinitycontrol to suppress the disturbance. After analysing the turnplate’s structure, the internal model Hinfinity control is applied to analyse the controller in the velocity loop. It shows that the method cannot only be used to design stable system and un stable system simulately but also attain the prescribedthe control performance index.
For the target function in the receeding horizon control, the explict expression of the outputpredictions are necessary. Then we construct the future output predictions based on the pastandcurrent input-output datas. A novel subspace predictive control based on subspace identification isdiscussed for joint system identification and control design. This combination enables automaticallytuning the parameters in model predictive control and avoids many steps in the LQG-controller design.It is independent of any controller prior information. When considered the constrain conditions, anellipsoid optimization algorithm is proposed to generate a sequence of ellipsoids with decreasingvolume. An upper bound on the maximum number of possible iterates steps is derived. It is used inthe flutter active control. The receeding horizon control of the nonlinear system is also discussed toconsider its optimization solution. We analyse this optimization problem from two aspects: setconstraint and no set constraint. Furthermore, we derive the necessary and sufficient condition ofwhether it has global optimization solution using separable theorem from convex theory. For themathematic optimization problem in UAV’s path planning, the optimal control input sequence is givenusing receeding horizon control and ellipsoid iterative optimization algorithm.
Acomplishment of above researches will supply a novel method for solving variety advancedcontrol problems, and supply an effective technique combined with system identification andadvanced control methods for precision servo control system and UAV’s path planning, which willimprove control performance.
针对精密伺服控制系统中的典型产品—转台，研究利用系统辨识的方法对转台控制系统中的三环传递函数进行辨识估计。在开环条件下转台速度环传递函数的递推辨识中，引入递推辨识奇异值分解算法，可获得较好的数值特性，能提高系统参数实时辨识的精度；对于输入和输出观测信号中都带有外界干扰的白噪声时，采用非线性可分离的最小二乘法可获得模型参数的一致性估计。而当输出观测噪声为有色噪声时，在辅助变量算法的基础上结合偏差补偿算法进行推广得到偏差补偿辅助变量辨识算法；对转台位置闭环系统的辨识，联合自回归滑动平均模型辨识的辅助变量法和用于状态空间模型的子空间辨识方法，得到闭环子空间最优辅助变量辨识法。
针对精密伺服控制中被控对象的数学模型未知时控制器的设计问题，研究一种模型参考自适应控制—基于数据驱动的虚拟参考反馈校正控制。该方法有效地解决闭环系统中未知对象模型下参数化控制器的设计，将控制器设计问题转化为参数辨识优化过程；针对闭环非线性系统中的控制器为一非线性函数，采用虚拟参考反馈校正控制的设计思想，根据此时控制器的输入输出观测数据构造一基于输出数据的线性仿射函数，通过最小化逼近误差，利用系统辨识的参数估计方法求取线性仿射函数中可调参数权值。研究虚拟参考反馈校正控制在转台位置环跟踪回路中的应用，由虚拟参考反馈校正控制得到的PID参数可使得PID控制系统的动态性能得到改进，具有跟踪不同频率信号的能力；针对转台中的非线性摩擦力矩，采用非线性函数的线性仿射函数逼近，便于控制之前的建模。
针对精密伺服控制对外部干扰的抑制问题，考虑闭环系统中对象模型存在不确定性因素，从系统辨识的角度研究内模控制中的内部模型参数的递推辨识，并对内模控制系统中的闭环试验信号进行设计；在考虑外部干扰作用下，引入内模H无穷控制达到抑制外部干扰的目的。根据对转台机理的分析，采用内模H无穷控制策略对其速率回路的校正器进行设计，表明该方法可用于同时对稳定系统和不稳定系统进行控制器设计，达到预先指定的控制性能指标。
针对滚动时域控制的优化目标函数中，需要使用到输出预测值的显式表达式。根据系统辨识中的子空间辨识理论，利用状态空间形式下过去和现在的输入输出数据构造将来时刻的输出预测值，为联合系统辨识和控制器设计，在子空间辨识的基础上，研究了一种新颖的滚动时域子空间预测控制。该控制方法可自动校正模型预测控制中的系统参数，克服了传统的线性二次高斯最优控制中繁琐的设计过程，且不依赖于任何控制器的先验信息。在考虑带有约束条件时，利用椭球优化算法来迭代地产生一系列体积逐渐减小的椭球序列，该序列最终能收敛到一个最优解，在算法的基础上推导了椭球优化算法达到收敛时所需要迭代次数的一个上界，可以用于颤振的主动抑制；从优化问题解存在的最优性角度考虑非线性系统的滚动时域控制，分别从有或无集合约束条件下，利用凸优化理论中的可分离定理推导出该优化问题是否存在全局最优解的充要条件。针对无人机航迹规划中的数学优化问题，使用滚动时域控制和椭球迭代算法进行求解最优控制输入序列。
上述研究内容的完成，既为解决各种先进控制问题提供了一种新的方法，又为实现精密伺服系统的控制和无人机航迹规划提供了一种结合系统辨识与先进控制方法的有效控制手段，有利于提高控制性能。
In control system design and analysis, model, control and state estimation are the three main bodies.And in the classical control theoty, because the considered control objects are always single inputsingle output systems, then the transfer function is the most suitable model to describe the controlobject’s law of motion. The main work of system identification is to develop some identificationalgorithms based on some point estimation theory such as least square algorithm, maximum likelihoodtechnique and curve fitting. The system identification theory is the main part in the whole controltheory, because it can provide the mdel for the control design. The most important is that the systemidentification theory can penetrate in the advanced control theory and directly design a controller basedon input-output measurement datas. Therefore, we consider three advanced control methods from thepoint of the system identification theory. For the precision servo control system and UAV’s pathplanning, researches on system identification and advanced control theory are carried out in this paper.
