PD-type Iterative Learning Control Algorithm Research Articles

Research on iterative learning control of lower limb exoskeleton of rehabilitation robot

It is difficult to establish an accurate mathematical model for the lower limb exoskeleton system of a rehabilitation robot, and there are unknown external disturbances. In this paper, an accurate model-independent closed-loop PD-type iterative learning control algorithm is adopted, which enables the system to track a given desired trajectory with uncertain dynamic models and parameters. The simulation results show that the algorithm can effectively improve the control accuracy of the trajectory tracking of the lower limb exoskeleton.

ILC for Non-Linear Hyperbolic Partial Difference Systems

This paper discusses the iterative learning control problem for a class of non-linear partial difference system hyperbolic types. The proposed algorithm is the PD-type iterative learning control algorithm with initial state learning. Initially, we introduced the hyperbolic system and the control law used. Subsequently, we presented some dilemmas. Then, sufficient conditions for monotone convergence of the tracking error are established under the convenient assumption. Furthermore, we give a detailed convergence analysis based on previously given lemmas and the discrete Gronwall’s inequality for the system. Finally, we illustrate the effectiveness of the method using a numerical example.

PD-Type Iterative Learning Control with Adaptive Learning Gains for High-Performance Load Torque Tracking of Electric Dynamic Load Simulator

To realize the high-performance load torque tracking of an electric dynamic load simulator system with random measurement noises and strong position disturbances, a PD-type iterative learning control (ILC) algorithm with adaptive learning gains is proposed in this paper. With the principle of system analyzing, a nonlinear discrete state-space model is established. The adaptive learning gains is used to suppress the effects of periodic disturbances and random measurement noises on the load torque tracking performance. A traditional PD feedback controller in parallel with the proposed ILC is designed to stabilize the system and render the ILC converge quickly. The convergence analysis of the proposed control method ensures the stability of the system. Compared with the fixed learning gains, the experiment results show that the proposed control method has better load torque tracking performance and can effectively suppress the adverse effects of periodic and aperiodic disturbances on tracking accuracy.

Mixed PD-Type Iterative Learning Control Algorithm for a Class of Parabolic Singular Distributed Parameter Systems

In this paper, the iterative learning control (ILC) problem is investigated for a class of time-invariant parabolic singular distributed parameter systems. Initially, the singular distributed parameter systems is decomposed into infinite number of singular systems based on the separation principle. Meanwhile, the slow-fast subsystems are introduced via singular value decomposition method. Then, a novel mixed PD-type ILC algorithm with finite dimension is designed for the low dimensional slow part and the corresponding convergence conditions are manifested. With the proposed controller, the output error of high dimensional fast complement can satisfy the given value instead of neglecting the effect of high dimensional modes. Furthermore, under the aforesaid ILC law and the appropriate number of the low dimensional slow part, the resulting tracking error of parabolic singular distributed parameter systems can converge to any small tracking accuracy. Finally, simulation results on the distributed building automatic temperature system verify the convergence and effectiveness of the mixed PD-type ILC algorithm.

PD-Type Iterative Learning Control for Uncertain Spatially Interconnected Systems

This paper puts forward a PD-type iterative learning control algorithm for a class of discrete spatially interconnected systems with unstructured uncertainty. By lifting and changing the variable of discrete space model, the uncertain spatially interconnected systems is converted into equivalent singular system, and the general state space model is derived in view of singular system theory. Then, the state error and output error information are used to design the iterative learning control law, transforming the controlled system into an equivalent repetitive process model. Based on the stability theory of repetitive process, sufficient condition for the stability of the system along the trial is given in the form of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed algorithm is verified by the simulation of ladder circuits.

A PD-type Iterative Learning Control Algorithm for One-dimension Linear Wave Equation

Many applications can be described by the wave equation, as a kind of important second order partial differential equations. This paper suggests applying PD-type iterative learning control (ILC) scheme with initial state learning (ISL) to a class of linear one-dimensional wave equation. A sufficient condition is given to insure the convergence of the tracking errors. Finally, a numerical simulation is presented to illustrate the efficiency of the proposed method.

