A Modified Iterative Learning Control Approach for the Active Suppression of Rotor Vibration Induced by Coupled Unbalance and Misalignment

This paper proposes a modified iterative learning control(MILC)periodical feedback-feedforward algorithm to reduce the vibration of a rotor caused by coupled unbalance and parallel misalignment.The control of the vibration of the rotor is provided by an active magnetic actuator(AMA).The iterative gain of the MILC algorithm here presented has a self-adjustment based on the magnitude of the vibration.Notch filters are adopted to extract the synchronous(1×Ω)and twice rotational frequency(2×Ω)components of the rotor vibration.Both the notch frequency of the filter and the size of feedforward storage used during the experiment have a real-time adaptation to the rotational speed.The method proposed in this work can provide effective suppression of the vibration of the rotor in case of sudden changes or fluctuations of the rotor speed.Simulations and experiments using the MILC algorithm proposed here are carried out and give evidence to the feasibility and robustness of the technique proposed.

Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.

Fault Estimation for a Class of Markov Jump Piecewise-Affine Systems: Current Feedback Based Iterative Learning Approach

In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating representation.Finally, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.

Fundamental Trackability Problems for Iterative Learning Control

Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.

Iterative Learning Controller Design for CNC Machine Tools

The repetitive processing and large quantity of single product represented by 3C products are urgently needed.However,for current processing operations,previous processing data have not been used in the optimization of control input.In order to utilize previous processing data to facilitate the next process and avoid adverse effects caused by repetitive disturbance and noise,the idea of iterative learning was introduced to improve the accuracy of machining.On the control level,since it is difficult to obtain high accuracy by traditional feedback control when faced with complex trajectories,an open⁃loop iterative learning controller and a position loop feedback controller were introduced,which worked fast with good convergence effects.Aiming at reducing the influence of accidental error,step type iterative learning was put forward.The iteration mechanism was stopped when the accuracy converged to the allowable range so as to reduce computational complexity,store the current iterative part of the control input,and make constant value compensation.However,in simulation and experiment,it was found that after superposition of the iterative learning controller,the phenomenon of partial divergence of the system tracking error occurred.Therefore,the speed and acceleration characteristics of input trajectories in time domain and frequency domain were analyzed.High⁃frequency noise was introduced in frequency domain,which was found to be the cause of the abovementioned phenomenon,and high⁃frequency components were filtered to solve the problem.To further improve the accuracy of convergence and avoid filtering effective high⁃frequency information in some area,a switchable filter based on the analysis of the frequency characteristics of input trajectory was proposed.Through SIMULINK simulation and dSPACE experimental verification,it was proved that the iterative learning controller of modifying controlled quantity and filter based iterative learning control method are effective.

Iterative Learning Control for Discrete-time Stochastic Systems with Quantized Information

An iterative learning control(ILC) algorithm using quantized error information is given in this paper for both linear and nonlinear discrete-time systems with stochastic noises. A logarithmic quantizer is used to guarantee an adaptive improvement in tracking performance. A decreasing learning gain is introduced into the algorithm to suppress the effects of stochastic noises and quantization errors. The input sequence is proved to converge strictly to the optimal input under the given index. Illustrative simulations are given to verify the theoretical analysis.

A PD-Type State-Dependent Riccati Equation With Iterative Learning Augmentation for Mechanical Systems

This work proposes a novel proportional-derivative(PD)-type state-dependent Riccati equation(SDRE)approach with iterative learning control(ILC)augmentation.On the one hand,the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers.On the other hand,the SDRE adds nonlinear and optimality characteristics to the controller,i.e.,increasing the stability margins.These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning.The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain K(x)for the control input law u=–R–1(x)BT(x)K(x)x.The sub-blocks of the overall gain R–1(x)BT(x)K(x),are not necessarily symmetric positive definite.A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as u=–KSP(x)e–KSD(x)?.The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems;and presents guaranteed uniform boundedness in finite-time between learning loops.The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation(SDDRE)to manipulate the final time.The SDDRE expresses a differential equation with a final boundary condition,which imposes a constraint on time that could be used for finitetime control.So,the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool.The learning rules benefit from the gradient descent method for both regulation and tracking cases.One of the advantages of this approach is a guaranteed-stability even from the first loop of learning.A mechanical manipulator,as an illustrative example,was simulated for both regulation and tracking problems.Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark.

Iterative Learning Disturbance Observer Based Attitude Stabilization of Flexible Spacecraft Subject to Complex Disturbances and Measurement Noises

To realize high-precision attitude stabilization of a flexible spacecraft in the presence of complex disturbances and measurement noises,an iterative learning disturbance observer(ILDO)is presented in this paper.Firstly,a dynamic model of disturbance is built by augmenting the integral of the lumped disturbance as a state.Based on it,ILDO is designed by introducing iterative learning structures.Then,comparative analyses of ILDO and traditional disturbance observers are carried out in frequency domain.It demonstrates that ILDO combines the advantages of high accuracy in disturbance estimation and favorable robustness to measurement noise.After that,an ILDO based composite controller is designed to stabilize the spacecraft attitude.Finally,the effectiveness of the proposed control scheme is verified by simulations.