For the precision servo control system’s typical product such an turnplate, the three kinds of transferfunctions exist in turnplate systems are identified and estimated using system identification methods.When considered the recursive identification of the turnplate veloocity loop’s transfer function underopen loop condition, we introduce a realize form in the recursive identification methods based onsingular value decomposition. The proposed method can not only obtain good nunerical property butalso improve the precision in real time identify system parameters. When the observed input-outputdatas are all corrupted with the white noise, the nonlinear separable least square algorithm is adopted toobtain the consistent estimations about eh model parameters. When the output noise is modeled as thecoloured noise, we extend the biased compensated method and instrumental variable methos to get thebias compensaten insturmental variable method. When identified the turnplate’s position closed loop,we combine the instrumental variable method in ARMA identification and subspace identification instate space model to propose a new closed loop subspace optimal instrumental variable method.
For the problem of the controller designed about the unknown model in the precision servo controlsystem, we diccuss a model reference adaptive control-virtual reference feedback tuning controlVRFT only based on data deriven. This control design method can effectively solve how to design theparametric controller about the unknown object’s model in closed loop system. It regulates th problemof designing controller into a procedure of parameters optimization. As the controllere’s expression inthe nonlinear closed loop is a nonlinear function, by using the idea of the VRFT, we construct a linearaffine function of the output datas, based on the parameter estimation iterative method. Through mixmizing the approximation error, we can seek the adjunct weights in the linear affine function.When applied the VRFT into the turnplate position tracking loop, the dynamic property of the PIDcontroller which is given from the VRFT has been improved and the tracking loop has the ability oftracking different frequency signal. For the nonlinear friction moment, we can also model thenonlinear nonlinear friction moment as a linear affine function, so as to be benefit to control.
For the problem of how to suppress the external disturbance, we study the model parametersrecursive identification for inteernal model control, When considering some uncertainty factors of theobject model in the closed loop. The optimal closed loop input signal for the internal model control isalso designed. Under the effect of the external disturbance, we introduce a internal model H infinitycontrol to suppress the disturbance. After analysing the turnplate’s structure, the internal model Hinfinity control is applied to analyse the controller in the velocity loop. It shows that the method cannot only be used to design stable system and un stable system simulately but also attain the prescribedthe control performance index.
For the target function in the receeding horizon control, the explict expression of the outputpredictions are necessary. Then we construct the future output predictions based on the pastandcurrent input-output datas. A novel subspace predictive control based on subspace identification isdiscussed for joint system identification and control design. This combination enables automaticallytuning the parameters in model predictive control and avoids many steps in the LQG-controller design.It is independent of any controller prior information. When considered the constrain conditions, anellipsoid optimization algorithm is proposed to generate a sequence of ellipsoids with decreasingvolume. An upper bound on the maximum number of possible iterates steps is derived. It is used inthe flutter active control. The receeding horizon control of the nonlinear system is also discussed toconsider its optimization solution. We analyse this optimization problem from two aspects: setconstraint and no set constraint. Furthermore, we derive the necessary and sufficient condition ofwhether it has global optimization solution using separable theorem from convex theory. For themathematic optimization problem in UAV’s path planning, the optimal control input sequence is givenusing receeding horizon control and ellipsoid iterative optimization algorithm.
Acomplishment of above researches will supply a novel method for solving variety advancedcontrol problems, and supply an effective technique combined with system identification andadvanced control methods for precision servo control system and UAV’s path planning, which willimprove control performance.
引文
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