Iterative learning control for distributed parameter systems based on non-collocated sensors and actuators

In this paper, an open-loop PD-type iterative learning control ( ILC ) scheme is first proposed for two kinds of distributed parameter systems ( DPSs ) which are described by parabolic partial differential equations using non-collocated sensors and actuators. Then, a closed-loop PD-type ILC algorithm is extended to a class of distributed parameter systems with a non-collocated single sensor and m actuators when the initial states of the system exist some errors. Under some given assumptions, the convergence conditions of output errors for the systems can be obtained. Finally, one numerical example for a distributed parameter system with a single sensor and two actuators is presented to illustrate the effectiveness of the proposed ILC schemes.

Consensus Tracking by Iterative Learning Control for Linear Heterogeneous Multiagent Systems Based on Fractional-Power Error Signals

This paper deals with the consensus tracking problem of heterogeneous linear multiagent systems under the repeatable operation environment, and adopts a proportional differential (PD)-type iterative learning control (ILC) algorithm based on the fractional-power tracking error. According to graph theory and operator theory, convergence condition is obtained for the systems under the interconnection topology that contains a spanning tree rooted at the reference trajectory named as the leader. Our algorithm based on fractional-power tracking error achieves a faster convergence rate than the usual PD-type ILC algorithm based on the integer-order tracking error. Simulation examples illustrate the correctness of our proposed algorithm.

A PD-Type Iterative Learning Algorithm for Semi-Linear Distributed Parameter Systems With Sensors/Actuators

In this paper, the control problem of semi-linear distributed parameter system (DPS) with sensors/actuators is considered using iterative learning control (ILC) method. During the learning process, the output signals of the system exist random data dropout which is described as a Bernoulli random variable. Then, a novel intermittent updating PD-type ILC algorithm is proposed on the basis of the available output information. In this kind ILC algorithm, the scheme only updates its control signal when the output signal is successfully transmitted. Hence, the intermittent updating PD-type ILC algorithm is presented for a semi-linear parabolic DPS based on single sensor and single actuator, and the convergence condition of the output error is obtained by using Bellman-Gronwall lemma and semigroup theory under some given assumptions. Secondly, this kind PD-type ILC law is extended to control the semi-linear DPS with multiple sensors and multiple actuators. Lastly, one example is given to demonstrate the effectiveness of the proposed scheme.

A PD-type iterative learning control algorithm for singular discrete systems

Based on a specific decomposition of discrete singular systems, in this paper, we study the problem of state tracking control by using PD-type algorithm of iterative learning control. The convergence conditions and theoretical analysis of the PD-type algorithm are presented in detail. An illustrative example supporting the theoretical results and the effectiveness of the PD-type iterative learning control algorithm for discrete singular systems is shown at the end of the paper.

A PD-Type Iterative Learning Control for a Class of Switched Discrete-Time Systems with Model Uncertainties and External Noises

A PD-type iterative learning control algorithm is applied to a class of linear discrete-time switched systems for tracking desired trajectories. The application is based on assumption that the switched systems repetitively operate over a finite time interval and the switching rules are arbitrarily prespecified. By taking advantage of the super-vector approach, a sufficient condition of the monotone convergence of the algorithm is deduced when both the model uncertainties and the external noises are absent. Then the robust monotone convergence is analyzed when the model uncertainties are present and the robustness against the bounded external noises is discussed. The analysis manifests that the proposed PD-type iterative learning control algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily preset switching rules. The attached simulations support the feasibility and the effectiveness.

PD-Type ILC Algorithm Research with Forgetting Factor for a Class of Linear Systems with Multiple Time Delays

Based on iterative learning control (ILC) algorithm with forgetting factor, the thought that the forgetting factor is a function of iteration numbers is proposed in this paper, which has simplified the convergence conditions. And the convergence analysis is given. Then, the study results of this paper are applied to a class of linear systems with multiple time delays and simulation results show that, under the improvements of the convergence conditions and the reasonable choice of forgetting factor function, the PD-type iterative learning control algorithm with forgetting factor applied to the linear systems with multiple time delays in this paper has effectiveness and superiority.