Iterative Learning Control Design Research Articles

Multivariable Iterative Learning Control Design for Precision Control of Flexible Feed Drives.

Advancements in machining technology demand higher speeds and precision, necessitating improved control systems in equipment like CNC machine tools. Due to lead errors, structural vibrations, and thermal deformation, commercial CNC controllers commonly use rotary encoders in the motor side to close the position loop, aiming to prevent insufficient stability and premature wear and damage of components. This paper introduces a multivariable iterative learning control (MILC) method tailored for flexible feed drive systems, focusing on enhancing dynamic positioning accuracy. The MILC employs error data from both the motor and table sides, enhancing precision by injecting compensation commands into both the reference trajectory and control command through a norm-optimization process. This method effectively mitigates conflicts between feedback control (FBC) and traditional iterative learning control (ILC) in flexible structures, achieving smaller tracking errors in the table side. The performance and efficacy of the MILC system are experimentally validated on an industrial biaxial CNC machine tool, demonstrating its potential for precision control in modern machining equipment.

Adaptive iterative learning control for high‐order nonlinear systems with different types of uncertainties

AbstractThe present work aims at investigating the adaptive iterative learning control (AILC) design for uncertain high‐order fully actuated nonlinear systems. In order to show the design principles, three types of nonlinear systems are considered, including systems with just parametric uncertainty, systems with both parametric and input distribution uncertainties as well as systems with both parametric uncertainty and an unknown control gain matrix. For different systems, the corresponding AILC schemes are proposed with different techniques in dealing with various system uncertainties, for which the convergence analysis are conducted rigorously based on the composite energy function. The effectiveness of the proposed AILC strategies is verified through numerical simulations.

A Performance Evaluation of Repetitive and Iterative Learning Algorithms for Periodic Tracking Control of Functional Electrical Stimulation System

Functional electrical stimulation (FES) is a medical device that delivers electrical pulses to the muscle, allowing patients with spinal cord injuries to perform activities such as walking, cycling, and grasping. It is critical for the FES to generate stimuli with the appropriate controller so that the desired movements can be precisely tracked. By considering the repetitive nature of the movements, the learning-based control algorithms are utilized for regulating the FES. Iterative learning control (ILC) and repetitive control (RC) are two learning algorithms that can be used to accomplish accurate repetitive motions. This study investigates a variety of ILC and RC designs with distinct learning functions; this constitutes our contribution to the field. The FES model of ankle angle, which is in a class of discrete-time linear systems is considered in this study. Two learning functions, i.e., proportional, and zero-phase learning functions, are simulated for the second-order FES model running at a sampling time of 0.1 s. The results indicate the superior performance of the ILC and RC in terms of convergence rate using the zero-phase learning function. ILC and RC with a zero-phase learning function can reach a zero root-mean-square error in two iterations if the model of the plant is correct. This is faster than proportional-based ILC and RC, which takes about 40 iterations. This indicates that the zero-phase learning function requires two iterations to ensure that the patient's ankle angle precisely tracks the intended trajectory. However, the tracking performance is degraded for both control methods, especially when the model is subject to uncertainties. This specific problem can lead to future research directions.

Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

In this article, a fractional-order adaptive iterative learning control scheme is proposed for a class of parameterized fractional-order systems with unknown control gain and backlash-like hysteresis nonlinearity under disturbance. Based on the sufficient condition for the stability of linear fractional-order systems, a sliding mode surface of tracking errors is constructed to facilitate the controller design and stability analysis. A new boundary layer function is designed by using Mittag-Leffler function to relax the restriction of the identical initial condition of iterative learning control design. The fractional-order differential-type adaptive laws and difference-type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. To deal with the influence of backlash-like hysteresis nonlinearity reminder term and unknown bounded external disturbance, a robust control term is designed by employing the hyperbolic tangent function with a convergent series sequence which can guarantee the learning convergence along iteration axis. By constructing Lyapunov-like composite energy function, the stability analysis is presented to prove the convergence of the system output to a small neighborhood of the desired trajectory and the boundedness of all the closed-loop signals. Finally, a simulation example of second-order nonlinear fractional-order system is presented, which demonstrates the effectiveness of the proposed fractional-order adaptive iterative learning control scheme.

Dynamic Neural Network Predictive Compensation-Based Point-to-Point Iterative Learning Control With Nonuniform Batch Length.

