Norm-optimal Iterative Learning Control Algorithm Research Articles

Norm-Optimal Iterative Learning Control for Wind Turbines During Grid Faults

Due to the increasing share of (offshore) wind turbines, more stringent requirements on power quality have been established. Importantly, the low-voltage ride-through grid requirement states that a wind turbine must remain connected to the electrical grid after a short intermittent grid fault. In the industry mainly gain-scheduled PID-controllers are used to mitigate the effects of grid faults on turbine operation, whereas more advanced solutions have been proposed in the literature such as model predictive control or multiple parallel PI-controllers. Remarkably, all controller implementations mentioned earlier are based on feedback control, where no feedforward strategies have been discussed in the literature. However, feedforward control could improve grid fault recovery performance by exploiting the relatively known fault characteristics by virtue of the specification in the Transmission System Operator requirements. Therefore, for the first time, a norm-optimal Iterative Learning Control (NO-ILC) algorithm is presented that solves these issues by learning the feedforward signal that optimally mitigates the effects of a grid fault. The NO-ILC algorithm applies model-free learning based on iterations, in which the framework of NO-ILC has been extended to include explicit input constraints. The goal of the NO-ILC is to reduce a (quadratic) cost function on specific input and output channels whilst conforming to specific input constraints by solving an optimisation problem, with, for this study blade pitch and rotor speed as respective input and output channels. It is shown that the NO-ILC algorithm can yield improved performance on a high-fidelity model, with a 45% decrease in the cost function used by NO-ILC compared to the nominal feedback control. The optimised feedforward signals resulting from NO-ILC can be used as an analysis tool to closer match the nominal grid fault feedback controllers response with that of NO-ILC, or directly applied as a library that can supplement the feedback controllers output during a grid fault.

Data-driven Norm Optimal Iterative Learning Control for Point-to-Point Tasks

Iterative learning control (ILC) is suitable for high-performance repetitive tasks since it learns from past trials to improve the tracking performance. Existing ILC designs often require a model, which can be difficult or expensive to obtain in practice. To address this problem, we recently developed a data-driven norm optimal ILC using the latest developments from data-driven control, namely, the Willems’ fundamental lemma. In this paper, we show that the idea can also be extended to point-to-point ILC tasks that focus on tracking some intermediate points of the whole trial. We propose a novel data-driven point-to-point norm optimal ILC algorithm that can achieve the same performance as the model-based algorithm but without using an analytical model. The design requires the available data to be persistently exciting of a sufficiently high order. To relax this requirement, a receding horizon based algorithm and a trial partition based algorithm are further developed with well-defined, but different convergence properties. Numerical examples are given to illustrate the proposed algorithms’ effectiveness.

Fast-Update Iterative Learning Control for Performance Enhancement With Application to Motion Systems

Iterative learning control (ILC) algorithms are typically used to improve the performance of repetitive processes. Numerous successful applications of ILC, such as computer numerical control (CNC) machining processes, robot manipulation, and lithography processes, have been reported. However, ILC often exhibits less than satisfactory performance since the control unit operates at a limited sampling rate in consideration of cost. In this study, the multiloop, multirate structure of servo motor control systems is taken advantage of and a fast-update multirate ILC (FILC) scheme is proposed for high-accuracy trajectory tracking, where compensation is updated at a rate faster than that of the original position loop without the need for redesigning the feedback controller. The key difficulty related to the design of the FILC lies in the extremely complex and time-varying dynamics inherent in multirate systems. To address this problem, a novel equivalent single-rate parametric model description of the multirate system is derived, which enables the use of the efficient norm optimal ILC algorithm. Consequently, a computationally efficient FILC is obtained to improve the performance. Subsequently, the proposed FILC is applied to the position control of the CNC motion stage. Simulation and experimental results are used to verify the effectiveness of the proposed method.