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Iterative learning-based many-objective history matching using deep neural network with stacked autoencoder

This paper presents an innovative data-integration that uses an iterative-learning method,a deep neural network(DNN)coupled with a stacked autoencoder(SAE)to solve issues encountered with many-objective history matching.The proposed method consists of a DNN-based inverse model with SAE-encoded static data and iterative updates of supervised-learning data are based on distance-based clustering schemes.DNN functions as an inverse model and results in encoded flattened data,while SAE,as a pre-trained neural network,successfully reduces dimensionality and reliably reconstructs geomodels.The iterative-learning method can improve the training data for DNN by showing the error reduction achieved with each iteration step.The proposed workflow shows the small mean absolute percentage error below 4%for all objective functions,while a typical multi-objective evolutionary algorithm fails to significantly reduce the initial population uncertainty.Iterative learning-based manyobjective history matching estimates the trends in water cuts that are not reliably included in dynamicdata matching.This confirms the proposed workflow constructs more plausible geo-models.The workflow would be a reliable alternative to overcome the less-convergent Pareto-based multi-objective evolutionary algorithm in the presence of geological uncertainty and varying objective functions.

Iterative Learning Fault Diagnosis Algorithm for Non-uniform Sampling Hybrid System

For a class of non-uniform output sampling hybrid system with actuator faults and bounded disturbances,an iterative learning fault diagnosis algorithm is proposed.Firstly,in order to measure the impact of fault on system between every consecutive output sampling instants,the actual fault function is transformed to obtain an equivalent fault model by using the integral mean value theorem,then the non-uniform sampling hybrid system is converted to continuous systems with timevarying delay based on the output delay method.Afterwards,an observer-based fault diagnosis filter with virtual fault is designed to estimate the equivalent fault,and the iterative learning regulation algorithm is chosen to update the virtual fault repeatedly to make it approximate the actual equivalent fault after some iterative learning trials,so the algorithm can detect and estimate the system faults adaptively.Simulation results of an electro-mechanical control system model with different types of faults illustrate the feasibility and effectiveness of this algorithm.

An Iterative Learning Approach to Identify Fractional Order KiBaM Model

This paper discusses the parameter and differentiation order identification of continuous fractional order Ki Ba M models in ARX(autoregressive model with exogenous inputs)and OE(output error model) forms. The least squares method is applied to the identification of nonlinear and linear parameters,in which the Grunwald-Letnikov definition and short memory principle are applied to compute the fractional order derivatives.An adaptive P-type order learning law is proposed to estimate the differentiation order iteratively and accurately. Particularly,a unique estimation result and a fast convergence speed can be arrived by using the small gain strategy, which is unidirectional and has certain advantages than some state-of-art methods. The proposed strategy can be successfully applied to the nonlinear systems with quasi-linear characteristics. The numerical simulations are shown to validate the concepts.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.

Combined disturbance-observer-based control and iterative learning control design for pulsed superconducting radio frequency cavities

The development of iterative learning control combined with disturbance-observer-based(DOB)control for the digital low-level radio frequency(LLRF)system of the International Linear Collider project is presented.The objective of this study is to compensate for both repetitive(or predictable)and unpredictable disturbances in a radio frequency system(e.g.,beam loading,Lorentz force detuning,and microphonics).The DOB control approach was verified using the LLRF system at the Superconducting Test Facility(STF)at KEK in the absence of a beam.The method comprising DOB control combined with an iterative learning control algorithm was then demonstrated in a cavity-simulator-based test bench,where a simulated beam was available.The results showed that the performance of the LLRF system was improved,as expected by this combined control approach.We plan to further generalize this approach to LLRF systems at the STF and the future International Linear Collider project.

Load Disturbance Conditions for Current Error Feedback and Past Error Feedforward State-Feedback Iterative Learning Control

Iterative learning control is a controlling tool developed to overcome periodic disturbances acting on repetitive systems. State-feedback ILC controller was designed based on the use of the small gain theorem. Stability conditions were reported in the case of past error and current error feedback schemes based on Singular values. Disturbances acting on the load of the system were reported for the case of past error feedforward only which kept the investigation of the current error feedback as an open question. This paper develops a comparison between the past error feedforward and current error feedback schemes disturbance conditions in singular values. As a result, the conditions found highly support the use of the past error over the current error feedback.

