Feedback Error Learning Method Research Articles

Feedback error learning neural network for stable control of nonlinear nonaffine systems

This study presents a stable feedback error learning (FEL) scheme for nonlinear nonaffine systems in the presence of uncertainty and disturbances. The distinguishing feature of the FEL method, which can have a significant effect on both transient and steady-state performance, has led us to adopt this approach. The nonlinear system studied here is nonaffine. In other words, the function that describes the dynamic equations of the system is an implicit function of the control input rather than a particular class of systems. We aim to develop a stable FEL control system with three components: a neural network (NN), a linear controller, and a robustifying control term. To this end, all the adaptation laws for the NN weights are derived from a Lyapunov function, ensuring that the closed-loop system is uniformly asymptotically stable (UAS). Thus, an NN learning control approach that effectively improves the transient performance, as well as the steady-state performance, is proposed, and its remarkable effectiveness is illustrated in comparison with the existing methods.

Torque–flux linkage recurrent neural network adaptive inversion control of torque for switched reluctance motor

In order to reduce the torque ripple for switched reluctance motor (SRM), the learning error preprocessing-based torque–flux linkage recurrent neural network adaptive inversion control (TFRNNAIC) for SRM torque is proposed by the filter preprocessing and the non-linear mechanism characteristics for SRM. In TFRNNAIC with the advantages of parallel and series–parallel structure, the torque feedback error learning method is employed to update the weights of the torque–flux linkage recurrent neural network. To suppress the ripple effectively in torque error used for the weight learning of the torque–flux linkage recurrent neural network and obtain an accurate TFRNNAIC, namely the torque–flux linkage model for SRM, the low-pass filter preprocessing for the torque error is used. Moreover, the other low-pass filter is executed to reduce the ripple in the output for the PD torque control. The superposition of outputs for TFRNNAIC and PD torque control is taken as the reference flux linkage. Compared with other control strategies, such as the classical parallel neural network control, the classical series–parallel neural network control and TFRNNAIC, the simulation results show that the learning error preprocessing-based TFRNNAIC for SRM torque is capable of effectively reducing the torque ripple for SRM with the good recurrent performance.

Adaptive Shape Control for Antenna Reflectors Based on Feedback Error Learning Algorithm

To achieve high-precision shape control of antenna reflectors in the presence of model errors, an adaptive shape control method based on the feedback error learning algorithm is proposed. First, the finite element model of a planar hexagonal reflector with 30 piezoelectric actuators is established, by which the influence coefficient matrix is derived. Second, the feedback error learning method is developed, and it can iteratively modify the inverse model of the reflector system through online learning, thus avoiding the effect of model errors on shape control precision. An adaptive step size adjustment strategy for the method is proposed to improve the convergence precision and speed. Then, the effectiveness of the proposed method is intensively studied in comparison with the traditional influence coefficient matrix method by numerical simulations. Numerical results demonstrate that the proposed method can achieve a fairly high precision for all kinds of model errors, whereas the model errors will greatly reduce the precision of the influence coefficient matrix method. The adaptive step size adjustment strategy can greatly improve the convergence precision and speed. Finally, experimental results further verified the above conclusions, which prove the effectiveness and practicability of the proposed method for the high-precision shape control.

Model reference fractional order control using type-2 fuzzy neural networks structure: Implementation on a 2-DOF helicopter

In this paper, an adaptive learning algorithm is proposed for an interval type-2 fuzzy fractional order controller. The use of fractional order controller adds more degrees of freedom which makes it possible to obtain superior performance in comparison with ordinary differential controllers. A fractional order reference model is used to define the desired trajectory of the nonlinear dynamic system. The structure of the system is based on the feedback error learning method. The stability of the adaptation laws is proved using Lyapunov theory. In order to test the efficiency and efficacy of the proposed learning and the control algorithm, the trajectory tracking problem of a magnetic rigid spacecraft is studied. The simulation results show that the proposed control algorithm outperforms the case when ordinary differential fuzzy controller is used. Furthermore, it is shown that it is possible to define a master chaotic system as a reference model and obtain synchronization between the two chaotic systems using the proposed approach. In the simulation part the synchronization between two Duffing–Holmes system is also achieved. In order to show the implementability of the proposed method, it is used to control a real time laboratory setup 2-DOF helicopter. It is shown that the proposed fractional order controller can be implemented in a low cost embedded system and can successfully control a highly nonlinear dynamic system.

Feedback error learning control of magnetic satellites using type-2 fuzzy neural networks with elliptic membership functions.