Adaptive Iterative Learning Control of an Industrial Robot during Neuromuscular Training

To prevent the reduction of muscle mass and loss of strength coming along with the human aging process, regular training with e.g. a leg press is suitable. However, the risk of training-induced injuries requires the continuous monitoring and controlling of the forces applied to the musculoskeletal system as well as the velocity along the motion trajectory and the range of motion. In this paper, an adaptive norm-optimal iterative learning control algorithm to minimize the knee joint loadings during the leg extension training with an industrial robot is proposed. The response of the algorithm is tested in simulation for patients with varus, normal and valgus alignment of the knee and compared to the results of a higher-order iterative learning control algorithm, a robust iterative learning control and a recently proposed conventional norm-optimal iterative learning control algorithm. Although significant improvements in performance are made compared to the conventional norm-optimal iterative learning control algorithm with a small learning factor, for the developed approach as well as the robust iterative learning control algorithm small steady state errors occur.

Iterative learning control of ventricular assist devices with variable cycle durations

In clinical practice ventricular assist devices are generally applied with a constant rotary speed. The lack of adaptivity to changes in hemodynamic conditions might result in underpumping or suction. In this paper, a norm-optimal iterative learning control algorithm incorporating variable cycle durations is developed and tested in silico to changes in afterload, contractility, and heart rate. To simulate exercise, a fourth experiment with parallel variations of preload, afterload, contractility and heart rate is done. For this purpose, a simplified simulation model of the cardiovascular system is used. The results confirm that the algorithm is able to prevent the dilatation of the ventricle and adapt to varying cycle lengths.

Iterative Learning Control of a Left Ventricular Assist Device: Nonlinear Model Integration

Abstract Norm-optimal iterative learning control algorithms use plant models to predict the system behavior. In this paper, we focus on improving the performance in the norm-optimal iterative learning control of left ventricular assist devices. For this purpose, the previously used simple plant model is replaced by a piecewise linearized version of a nonlinear cardiovascular system model including the left ventricular assist device. Simulations are carried out to study the controller response to end-diastolic volume setpoint and preload changes. The results show minor improvements regarding the tracking performance and the rejection of disturbances but also an increase of computational effort compared to the previous algorithm.

Parameter-optimal iterative learning control using polynomial representations of the inverse plant

Based on the observation that iterative learning control (ILC) can be based on the inverse plant but that the approach can be degraded by modelling errors, particularly at high frequencies, this article investigates the construction and properties of a multi-parameter parameter-optimal ILC algorithm that uses an approximate polynomial representation of the inverse with natural high-frequency attenuation. In its simplest form, the algorithm replicates the original work of Owens and Feng but, more generally, it is capable of producing significant improvements to the observed convergence rate. As the number of parameters increases, convergence rates approach that of the ideal plant inverse algorithm. Introducing compensation into the algorithm provides a formal link to previously published gradient and norm-optimal ILC algorithms and indicates that the polynomial approach can be regarded as approximations to those control laws. Simulation examples verify the theoretical performance predictions.

Accelerated predictive norm-optimal iterative learning control

This paper proposes a novel technique for accelerating the convergence of the previously published predictive norm-optimal iterative learning control (NOILC) methodology. The basis of the results is a formal proof that the predictive NOILC algorithm is equivalent to a successive projection algorithm between linear varieties in a suitable product Hilbert space. This leads to two proposed accelerated algorithms together with well-defined convergence properties. The results show that the proposed accelerated algorithms are capable of ensuring monotonic error norm reductions and can outperform predictive NOILC by more rapid reductions in error norm from iteration to iteration. In particular, examples indicate that the approach can improve the performance of predictive NOILC for the problematic case of non-minimum phase systems. Realization of the algorithms is discussed and numerical simulations are provided for comparative purposes and to demonstrate the numerical performance and effectiveness of the proposed methods.

