Data-Driven Learning Control Algorithms for Unachievable Tracking Problems

For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to investigate solutions using the Ptype learning control scheme. Initially, we demonstrate the necessity of gradient information for achieving the best approximation.Subsequently, we propose an input-output-driven learning gain design to handle the imprecise gradients of a class of uncertain systems. However, it is discovered that the desired performance may not be attainable when faced with incomplete information.To address this issue, an extended iterative learning control scheme is introduced. In this scheme, the tracking errors are modified through output data sampling, which incorporates lowmemory footprints and offers flexibility in learning gain design.The input sequence is shown to converge towards the desired input, resulting in an output that is closest to the given reference in the least square sense. Numerical simulations are provided to validate the theoretical findings.

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.

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.

LMI_based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.

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.

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.

2D VARIABLE FACTOR LEARNING CONTROLLER AND ITS APPLICATION IN PNEUMATIC SERVO SYSTEM

A new learning control law is presented which can obtain learning gain matrices from a recursive identifier along the learning axis. The system convergence is proved when disturbances exist in the system. Finally it is applied to pneumatic servo control system, the experiment results show its validity.

Generalized projective synchronization of chaotic systems via adaptive learning control

In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.

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.

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.

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.

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.

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,

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.

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.