迭代学习控制及其在故障诊断中的应用研究
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摘要
由于迭代学习控制无需被控系统的精确数学模型，只需要利用实际系统输出和期望输出产生的偏差信号，经过简单的迭代运算来修正不理想的控制信号，以实现在有限时间区间内对期望轨迹的完全跟踪，并且该算法在线计算量小，结构简单便于工程实现。因此迭代学习控制自被提出以来，一直是控制领域里的研究热点之一。为了使存在任意初态偏移的非线性系统能够有限时间区间内完全跟踪理想轨迹，并放宽收敛条件，加快算法的收敛速度，论文对迭代学习控制的初值问题和收敛速度问题进行了深入研究。同时，由于现代控制系统越来越复杂，增加了系统发生故障的可能性。因此，为了提高控制系统的安全性和可靠性，精确估计出系统发生的故障，以便更好地对系统进行容错控制，论文将迭代学习控制理论应用到系统的故障诊断中，分别对基于比例差分型迭代学习的连续系统故障诊断方法和基于离散迭代学习的离散系统故障诊断方法进行了深入研究。论文的主要工作如下：
1.首先分析了系统初值对D型和PD型迭代学习控制的影响，然后，为了放宽系统在任意初态条件下的收敛条件，提高算法的收敛速度，放松算法对初始状态函数的要求，分别研究了一类控制时滞和状态时滞非线性系统在任意初态偏移下的迭代学习控制问题，对系统的初始状态和输入同时采用迭代学习策略，并利用算子谱理论证明了算法的收敛性，给出了系统收敛的谱半径形式的充分条件。
2.为了加快算法的收敛速度和解决初态偏移问题，对带有初始状态学习的指数变增益迭代学习控制算法进行了研究，并基于算子理论严格证明了系统在任意初始状态下的收敛性，给出了系统收敛的谱半径形式的充分条件；为了在迭代学习控制律中回避误差的微分信号，同时又能使系统的收敛速度得到提高，增强其鲁棒性，提出了一种具有反馈信息的比例差分型迭代学习控制算法，并基于压缩映射方法严格证明了系统在λ-范数和Lebesgue-p范数意义下的收敛性，给出了算法收敛的充分条件。最后，基于几何分析方法，对迭代学习律采用输出向量空间的角度关系来调节，加快了离散时变系统的收敛速度。
3.将预测控制中的滚动优化思想和迭代学习控制原理应用到故障诊断中，针对连续系统提出了一种基于比例差分型迭代学习的故障诊断方法。通过引入的虚拟故障构建起故障估计器，并利用估计器输出和系统实际输出产生的残差信号以及迭代轴上相邻两次残差的差分信号，在选取的优化时域周期内对引入的虚拟故障进行逐次修正，使其随着迭代次数的增加逐渐逼近系统的实际故障，从而达到对故障估计的目的。并基于压缩映射方法对故障估计器的收敛性进行了证明，给出了算法收敛的充分条件。
4.结合滚动优化思想和迭代学习控制理论，将离散迭代学习策略应用到离散时变系统的故障诊断中，提出了一种基于离散迭代学习的故障诊断方法。利用引入的虚拟故障建立离散形式的故障估计器，并利用实际系统输出和估计器输出产生的残差信号，在优化时域内对引入的虚拟故障通过离散迭代学习算法来逐次调节，使其随着迭代次数的增加逐渐逼近系统的实际故障。并基于压缩映射方法，对算法在λ-范数度量意义下的收敛性进行证明，给出了算法的收敛条件。
Because the iterative learning control does not need precise mathematics modes but onlyneeds deviation signals generated by practical and desired outputs, it can realize the completetracking for desired trajectories in the finite time interval by simple iterative computation tocorrect non-ideal control signals. In addition, the iterative learning control has small onlinecomputation and simple structure, easy to be implemented in engineering. Therefore, since theiterative learning control is proposed, it has been one of the research focuses in the controlfield. In order to enable nonlinear systems with arbitrary initial state offsets to completelytrack ideal trajectories in the finite time intervals, relax the convergence conditions, andaccelerate the convergent speed of the algorithm, this paper makes a deep research on initialvalue question and convergent speed question of the iterative learning control. Meanwhile,increasingly complex modern control system increases the possibility of the system failure.Therefore, in order to improve safety and reliability of the control system and preciselyestimate the system failure for better fault-tolerant control for the system, this paper appliesthe iterative learning control theory to fault diagnosis of the system, and makes a deepresearch on continuous system fault diagnosis method based on the proportional differenceiterative learning and discrete system fault diagnosis method based on discrete iterativelearning, respectively:
1. This paper analyzes effects of the system initial value on the D-type and PD-typeiterative leaning control. In order to relax convergent condition of the system with arbitraryinitial state, improve the convergent speed of the algorithm, relax the requirements of thealgorithm for initial state function, this paper studies the iterative learning control question ofa class of control time-delay and state time-delay nonlinear systems with arbitrary initial stateoffsets. Meantime, the iterative leaning scheme is adopted for the initial state and input of thesystem. In addition, the convergence of the algorithm is proven by spectral theory of operator,and the sufficient convergent condition with the form of spectral radius is provided.