Accelerated norm-optimal iterative learning control

This paper proposes a novel technique for accelerating the convergence of the previously published norm-optimal iterative learning control (NOILC) methodology. The basis of the results is a formal proof of an observation made by the first author, namely that the NOILC algorithm is equivalent to a successive projection algorithm between linear varieties in a suitable product Hilbert space. This leads to two proposed accelerated algorithms together with well-defined convergence properties. The results show that the proposed accelerated algorithms are capable of ensuring monotonic error norm reductions and can outperform NOILC by more rapid reductions in error norm from iteration to iteration. In particular, examples indicate that the approach can improve the performance of NOILC for the problematic case of non-minimum phase systems. Realisation of the algorithms is discussed and numerical simulations are provided for comparative purposes and to demonstrate the numerical performance and effectiveness of the proposed methods.

Accelerated norm-optimal iterative learning control algorithms using successive projection

This article proposes a novel technique for accelerating the convergence of the previously published norm-optimal iterative learning control (NOILC) methodology. The basis of the results is a formal proof of an observation made by D.H. Owens, namely that the NOILC algorithm is equivalent to a successive projection algorithm between linear varieties in a suitable product Hilbert space. This leads to two proposed accelerated algorithms together with well-defined convergence properties. The results show that the proposed accelerated algorithms are capable of ensuring monotonic error norm reductions and can outperform NOILC by more rapid reductions in error norm from iteration to iteration. In particular, examples indicate that the approach can improve the performance of NOILC for the problematic case of non-minimum phase systems. Realisation of the algorithms is discussed and numerical simulations are provided for comparative purposes and to demonstrate the numerical performance and effectiveness of the proposed methods.

Convex modifications to an iterative learning control law*1

In this paper, a predictive norm-optimal iterative learning control algorithm from Amann, Owens, and Rogers (Int. J. Control 69 (2) (1998) 203–226) is analyzed. The main new result of this is that any of the predictive inputs from the predictive algorithm can be used in the control of the plant. This results in a faster convergence rate than that obtained with the approach proposed by Amann, Owens, and Rogers. Furthermore, the nature of the convergence of this new scheme is analysed in detail in terms of the free parameters of the algorithm.

Convex modifications to an iterative learning control law

In this paper, a predictive norm-optimal iterative learning control algorithm from Amann, Owens, and Rogers (Int. J. Control 69 (2) (1998) 203–226) is analyzed. The main new result of this is that any of the predictive inputs from the predictive algorithm can be used in the control of the plant. This results in a faster convergence rate than that obtained with the approach proposed by Amann, Owens, and Rogers. Furthermore, the nature of the convergence of this new scheme is analysed in detail in terms of the free parameters of the algorithm.

Genetic algorithms in norm-optimal linear and non-linear iterative learning control

In this paper it is analysed whether or not it is possible to apply the norm-optimal iterative learning control algorithm to non-linear plant models. As a new theoretical result it is shown that if the non-linear plant meets a certain technical invertibility condition, the sequence of tracking errors generated by the norm-optimal algorithm will converge geometrically to zero. However, due to the non-linear nature of the plant, it is typically impossible to calculate analytically the sequence of input functions produced by the norm-optimal algorithm. Therefore it is proposed that genetic algorithms can be used as a computational tool to calculate the sequence of norm-optimal inputs. The proposed approach benefits from the design of a low-pass FIR filter. This filter successfully removes unwanted high frequency components of the input signal, which are generated by the genetic algorithm method due to the random nature of the genetic algorithm search. Simulations are used to illustrate the performance of this new approach, and they demonstrate good results in terms of convergence speed and tracking of the reference signal regardless of the nature of the plant.

CONVEX MODIFICATIONS TO AN ITERATIVE LEARNING CONTROL LAW

In this paper a predictive norm-optimal iterative learning control algorithm from (Amann et al., 1998) is analyzed. As a main new result in this paper it is shown that if also the predictive inputs from the algorithm are used in the control of the plant, a faster convergence can be achieved than with the approach in (Amann et al., 1998). Furthermore, the nature of the convergence of this new scheme is analyzed in detail in terms of the free parameters of the algorithm.