P-type Iterative Learning for Non-parameterized Systems with Uncertain Local Lipschitz Terms

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 152
Author(s):  
Dongqi Ma ◽  
Hui Lin

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.


Author(s):  
J. H. Wu ◽  
H Ding

This paper studies the repetitive motion control of a high-acceleration and high-precision platform driven by linear motors. The control scheme comprises an anticipatory iterative learning control (A-ILC) component and a cascaded control structure including an inner-loop velocity PI controller and an outer-loop position P controller. During the motion process, the cascaded controller remains invariant while the A-ILC adjusts the reference command cycle by cycle to achieve better performance. Experiments are carried out to validate the proposed control structure. The results confirm that the proposed control scheme can improve the system performance significantly in both low-speed trajectory tracking motions and fast point-to-point motion. In the experiments, P-type and D-type ILCs are also utilized to adjust the reference command. Compared with the A type, P-type ILC leads to larger tracking error bounds and D-type ILC lacks a fast convergence rate for low-speed motions, while for fast point-to-point motion these two types of ILC are unable to work well.


Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Yun-Shan Wei ◽  
Qing-Yuan Xu

For linear discrete-time systems with randomly variable input trail length, a proportional- (P-) type iterative learning control (ILC) law is proposed. To tackle the randomly variable input trail length, a modified control input at the desirable trail length is introduced in the proposed ILC law. Under the assumption that the initial state fluctuates around the desired initial state with zero mean, the designed ILC scheme can drive the ILC tracking errors to zero at the desirable trail length in expectation sense. The designed ILC algorithm allows the trail length of control input which is different from system state and output at a specific iteration. In addition, the identical initial condition widely used in conventional ILC design is also mitigated. An example manifests the validity of the proposed ILC algorithm.


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