This article discusses the problem of nonuniform running length in incomplete tracking control, which often occurs in industrial processes due to artificial or environmental changes, such as chemical engineering. It affects the design and application of iterative learning control (ILC) that relies on the strictly repetitive property. Therefore, a dynamic neural network (NN) predictive compensation strategy is proposed under the point-to-point ILC framework. To handle the difficulty of establishing an accurate mechanism model for real process control, the data-driven approach is also introduced. First, applying the iterative dynamic linearization (IDL) technique and radial basis function NN (RBFNN) to construct the iterative dynamic predictive data model (IDPDM) relies on input-output (I/O) signal, and the extended variable is defined by a predictive model to compensate for the incomplete operation length. Then, a learning algorithm based on multiple iteration errors is proposed using an objective function. This learning gain is constantly updated through the NN to adapt to changes in the system. In addition, the composite energy function (CEF) and compression mapping prove that the system is convergent. Finally, two numerical simulation examples are given.

Experimentally Validated Vector Lyapunov Function-Based Iterative Learning Control Design Under Input Saturation

Experimentally Validated Vector Lyapunov Function-Based Iterative Learning Control Design Under Input Saturation

Improving Tracking Accuracy for Repetitive Learning Systems by High-Order Extended State Observers.

For systems executing repetitive tasks, how to realize the perfect tracking objective is generally desirable, for which an effective method called "iterative learning control (ILC)" emerges thanks to the incorporation of the repetitive execution of systems into an ILC design framework. However, nonrepetitive (iteration-varying) uncertainties are often inevitable in practice and greatly degrade the tracking accuracy of ILC, which has not been treated well, regardless of considerable robust ILC results. This motivates this article to develop a new design method to improve the tracking accuracy of ILC by adopting a high-order extended state observer (ESO) to address ill effects of nonrepetitive uncertainties and uncertain system models. With the designed ESO-based ILC, the robust tracking of any desired trajectory can be achieved such that the tracking error can be decreased to vary in a small bound depending continuously on the bounds of high-order variations of nonrepetitive uncertainties with respect to the iteration. It makes the tracking accuracy of ILC possible to be regulated through the design of ESO, of which the validity is demonstrated by including a simulation example.

Iterative learning control design for a discrete-time system under delay along the sample trajectory and input backlash

Iterative learning control design for a discrete-time system under delay along the sample trajectory and input backlash

Feedback higher-order iterative learning control for nonlinear systems with non-uniform iteration lengths and random initial state shifts

For nonlinear discrete-time systems with non-uniform iteration lengths and random initial state shifts, this paper developed a feedback higher-order iterative learning control (ILC) approach. To compensate the absent information of last iteration caused by non-uniform iteration lengths, the tracking information in both iteration domain and time domain is included in ILC design with the help of higher-order control and feedback control, respectively, while the general ILC schemes just adopt the information in iteration domain. A sufficient condition based on the higher-order ILC gains is derived. It is guaranteed that as the iteration number goes to infinity, the asymptotic bound of tracking error is proportional to random initial state shifts in mathematical expectation sense. Specifically, as the expectation of initial state shifts is zero, the ILC tracking error can be controlled to zero along the iteration direction. Two examples with different initial conditions are provided to validate the proposed ILC approach.

Vibration Suppression of a High-Rise Building With Adaptive Iterative Learning Control.

This article considers the design of an adaptive iterative learning controller for high-rise buildings with active mass dampers (AMDs). High-rise buildings in this article are seen as distributed parameter systems, in which the characteristics of every point in buildings should be considered. Two partial differential equations (PDEs) and several ordinary differential equations are used to describe the model of buildings. To achieve the control target that is to suppress the vibration induced by high winds, an adaptive iterative learning controller is proposed for the flexible building system with boundary disturbance. The convergency of the adaptive iterative learning control (AILC) approach is proven by serious theory analysis. In simulations and experiments, this article uses both the analysis of figures and quantitative analysis (root-mean-square values) to illustrate the efficiency of the AILC scheme.

Fault-tolerant design of non-linear iterative learning control using neural networks

The design of neural-network-based iterative learning control for non-linear systems is addressed in the setting of a fault tolerant control regime. Taking advantage of the repetitive character of the control task, the inherent uncertainty related to a potential faulty system state can be properly accommodated in terms of a data-driven iterative learning scheme with neural networks used for forward/inverse modeling as well as for controller synthesis. The resulting control technique is supposed to be flexible enough to accurately compensate the faults occurring on both the sensors and actuators and, additionally, take into account the disturbances and noise acting on the system. A complete characterization of the novel fault-tolerant iterative learning scheme is provided including system identification, fault detection and accommodation. Also, the painstaking convergence analysis is presented and the resulting sufficient conditions can be constructively used to determine the update of control law in the consecutive process trial. The excellent performance of the developed control scheme is illustrated by a nontrivial example of tracking control for a magnetic brake system on various scenarios involving actuator and/or sensor faults.