A novel type-2 fuzzy membership function (MF) in the form of an ellipse has recently been proposed in literature, the parameters of which that represent uncertainties are de-coupled from its parameters that determine the center and the support. This property has enabled the proposers to make an analytical comparison of the noise rejection capabilities of type-1 fuzzy logic systems with its type-2 counterparts. In this paper, a sliding mode control theory-based learning algorithm is proposed for an interval type-2 fuzzy logic system which benefits from elliptic type-2 fuzzy MFs. The learning is based on the feedback error learning method and not only the stability of the learning is proved but also the stability of the overall system is shown by adding an additional component to the control scheme to ensure robustness. In order to test the efficiency and efficacy of the proposed learning and the control algorithm, the trajectory tracking problem of a magnetic rigid spacecraft is studied. The simulations results show that the proposed control algorithm gives better performance results in terms of a smaller steady state error and a faster transient response as compared to conventional control algorithms.

Plate Width Control Based on Neural Network in Hot Mill

Based upon the model analysis on hot roll width control system, an online adaptive PD combined with Neural Network control method is proposed to account for the complicated process dynamics characterized by nonlinear, parameter uncertain and load disturbances etc. The NN model was introduced as a feed-forward controller to study the controlled plant inverse dynamic. The controller is independent of the exact controlled system modeling, and the control parameter can be regulated online by using the measured input/output datum based on feedback error learning method. The PD controller act as feedback one to ensure the robustness. The proposed scheme is simulated on vertical roller of hot strip mill. The control performance is analyzed in detail in terms of the system response speed and accuracy, as well as robustness to rolling temperature variation.

온라인 피드백 에러 학습을 이용한 이동 로봇의 자율주행 알고리즘 개발

본 논문에서는, 신경망을 이용한 뉴로 인터페이스 설계를 통해 논홀로노믹 이동 로봇을 제어하는 방법을 제시하였다. 특히, 가상의 마스터-슬레이브 로봇 개념을 이용하여, 부분적으로 안정된 마스터 로봇의 역 동적모델이 피드백-에러 학습법을 적용한 신경망을 통해 온라인으로 획득되도록 하였다. 이 피드백 제어기는 PD 보상기에 기초를 두고 있다. 온라인 학습을 위한 신경망은 입력층이 6개의 입력세포들(<TEX>$x_i$</TEX>, i=1~6)로 구성되어있으며, 1개의 은닉층에는 2개의 은닉세포(<TEX>$o_j$</TEX>, j=1~2), 출력층은 2개의 출력세포(<TEX>${\tau}_k$</TEX>, k=1~2)로 구성되었고, 신경망의 온라인 학습을 위하여 최소자승법에 의한 오류역전파 알고리즘을 이용하였다. 본 연구에서 개발된 뉴로 인터페이스의 경로추적제어에 관한 성능은 2-wheel 독립구동이 가능한 논홀로노믹 이동 로봇의 시뮬레이션으로 증명하였다. In this study, a method of designing a neurointerface using neural network (NN) is proposed for controlling nonholonomic mobile robots. According to the concept of virtual master-slave robots, in particular, a partially stable inverse dynamic model of the master robot is acquired online through the NN by applying a feedback-error learning method, in which the feedback controller is assumed to be based on a PD compensator for such a nonholonomic robot. The NN for the online feedback-error learning can composed that the input layer consists of six units for the inputs <TEX>$x_i$</TEX>, i=1~6, the hidden layer consists of two hidden units for hidden outputs <TEX>$o_j$</TEX>, j=1~2, and the output layer consists of two units for the outputs <TEX>${\tau}_k$</TEX>, k=1~2. A tracking control problem is demonstrated by some simulations for a nonholonomic mobile robot with two-independent driving wheels. The initial q value was set to [0, 5, <TEX>${\pi}$</TEX>].

Estimation of Physical Parameters Using Learning Algorithm in Precision Positioning Control

In this paper, a high precision control and a state estimation methods based on the learning algorithm are proposed. By means of the feedback error-learning method, at first, the variation of physical parameter is identified. Then, online estimation can be performed comparing the learned weighting coefficients in the neural network. The proposed method is applied to a precision control system, and is verified through the experiments.