2. In order to accelerate the speed of convergence of the algorithm and solve the questionof the initial state offsets, this paper studies the iterative learning control algorithm with initialstate learning of exponentially variable gain, strictly proves the convergence of the systemwith arbitrary initial states, and provides the sufficient convergent condition with the form ofspectral radius. In order to avoid differential signals of errors in the iterative leaning controllaw, improve the convergent speed of the algorithm, and enhance its robustness, this paperpresents an iterative learning control algorithm with feedback proportional differences, strictly proves the system convergence under λ-norm and Lebesgue-p norm, and provides thesufficient convergent condition. In addition, this paper adjusts the iterative learning law fromthe angular relationship of the output vector space based on geometric analysis method, andaccelerates the speed of convergence of the discrete time-variant system.
3. This paper applies rolling optimization ideas of the predictive control and the iterativelearning control principle into fault diagnosis. Aiming at the continuous system, this paperpresents a kind of fault diagnosis based on proportional difference iterative learning. By usingthe introduced virtual fault to construct fault tracking estimator, this paper uses the residuals,generated by estimator output and the system practical output, and the difference-vale signalof the adjacent two residuals to gradually revise the introduced virtual faults, which can causethe virtual faults to close to the practical faults in systems, thereby reaching the aim of faultdetection for systems. This paper proves the convergence of the fault tracking estimator bycontraction mapping, and provides the sufficient condition of the convergence.
4. Combining rolling optimization ideas and the iterative learning control principle, thispaper proposes a kind of fault diagnosis based on discrete iterative learning. By using theintroduced virtual fault to construct discrete fault tracking estimator, this paper uses theresiduals generated by estimator output and the system practical output, and uses discreteiterative learning algorithm to gradually revise the introduced virtual faults in the optimizationtime intervals, causing the virtual faults to close to the practical faults in systems with theincrease of iterations. This paper proves the convergence under λ-norm by contractionmapping, and provides the sufficient condition of the convergence.
1.首先分析了系统初值对D型和PD型迭代学习控制的影响，然后，为了放宽系统在任意初态条件下的收敛条件，提高算法的收敛速度，放松算法对初始状态函数的要求，分别研究了一类控制时滞和状态时滞非线性系统在任意初态偏移下的迭代学习控制问题，对系统的初始状态和输入同时采用迭代学习策略，并利用算子谱理论证明了算法的收敛性，给出了系统收敛的谱半径形式的充分条件。
2.为了加快算法的收敛速度和解决初态偏移问题，对带有初始状态学习的指数变增益迭代学习控制算法进行了研究，并基于算子理论严格证明了系统在任意初始状态下的收敛性，给出了系统收敛的谱半径形式的充分条件；为了在迭代学习控制律中回避误差的微分信号，同时又能使系统的收敛速度得到提高，增强其鲁棒性，提出了一种具有反馈信息的比例差分型迭代学习控制算法，并基于压缩映射方法严格证明了系统在λ-范数和Lebesgue-p范数意义下的收敛性，给出了算法收敛的充分条件。最后，基于几何分析方法，对迭代学习律采用输出向量空间的角度关系来调节，加快了离散时变系统的收敛速度。
3.将预测控制中的滚动优化思想和迭代学习控制原理应用到故障诊断中，针对连续系统提出了一种基于比例差分型迭代学习的故障诊断方法。通过引入的虚拟故障构建起故障估计器，并利用估计器输出和系统实际输出产生的残差信号以及迭代轴上相邻两次残差的差分信号，在选取的优化时域周期内对引入的虚拟故障进行逐次修正，使其随着迭代次数的增加逐渐逼近系统的实际故障，从而达到对故障估计的目的。并基于压缩映射方法对故障估计器的收敛性进行了证明，给出了算法收敛的充分条件。
4.结合滚动优化思想和迭代学习控制理论，将离散迭代学习策略应用到离散时变系统的故障诊断中，提出了一种基于离散迭代学习的故障诊断方法。利用引入的虚拟故障建立离散形式的故障估计器，并利用实际系统输出和估计器输出产生的残差信号，在优化时域内对引入的虚拟故障通过离散迭代学习算法来逐次调节，使其随着迭代次数的增加逐渐逼近系统的实际故障。并基于压缩映射方法，对算法在λ-范数度量意义下的收敛性进行证明，给出了算法的收敛条件。
Because the iterative learning control does not need precise mathematics modes but onlyneeds deviation signals generated by practical and desired outputs, it can realize the completetracking for desired trajectories in the finite time interval by simple iterative computation tocorrect non-ideal control signals. In addition, the iterative learning control has small onlinecomputation and simple structure, easy to be implemented in engineering. Therefore, since theiterative learning control is proposed, it has been one of the research focuses in the controlfield. In order to enable nonlinear systems with arbitrary initial state offsets to completelytrack ideal trajectories in the finite time intervals, relax