Extension of iterative learning control design for batch processes with time-delay in the input subject to random cycle-varying uncertainties

For uncertain time-delay batch processes with repetitive nature, this work deals with an unresolved problem of robust iterative learning control (ILC) design, in which we simultaneously remove the conventional assumptions of cycle-invariant uncertainties in reference trajectories, initial states, external disturbances, process dynamics, and time-delay. Moreover, we consider the variation of all existing uncertainties from a random point of view. Based on the idea of the internal model control (IMC) and indirect ILC, a novel IMC-based ILC structure is proposed. Then, we derive the practical convergence conditions, which have two design functions. By introducing a simple method for adjusting these functions, not only can we ensure that the expected tracking error converges monotonically to zero-neighborhood (in the L2-norm sense) but we can also achieve an acceptable convergence rate. Moreover, it is shown that the satisfaction of derived convergence conditions can always be guaranteed for any process. Simulation tests are provided to demonstrate the effectiveness of the proposed design.

Distributed MPC-ILC Thermal Control Design for Large-Scale Multi-Zone Building HVAC System

With building heating, ventilation, and air conditioning (HVAC) systems accounting for 50% the energy consumption in the building sector in the United States, there is a need to develop and implement optimal control strategies for building HVAC systems that reduce energy consumption while achieving thermal comfort for users. In the author's previous work, an integrated model predictive control (MPC) and iterative learning control (ILC) design approach was presented that took advantage of both controllers. It did not rely on model accuracy compared to conventional MPC and reduced the learning curve compared to conventional ILC. Albeit the previous numerical results showed fast convergence in most of the VAV subsystems, the gap between room air temperature and its set point remains noticeable in several zones. This paper further proposes an approach to extend the centralized MPC-ILC controller to take into account the distributed factor and the spatial distribution of the thermal zones of the VAV system. The improved control strategy allows all VAVs to interact with each other and contribute collectively to the overall convergence of the whole system. The proposed controller is implemented on a thirty-two zone VAV reheat system and compared with different controllers, including our previous MPC-ILC design. The outcomes show that the proposed controller results in faster and closer convergence among all zones even when the number of subsystems is large.

Alternating projection‐based iterative learning control for discrete‐time systems with non‐uniform trial lengths

AbstractThis article develops a novel framework for iterative learning control (ILC) design of discrete‐time systems with non‐uniform trial lengths by using the method of alternating projections. In contrast to existing results for the non‐uniform trial length problem, this article uses the Hilbert space setting and hence the linear discrete‐time system dynamics with non‐uniform trial lengths can be represented by multiple affine subspaces (or linear varieties). Motivated by the successive projection design between two closed convex sets, the considered ILC problem can be transformed into alternating projections between multiple sets, then the Hilbert space setting is used to establish key systems theoretic properties. Moreover, an optimal ILC design is developed for systems with non‐uniform trial lengths, which is also extended to the case of input constraints. A numerical case study is given to illustrate the applicability of the new design.

Design and Implementation of Iterative Learning Control for an Electro-Hydraulic Servo System

In order to produce an accurate movement of double-acting hydraulic cylinder of the Electro-Hydraulic Servo System (EHSS), an Iterative Learning Controller (ILC) approach is implemented in this work. Nonlinearity and imprecision occurs in the hydraulic systems because of friction. Traditional controllers are incapable of providing effective control performance throughout the entire operating range and insufficient to handle repetitive task. To manage the repetitive task, a memory-based learning control analysis is suitable. This research focuses to construct the ILC for governing the servo spool valve, which is responsible for the hydraulic cylinder displacement. The proposed ILC consists of learning filter, learning gain and robustness filter. Proportional, Integral and Derivative (PID) controller is devised to validate the outcome of ILC. Controllers are constructed based on the system modelling. The effectiveness of the suggested controller is shown through simulation and experimental findings. ILC provides an average of 50% minimal overshoot and settles 7 sec before the PID controller is designed. Due to model uncertainty, PID controller results 0.2 sec better rise time than ILC. In ILC's architecture objective function is designed to achieve minimal overshoot and quick settling of hydraulic cylinder. So, no consideration is given to the error indices. These findings will help hydraulic stamping application, which requires the accurate displacement of piston to avoid damage of work piece. These results show that the proposed controller achieves desired outcome displacement of hydraulic cylinder.