Application of a flexible structure artificial neural network on a servo-hydraulic rotary actuator

In this article the results of the application of a flexible structure artificial neural network for controlling the angular velocity of a servo-hydraulic rotary actuator are discussed. A mathematical model for the system is derived, and a flexible artificial neural network (ANN)-based controller with the feedback error learning method as a learning algorithm is applied to the system. The neural network-based controller has a feed-forward structure and three layers. The flexible bipolar sigmoid function was used as the activation function of the network. The simulation and experimental results show good performance of the developed method in learning the inverse dynamic of the system and controlling the angular velocity of the rotary hydro motor. The advantages of the developed method for servo-hydraulic actuators over other traditional approaches are discussed.

A method for combustion phasing control using cylinder pressure measurement in a CRDI diesel engine

The start of combustion (SOC) in the combustion chamber has a considerable influence upon all performances of the engine. In this paper, cylinder pressure was investigated as a means for the closed-loop SOC control of a common-rail direct injection (CRDI) diesel engine. In order to detect the SOC, the crank angle position where the difference pressure became 10 bar was selected as the pressure variable. Using this pressure variable as a feedback variable, an adaptive feedforward control was proposed. The feedforward controller consisted of the radial basis function network (RBFN) and the feedback error learning method, which was used for the training of the network. The proposed SOC control strategy showed a far better regulation performance than that of the linear feedback controller. A further extension of the strategy based on the individual cylinder pressure feedback, the individual cylinder SOC control strategy, effectively reduced cylinder-by-cylinder SOC variation in steady and transient engine operations.

Stability of feedback error learning method with time delay

Feedback error learning method was recently proposed by Kawato et al. [A heirarchical neural-network model for control and learning of voluntary movements, Biol. Cybernet. 57 (1987) 169–185.] as a possible architecture of brain motor control which is supported by experimental results in neurophysiology. In this paper, we analyze it as a two-degree-of-freedom adaptive control for general time invariant linear plant with adaptive controller in the feedforward path. A time delay is allowed in the feedback loop as in the neuronal pathways of motor control. We derive stability condition of the feedback error learning method based on the strict positiveness of the closed loop system. The control performance of the feedback error learning method as a design strategy of adaptive control has been demonstrated by simulation results.

Feedback Error Learning Control Without Recourse to Positive Realness

Feedback error learning (FEL) method has been proposed by Kawato et al. as a scheme of brain motor control in neurophysiology. Recently, Miyamura and Kimura have established a control theoretical validity of the FEL method in the framework of adaptive control and proved its stability based on the strictly positive realness. In this note, we propose another scheme for the feedback error learning method which does not require any positive real conditions.

STABILITY OF FEEDBACK ERROR LEARNING METHOD FOR GENERAL PLANTS WITH TIME DELAY

Feedback error learning method was recently proposed by Kawato et.al. (M. Kawato and Suzuki, 1987) as a possible architecture of brain motor control which is supported by experimental results in neurophysiology. In this paper, we analyze it as a two-degree-of-freedom adaptive control for general time invariant linear plant with adaptive controller in the feedforward path. A time delay is allowed in the feedback loop as in the neuronal pathways of motor control. We derive stability condition of the feedback error learning method based on the strict positiveness of the closed loop system. The control performance of the feedback error learning method as a design strategy of adaptive control has been demonstrated by simulation results.

Stability of feedback error learning scheme

This paper aims to establish control theoretical validity of the feedback error learning scheme proposed as an architecture of brain motor control with deep physiological root in computational neuroscience. The feedback error learning method is formulated as a two-degree-of-freedom adaptive control. The stability of the adaptive control law is proved based on the strict positive realness, under the assumption that the plant is stable and stably invertible. Extension to non-invertible cases is also discussed. Some simulation results are given to illustrate the effectiveness of the method.

Feedback error learning neural networks for spark advance control using cylinder pressure

This paper presents a spark advance control strategy based on the location of peak pressure (LPP) in spark ignition engines using artificial neural networks. The well-known problems of the LPP-based spark advance control method are that many samples of data are required and there is a problem detecting the combustion phasing owing to hook-back during lean burn operation. In order to solve these problems, a feedforward multilayer perceptron network (MLPN) is introduced in this study. The LPP and hook-back are estimated using the MLPN, which needs only five samples of output voltage from the cylinder pressure sensor. The estimated LPP can be regarded as an index for combustion phasing and can also be used as a minimum spark advance for best torque (MBT) control parameter. The performance of the spark advance controller is improved by adding a feedforward controller which reflects the abrupt changes of the engine operating conditions such as engine speed and manifold absolute pressure. The feedforward controller consists of the radial basis function network, and the feedback error learning method is used for the training of the network. In addition, the proposed control algorithm does not need sensor calibration and pegging (bias calculation) procedures because the MLPN estimates the LPP from the raw sensor output voltage. The feasibility of this methodology to control spark advances is closely examined through steady and transient engine operations. The experimental results have revealed that the LPP shows favourable agreement with the optimal value even during the transient operation of the engine.

