scholarly journals Convergence Analysis of Iterative Learning Control for Two Classes of 2-D Linear Discrete Fornasini–Marchesini Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Kai Wan
Keyword(s):  
Convergence Analysis ◽  
Iterative Learning Control ◽  
Three Dimensional ◽  
Discrete Systems ◽  
Learning Control ◽  
Iterative Learning ◽  
Linear Matrix ◽  
Direct Transmission ◽  
Learning Gain ◽  
Linear Discrete Systems

This paper first investigates convergent property of two iterative learning control (ILC) laws for two kinds of two-dimensional linear discrete systems described by the first Fornasini–Marchesini model (2-D LDFFM with a direct transmission from inputs to outputs and 2-D LDFFM with input delay). Different from existing ILC results for 2-D LDFFM, this paper provides convergence analysis in a three-dimensional (3-D) framework. By using row scanning approach (RSA) or column scanning approach (CSA), it is theoretically proved no matter which method is adopted, perfect tracking on the desired reference surface is accomplished. In addition, linear matrix inequality (LMI) technique is utilized to computer the learning gain of the ILC controller. The effectiveness and feasibility of the designed ILC law are illustrated through numerical simulation on a practical thermal process.

scholarly journals Accelerated Iterative Learning Control of Speed Ripple Suppression for a Seeker Servo Motor

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 152
Author(s):  
Dongqi Ma ◽  
Hui Lin
Keyword(s):  
Permanent Magnet ◽  
Iterative Learning Control ◽  
Mathematical Proof ◽  
Permanent Magnet Synchronous Motor ◽  
Learning Control ◽  
Synchronous Motor ◽  
Iterative Learning ◽  
Learning Gain ◽  
Periodic Load ◽  
P Type

To suppress the speed ripple of a permanent magnet synchronous motor in a seeker servo system, we propose an accelerated iterative learning control with an adjustable learning interval. First, according to the error of current iterative learning for the system, we determine the next iterative learning interval and conduct real-time correction on the learning gain. For the learning interval, as the number of iterations increases, the actual interval that needs correction constantly shortens, accelerating the convergence speed. Second, we analyze the specific structure of the controller while applying reasonable assumptions pertaining to its condition. Using the λ-norm, we analyze and apply our mathematical knowledge to obtain a strict mathematical proof on the P-type iterative learning control and obtain the condition of convergence for the controller. Finally, we apply the proposed method for periodic ripple inhibition of the torque rotation speed of the permanent magnet synchronous motor and establish the system model; we use the periodic load torque to simulate the ripple torque of the synchronous motor. The simulation and experimental results indicate the effectiveness of the method.

scholarly journals Application of Norm Optimal Iterative Learning Control to Quadrotor Unmanned Aerial Vehicle for Monitoring Overhead Power System

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3223
Author(s):  
Husam A. Foudeh ◽  
Patrick Luk ◽  
James Whidborne
Keyword(s):  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Power Lines ◽  
Learning Gain ◽  
Good Convergence ◽  
Gain Variation ◽  
Exogenous Disturbances ◽  
Gradient Based ◽  
Overhead Power Lines

Wind disturbances and noise severely affect Unmanned Aerial Vehicles (UAV) when monitoring and finding faults in overhead power lines. Accordingly, we propose repetitive learning as a new solution for the problem. In particular, the performance of Iterative Learning Control (ILC) that are based on optimal approaches are examined, namely (i) Gradient-based ILC and (ii) Norm Optimal ILC. When considering the repetitive nature of fault-finding tasks for electrical overhead power lines, this study develops, implements and evaluates optimal ILC algorithms for a UAV model. Moreover, we suggest attempting a learning gain variation on the standard optimal algorithms instead of heuristically selecting from the previous range. The results of both simulations and experiments of gradient-based norm optimal control reveal that the proposed ILC algorithm has not only contributed to good trajectory tracking, but also good convergence speed and the ability to cope with exogenous disturbances such as wind gusts.

Iterative learning control with complex conjugate gradient optimization algorithm for multiaxial road durability test rig

2018 ◽  
Vol 233 (7) ◽  
pp. 2349-2360 ◽  
Author(s):  
Xiao Wang ◽  
Dacheng Cong ◽  
Zhidong Yang ◽  
Shengjie Xu ◽  
Junwei Han
Keyword(s):  
Conjugate Gradient ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Gradient Algorithm ◽  
Complex Conjugate ◽  
Test Rig ◽  
Learning Gain ◽  
Durability Test ◽  
Optimal Learning

Service load replication performed on multiaxial hydraulic test rigs has been widely applied in automotive engineering for durability testing in laboratory. The frequency-domain off-line iterative learning control is used to generate the desired drive file, i.e. the input signals which drive the actuators of the test rig. During the iterations an experimentally identified linear frequency-domain system model is used. As the durability test rig and the specimen under test have a strong nonlinear behavior, a large number of iterations are needed to generate the drive file. This process will cause premature deterioration to the specimen unavoidably. In order to accelerate drive file construction, a method embedding complex conjugate gradient algorithm into the conventional off-line iterative learning control is proposed to reproduce the loading conditions. The basic principle and monotone convergence of the method is presented. The drive signal is updated according to the complex conjugate gradient and the optimal learning gain. An optimal learning gain can be obtained by an estimate loop. Finally, simulations are carried out based on the identified parameter model of a real spindle-coupled multiaxial test rig. With real-life spindle forces from the wheel force transducer in the proving ground test to be replicated, the simulation results indicate that the proposed conventional off-line iterative learning control with complex conjugate gradient algorithm allows generation of drive file more rapidly and precisely compared with the state-of-the-art off-line iterative learning control. Few have been done about the proposed method before. The new method is not limited to the durability testing and can be extended to other systems where repetitive tracking task is required.

scholarly journals Novel Fuzzy PID-Type Iterative Learning Control for Quadrotor UAV

Sensors ◽  
2018 ◽  
Vol 19 (1) ◽  
pp. 24 ◽  
Author(s):  
Jian Dong ◽  
Bin He
Keyword(s):  
Fuzzy Control ◽  
Iterative Learning Control ◽  
Control Method ◽  
External Disturbance ◽  
Learning Control ◽  
Iterative Learning ◽  
System Stability ◽  
Learning Gain ◽  
Control Precision ◽  
Quadrotor Aircraft

Due to the under-actuated and strong coupling characteristics of quadrotor aircraft, traditional trajectory tracking methods have low control precision, and poor anti-interference ability. A novel fuzzy proportional-interactive-derivative (PID)-type iterative learning control (ILC) was designed for a quadrotor unmanned aerial vehicle (UAV). The control method combined PID-ILC control and fuzzy control, so it inherited the robustness to disturbances and system model uncertainties of the ILC control. A new control law based on the PID-ILC algorithm was introduced to solve the problem of chattering caused by an external disturbance in the ILC control alone. Fuzzy control was used to set the PID parameters of three learning gain matrices to restrain the influence of uncertain factors on the system and improve the control precision. The system stability with the new design was verified using Lyapunov stability theory. The Gazebo simulation showed that the proposed design method creates effective ILC controllers for quadrotor aircraft.

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