Iteration dependent interval based open‐closed‐loop iterative learning control for time varying systems with vector relative degree

AbstractFor linear time varying (LTV) multiple input multiple output (MIMO) systems with vector relative degree, an open‐closed‐loop iterative learning control (ILC) strategy is developed in this article, where the time interval of operation is iteration dependent. To compensate the missing tracking signal caused by iteration dependent interval, the feedback control is introduced in ILC design. As the tracking signal of many continuous iterations is lost in a certain interval, the feedback control part can employ the tracking signal of current iteration for compensation. Under the assumption that the initial state vibrates around the desired initial state uniformly in mathematical expectation sense, the expectation of ILC tracking error can converge to zero as the number of iteration tends to infinity. Under the circumstance that the initial state varies around the desired initial state with a bound, as the number of iteration tends to infinity, the expectation of ILC tracking error can be driven to a bounded range, whose upper bound is proportional to the fluctuation. It is revealed that the convergence condition is dependent on the feedforward control gains, while the feedback control can accelerate convergence speed by selecting appropriate feedback control gains. As a special case, the controlled system with integrated high relative degree is also addressed by proposing a simplified iteration dependent interval based open‐closed‐loop ILC method. Finally, the effectiveness of the developed iteration dependent interval based open‐closed‐loop ILC is illustrated by a simulation example with two cases on initial state.

Conic Input Mapping Design of Constrained Optimal Iterative Learning Controller for Uncertain Systems.

In this article, we study the optimal iterative learning control (ILC) for constrained systems with bounded uncertainties via a novel conic input mapping (CIM) design methodology. Due to the limited understanding of the process of interest, modeling uncertainties are generally inevitable, significantly reducing the convergence rate of the control systems. However, huge amounts of measured process data interacting with model uncertainties can easily be collected. Incorporating these data into the optimal controller design could unlock new opportunities to reduce the error of the current trail optimization. Based on several existing optimal ILC methods, we incorporate the online process data into the optimal and robust optimal ILC design, respectively. Our methodology, called CIM, utilizes the process data for the first time by applying the convex cone theory and maps the data into the design of control inputs. CIM-based optimal ILC and robust optimal ILC methods are developed for uncertain systems to achieve better control performance and a faster convergence rate. Next, rigorous theoretical analyses for the two methods have been presented, respectively. Finally, two illustrative numerical examples are provided to validate our methods with improved performance.

Emerging robust and data‐driven control methods for uncertain learning systems

Emerging robust and data‐driven control methods for uncertain learning systems

Optimal iterative learning control design for continuous-time systems with nonidentical trial lengths using alternating projections between multiple sets

Iterative learning control (ILC) applies to systems that repeat the same finite duration task repeatedly. Each repetition is usually termed as a trial, and the associated duration is called the trial length. Once a trial is completed, all information is available for use in updating the control input for the subsequent trial. The vast majority of the currently available designs demand a strictly identical trial length. This paper gives a new result on the design and analysis for continuous-time linear dynamics based on a modified alternating projection method, where the trial lengths may be nonidentical. This result employs multiple sets to represent the actual varying trial length dynamics and is developed by reformulating the problem to one that minimizes the defined distance in a Hilbert space setting. Compared to the standard alternating projections using two sets, the theory of alternating projections between multiple sets is employed to obtain deterministic convergence result for the nonidentical trial length problem. A numerical case study is also given to illustrate the application of the new design.

Feedback-aided PD-type iterative learning control for time-varying systems with non-uniform trial lengths

In most implementations of iterative learning control (ILC) for trajectory tracking, it is usually required that the trial lengths of different iterations are uniform. However, this requirement may not always be ensured in practical applications. In this paper, a feedback-aided PD-type ILC design for time-varying systems with non-uniform trial lengths is proposed. Although the actual trial lengths are non-uniform, the designed update sequences provide uniform full-length signals for the update process. Meanwhile, information from the most recent valid iterations can be better used than the mechanisms that compensate with hypothesized data, such as zero. Their recursive generation also reduces the storage burden compared to search strategies. The feedback error signal can be additionally used as part of the correction term to improve the system performance compared to the traditional open-loop approaches. Under a deterministic model, the main convergence results are obtained by combining the [Formula: see text]-norm technique with the inductive analysis approach. At last, a linear numerical simulation and a nonlinear single-joint robot simulation are performed, respectively, to show that the proposed design can achieve the asymptotic tracking of the desired trajectories for time-varying systems with non-uniform trial lengths.