Research On Iterative Learning Control And Its Application On Fault Diagnosis

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.