Robust Iterative Learning Controller for the Non-zero Initial Error Problem on Robot Manipulator

Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, have been used to control this kind of system, but there are some deficiencie s in those methods: some need accurate and some need complicated operation and e tc. In recent years, in need of controlling the industrial robots, aiming at com pletely tracking the ideal input for the controlled subject with repetitive character, a new research area, ILC (iterative learning control), has been devel oped in the control technology and theory. The iterative learning control method can make the controlled subject operate as desired in a definite time span, merely making use of the prior control experie nce of the system and searching for the desired control signal according to the practical and desired output signal. The process of searching is equal to that o f learning, during which we only need to measure the output signal to amend the control signal, not like the adaptive control strategy, which on line assesses t he complex parameters of the system. Besides, since the iterative learning contr ol relies little on the prior message of the subject, it has been well used in a lot of areas, especially the dynamic systems with strong non-linear coupling a nd high repetitive position precision and the control system with batch producti on. Since robot manipulator has the above-mentioned character, ILC can be very well used in robot manipulator. In the ILC, since the operation always begins with a certain initial state, init ial condition has been required in almost all convergence verification. Therefor e, in designing the controller, the initial state has to be restricted with some condition to guarantee the convergence of the algorithm. The settle of initial condition problem has long been pursued in the ILC. There are commonly two kinds of initial condition problems: one is zero initial error problem, another is non-zero initial error problem. In practice, the repe titive operation will invariably produce excursion of the iterative initial stat e from the desired initial state. As a result, the research on the second in itial problem has more practical meaning. In this paper, for the non-zero initial error problem, one novel robust ILC alg orithms, respectively combining PD type iterative learning control algorithm wit h the robust feedback control algorithm, has been presented. This novel robust ILC algorithm contain two parts: feedforward ILC algorithm and robust feedback algorithm, which can be used to restrain disturbance from param eter variation, mechanical nonlinearities and unmodeled dynamics and to achieve good performance as well. The feedforward ILC algorithm can be used to improve the tracking error and perf ormance of the system through iteratively learning from the previous operation, thus performing the tracking task very fast. The robust feedback algorithm could mainly be applied to make the real output of the system not deviate too much fr om the desired tracking trajectory, and guarantee the system’s robustness w hen there are exterior noises and variations of the system parameter. In this paper, in order to analyze the convergence of the algorithm, Lyapunov st ability theory has been used through properly selecting the Lyapunov function. T he result of the verification shows the feasibility of the novel robust iterativ e learning control in theory. Finally, aiming at the two-freedom rate robot, simulation has been made with th e MATLAB software. Furthermore, two groups of parameters are selected to validat e the robustness of the algorithm.

Arranging transient process used in iterative learning control system

Considering the same initial state error in each repetitive operation in the iterative learning system, a method of arranging the transient process is given. During the current iteration, the system will track the transient function firstly, and then the expected trajectory. After several iterations, the learning system output will trend to the arranged curve, which has avoided the effect of the initial error on the controller. Also the transient time can be changed as you need, which makes the designing simple and the operation easy. Then the detailed designing steps are given via the robot system. At last the simulation of the robot system is given, which shows the validity of the method.

Open-loop and closed-loop D^(α)-type iterative learning control for fractional-order linear multi-agent systems with state-delays

This study focuses on implementing consensus tracking using both open-loop and closed-loop Dα-type iterative learning control(ILC)schemes,for fractional-order multi-agent systems(FOMASs)with state-delays.The desired trajectory is constructed by introducing a virtual leader,and the fixed communication topology is considered and only a subset of followers can access the desired trajectory.For each control scheme,one controller is designed for one agent individually.According to the tracking error between the agent and the virtual leader,and the tracking errors between the agent and neighboring agents during the last iteration(for open-loop scheme)or the current running(for closed-loop scheme),each controller continuously corrects the last control law by a combination of communication weights in the topology to obtain the ideal control law.Through the rigorous analysis,sufficient conditions for both control schemes are established to ensure that all agents can achieve the asymptotically consistent output along the iteration axis within a finite-time interval.Sufficient numerical simulation results demonstrate the effectiveness of the control schemes,and provide some meaningful comparison results.

Accelerated Iterative Learning Control for Linear Discrete Systems with Parametric Perturbation and Measurement Noise

An iterative learning control algorithm based on error backward association and control parameter correction has been proposed for a class of linear discrete time-invariant systems with repeated operation characteristics,parameter disturbance,and measurement noise taking PD type example.Firstly,the concrete form of the accelerated learning law is presented,based on the detailed description of how the control factor is obtained in the algorithm.Secondly,with the help of the vector method,the convergence of the algorithm for the strict mathematical proof,combined with the theory of spectral radius,sufficient conditions for the convergence of the algorithm is presented for parameter determination and no noise,parameter uncertainty but excluding measurement noise,parameters uncertainty and with measurement noise,and the measurement noise of four types of scenarios respectively.Finally,the theoretical results show that the convergence rate mainly depends on the size of the controlled object,the learning parameters of the control law,the correction coefficient,the association factor and the learning interval.Simulation results show that the proposed algorithm has a faster convergence rate than the traditional PD algorithm under the same conditions.

Neural networks-based iterative learning control consensus for periodically time-varying multi-agent systems

In this paper,the problem of adaptive iterative learning based consensus control for periodically time-varying multi-agent systems is studied,in which the dynamics of each follower are driven by nonlinearly parameterized terms with periodic disturbances.Neural networks and Fourier base expansions are introduced to describe the periodically time-varying dynamic terms.On this basis,an adaptive learning parameter with a positively convergent series term is constructed,and a distributed control protocol based on local signals between agents is designed to ensure accurate consensus of the closed-loop systems.Furthermore,consensus algorithm is generalized to solve the formation control problem.Finally,simulation experiments are implemented through MATLAB to demonstrate the effectiveness of the method used.