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.

Stability of Iterative Learning Control with Data Dropouts via Asynchronous Dynamical System

In this paper, the stability of iterative learning control with data dropouts is discussed. By the super vector formulation, an iterative learning control （ILC） system with data dropouts can be modeled as an asynchronous dynamical system with rate constraints on events in the iteration domain. The stability condition is provided in the form of linear matrix inequalities （LMIS） depending on the stability of asynchronous dynamical systems. The analysis is supported by simulations.

PD-type iterative learning control for nonlinear time-delay system with external disturbance

The PD-type iterative learning control design of a class of affine nonlinear time-delay systems with external disturbances is considered. Sufficient conditions guaranteeing the convergence of the n-norm of the tracking error are derived. It is shown that the system outputs can be guaranteed to converge to desired trajectories in the absence of external disturbances and output measurement noises. And in the presence of state disturbances and measurement noises, the tracking error will be bounded uniformly. A numerical simulation example is presented to validate the effectiveness of the proposed scheme.

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.

Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control （AILC） scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality （LMI） method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative （PID） feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function （CEF）, we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

Robust iterative learning control for nonlinear systems with measurement disturbances

The iterative learning control （ILC） has been demon-strated to be capable of considerably improving the tracking perfor-mance of systems which are affected by the iteration-independent disturbance. However, the achievable performance is greatly degraded when iteration-dependent, stochastic disturbances are pre-sented. This paper considers the robustness of the ILC algorithm for the nonlinear system in presence of stochastic measurement disturbances. The robust convergence of the P-type ILC algorithm is firstly addressed, and then an improved ILC algorithm with a decreasing gain is proposed. Theoretical analyses show that the proposed algorithm can guarantee that the tracking error of the nonlinear system tends to zero in presence of measurement dis-turbances. The analysis is also supported by a numerical example.

Iterative Learning Control Algorithm with a Fixed Step

Iterative Learning Control （ILC） captures interests of many scholars because of its capability of high precision control implement without identifying plant mathematical models, and it is widely applied in control engineering. Presently, most ILC algorithms still follow the original ideas of ARIMOTO, in which the iterative-learning-rate is composed by the control error with its derivative and integral values. This kind of algorithms will result in inevitable problems such as huge computation, big storage capacity for algorithm data, and also weak robust. In order to resolve these problems, an improved iterative learning control algorithm with fixed step is proposed here which breaks the primary thought of ARIMOTO. In this algorithm, the control step is set only according to the value of the control error, which could enormously reduce the computation and storage size demanded, also improve the robust of the algorithm by not using the differential coefficient of the iterative learning error. In this paper, the convergence conditions of this proposed fixed step iterative learning algorithm is theoretically analyzed and testified. Then the algorithm is tested through simulation researches on a time-variant object with randomly set disturbance through calculation of step threshold value, algorithm robustness testing,and evaluation of the relation between convergence speed and step size. Finally the algorithm is validated on a valve-serving-cylinder system of a joint robot with time-variant parameters. Experiment results demonstrate the stability of the algorithm and also the relationship between step value and convergence rate. Both simulation and experiment testify the feasibility and validity of the new algorithm proposed here. And it is worth to noticing that this algorithm is simple but with strong robust after improvements, which provides new ideas to the research of iterative learning control algorithms.

PI-type Iterative Learning Control for Nonlinear Electro-hydraulic Servo Vibrating System

For the electro-hydraulic servo vibrating system（ESVS） with the characteristics of non-linearity and repeating motion, a novel method, PI-type iterative learning control（ILC）, is proposed on the basis of traditional PID control. By using memory ability of computer, the method keeps last time＇s tracking error of the system and then applies the error information to the next time＇s control process. At the same time, a forgetting factor and a D-type learning law of feedforward fuzzy-inferring referenced displacement error under the optimal objective are employed to enhance the systemic robustness and tracking accuracy. The results of simulation and test reveal that the algorithm has a trait of high repeating precision, and could restrain the influence of nonlinear factors like leaking, external disturbance, aerated oil, etc. Compared with traditional PID control, it could better meet the requirement of nonlinear electro -hydraulic servo vibrating system.

Error analysis for remote nonlinear iterative learning control system with wireless channel noise

In this paper, the iterative learning control problem is considered for a class of remote control system over wireless network communication channel. The control performance of remote iterative learning control （R-ILC） system is analyzed and an error boundary of the stable output of the R-ILC system is obtained for the boundary stochastic noise channel. Finally, we obtain some rules to reduce the fluctuation caused by wireless channel noise through the analysis results for fluctuation boundary. The simulation results prove the proposed rule is correct.

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.

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.

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.

Adaptive Iterative Learning Control for Nonlinear Time-delay Systems with Periodic Disturbances Using FSE-neural Network

An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion （FSE） are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions （such as global Lipschitz condition） is relaxed. Furthermore, by using appropriate Lyapunov-Krasovskii functionals, all signs in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded, and the output of the system is proved to converge to the desired trajectory. A simulation example is provided to illustrate the effectiveness of the control scheme.

Filter-based iterative learning control for linear large-scale industrial processes

In the procedure of the steady-state hierarchical optimization with feedback for large-scale industrial processes, a sequence of set-point changes with different magnitudes is carried out on the optimization layer. To improve the dynamic performance of transient response driven by the set-point changes, a filter-based iterative learning control strategy is proposed. In the proposed updating law, a local-symmetric-integral operator is adopted for eliminating the measurement noise of output information,a set of desired trajectories are specified according to the set-point changes sequence, the current control input is iteratively achieved by utilizing smoothed output error to modify its control input at previous iteration, to which the amplified coefficients related to the different magnitudes of set-point changes are introduced. The convergence of the algorithm is conducted by incorporating frequency-domain technique into time-domain analysis. Numerical simulation demonstrates the effectiveness of the proposed strategy,

Adaptive adjustment of iterative learning control gain matrix in harsh noise environment

For the robustness problem of open-loop P-type iterative learning control under the influence of measurement noise which is inevitable in actual systems, an adaptive adjustment algorithm of iterative learning nonlinear gain matrix based on error amplitude is proposed and two nonlinear gain functions are given. Then with the help of Bellman-Gronwall lemma, the robustness proof is derived. At last, an example is simulated and analyzed. The results show that when there exists measurement noise, the proposed learning law adjusts the learning gain matrix on line based on error amplitude, thus can make a compromise between learning convergence rate and convergence accuracy to some extent： the fast convergence rate is achieved with high gain in initial learning stage, the strong robustness and high convergence accuracy are achieved at the same time with small gain in the end learning stage, thus better learning results are obtained.

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.