the convergence conditions, andaccelerate the convergent speed of the algorithm, this paper makes a deep research on initialvalue question and convergent speed question of the iterative learning control. Meanwhile,increasingly complex modern control system increases the possibility of the system failure.Therefore, in order to improve safety and reliability of the control system and preciselyestimate the system failure for better fault-tolerant control for the system, this paper appliesthe iterative learning control theory to fault diagnosis of the system, and makes a deepresearch on continuous system fault diagnosis method based on the proportional differenceiterative learning and discrete system fault diagnosis method based on discrete iterativelearning, respectively:
1. This paper analyzes effects of the system initial value on the D-type and PD-typeiterative leaning control. In order to relax convergent condition of the system with arbitraryinitial state, improve the convergent speed of the algorithm, relax the requirements of thealgorithm for initial state function, this paper studies the iterative learning control question ofa class of control time-delay and state time-delay nonlinear systems with arbitrary initial stateoffsets. Meantime, the iterative leaning scheme is adopted for the initial state and input of thesystem. In addition, the convergence of the algorithm is proven by spectral theory of operator,and the sufficient convergent condition with the form of spectral radius is provided.
2. In order to accelerate the speed of convergence of the algorithm and solve the questionof the initial state offsets, this paper studies the iterative learning control algorithm with initialstate learning of exponentially variable gain, strictly proves the convergence of the systemwith arbitrary initial states, and provides the sufficient convergent condition with the form ofspectral radius. In order to avoid differential signals of errors in the iterative leaning controllaw, improve the convergent speed of the algorithm, and enhance its robustness, this paperpresents an iterative learning control algorithm with feedback proportional differences, strictly proves the system convergence under λ-norm and Lebesgue-p norm, and provides thesufficient convergent condition. In addition, this paper adjusts the iterative learning law fromthe angular relationship of the output vector space based on geometric analysis method, andaccelerates the speed of convergence of the discrete time-variant system.
3. This paper applies rolling optimization ideas of the predictive control and the iterativelearning control principle into fault diagnosis. Aiming at the continuous system, this paperpresents a kind of fault diagnosis based on proportional difference iterative learning. By usingthe introduced virtual fault to construct fault tracking estimator, this paper uses the residuals,generated by estimator output and the system practical output, and the difference-vale signalof the adjacent two residuals to gradually revise the introduced virtual faults, which can causethe virtual faults to close to the practical faults in systems, thereby reaching the aim of faultdetection for systems. This paper proves the convergence of the fault tracking estimator bycontraction mapping, and provides the sufficient condition of the convergence.
4. Combining rolling optimization ideas and the iterative learning control principle, thispaper proposes a kind of fault diagnosis based on discrete iterative learning. By using theintroduced virtual fault to construct discrete fault tracking estimator, this paper uses theresiduals generated by estimator output and the system practical output, and uses discreteiterative learning algorithm to gradually revise the introduced virtual faults in the optimizationtime intervals, causing the virtual faults to close to the practical faults in systems with theincrease of iterations. This paper proves the convergence under λ-norm by contractionmapping, and provides the sufficient condition of the convergence.
引文
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