Position Control of a Cylinder Using a Hydraulic Bridge Circuit With ER Valves

This paper presents the position control of a double-rod cylinder system using a hydraulic bridge circuit with four electro-rheological (ER) valves. After synthesizing a silicone oil-based ER fluid, a Bingham property of the ER fluid is first tested as a function of electric field in order to determine operational parameters for the ER valves. On the basis of the level of the field-dependent yield stress of the composed ER fluid, four cylindrical ER valves are designed and manufactured. Subsequently, step responses for pressure drops of the ER valve are empirically analyzed with respect to the intensity of the electric field. A cylinder system with a cart is then constructed using a hydraulic bridge circuit with four ER valves, and its governing equation of motion is derived. A neural network control scheme incorporating the proportional-integral-derivative (PID) controller is formulated through the feedback error learning method, and experimentally implemented for the position control of the cylinder system. Both regulating and tracking position control responses for square and sinusoidal trajectories are presented in time domain. In addition, a tracking durability of the control system is provided to demonstrate the practical feasibility of the proposed methodology. [S0022-0434(00)00701-2]

Neural network control for automatic braking control system

We have developed an automatic braking control system for automobiles applying a three-layer neural network model. This system enables the vehicle to decelerate smoothly and to stop at the specified position behind the vehicle ahead. This paper focuses on the use of the three-layer neural network model in the automatic braking control system. Because vehicle dynamics is varied by the variations in road conditions or vehicle characteristics, it cannot be represented accurately by mathematical models. According to this reason, the conventional control methods, such as proportional integrative derivative (PID) control, cannot achieve satisfactory control performance. Therefore, we have constructed the neural network adaptive control system based on the feedback error learning method. This learning method enables the system to adapt to the changes in road grade and vehicle weight without using any specific sensors. Experimental results show satisfactory control performance and reveal that the neural network adaptive control system based on the feedback error learning method is available for the automatic braking control system.

Asymptotic Convergence of Feedback Error Learning Method and Improvement of Learning Speed.

This paper deals with the improvement of learning speed based on the analysis of convergence of the feedback error learning method. We derive and obtain the condition for the asymptotic convergence of the feedback error learning method for each trial. This condition is the relationship between the learning rate and the α function, which is calculated from the input-output relationship of the system. Using the α function, we propose a high-speed learning method for a tracking control system. We present the simulation results for the tracking control system of a one-link robot manipulator for two cases as follows : (1) use of the general feedback error learning method and (2) use of the proposed high-speed learning method. The simulation results show the effectiveness of the proposed conditions and learning method.

Flexibility Control of Flexible Structures. 5th Report. Position and Orientation Control of Flexible Plate Using Neural Network.

This paper deals with modeling and control problems of the three joints robot handling a flexible plate in the vertical plane under gravity. The dynamics model is obtained using Hamilton's principle, and the ordinary differential equations are obtained using modal analysis. According to the desired tip position and orientation, we present an iterative algorithm to solve the inverse kinematics. The design method of the feedforward position and orientation control system is presented in two ways : ( 1 ) By solving the inverse dynamics based on the desired trajectory, we can obtain the desired torque. ( 2 ) By the use of neural networks, we can obtain the desired torque. The second method involves the use of four three-layer neural networks to reduce the feedback errors of three joints angles and the first bending vibration based on the feedback error learning method with the desired trajectories including the static bending deflection curve. We present trajectory control results for both methods. A comparison between the two methods is presented in this paper. From the simulation results, the second method, using neural networks, is useful for reducing position and orientation errors. Moreover, the second method has ability to learn and thus improve control performance against some parameter errors in the model.

Flexibility Control of Flexible Structures. 6th Report. Asymptotic Covergence of Learning Process in Neural Network Controller Considering Spillover.

This paper deals with trajectory control of a flexible plate handling system using the neural network learning method. The conditions for the asymptotic convergence of the feedback error learning method for each trial are obtained. The influence of vibration modes not modeled on the conditions for the asymptotic convergence is discussed. Based on the result, obtained here, we present a fast learning method for trajectory control of a flexible plate handling system. The control system consists of a low-pass filter and two neural networks. The learning method is to change the learning rate according to the convergence conditions. A one-joint robot handling flexible plate is simulated, and the simulation results show the effectiveness of the proposed conditions and learning method.