Modified Quasi-Newton Optimization Algorithm-Based Iterative Learning Control for Multi-Axial Road Durability Test Rig

Abstract

The iterative learning control (ILC) based on the linear frequency-domain model has been employed to replicate the road conditions for the vehicle durability testing in the laboratory. Generally, the vehicle and the multi-axial hydraulic test rig behave strong nonlinearities, which requires a large number of iterations to correct the tracking error. Hence, the process of drive file (i.e., the input signals which drive the actuators of the test rig) generation is time-lengthy and tedious. A method that combines the ILC with the Quasi-Newton algorithm over the complex space (QNILC) is developed to speed up the drive file construction for the multi-axial vibration test rig. The impedance matrix can be updated with Broyden's method to reduce the modeling errors and make the iteration more robust. An auxiliary estimating loop is inserted into the iteration process to attain an optimal learning gain. The convergence of the proposed method has been proven to be monotonic. This approach is validated through simulation, where the target signals are the real-life spindle forces gathered from the wheel force transducer. The simulation results demonstrate that the QNILC can improve the convergence rate and increase the tracking accuracy than the current offline ILC. The QNILC reduces the iteration number from nine down to five to converge to the desirable index compared with the offline ILC using gain 0.5. The new method based on the optimization algorithm can extend to other repetitive tracking processes. INDEX TERMS Road durability testing, iterative learning control, Broyden's method, optimal learning gain, the multi-axial road test rig.

Iterative Learning Control Based on Nesterov Accelerated Gradient Method

“…In the end, two simulation examples are given to verify the theoretical results. Although the quasi-Newton-type ILC algorithms have been proposed in [19], [20], these algorithms are still often slow in practice.…”

“…iterations increases. In [17]- [20], as effective optimization techniques, the Newton method and quasi-Newton method have been used to construct the optimal ILC laws. Moreover, a gradient-type ILC algorithm was designed in [21] for a class of linear discrete-time systems, then a complete analysis of the robust monotone convergence of the algorithm was presented with the help of necessary and sufficient matrix inequalities and frequency domain conditions.…”

Neuro-fuzzy iterative learning control for 4-poster test rig

“…In these studies, the weighting coefficient is updated with an adaptation rule, which is a function of the error ratio of previous trials. To update ILC gain, numerical optimization methods are used, such as Newton Method in Lin and Owens (2007), Quasi-Newton Method in Wang et al (2019b), complex conjugate direction method in Wang et al (2019a). The main advantage of the optimization-based ILC methods is that these methods can be easily applied to conventional inverse model-based ILC algorithms and satisfy monotonic convergence.…”

Novel Generalized Predictive Iterative Learning Speed Controller for Ultrasonic Motors

“…Thus the cost of the system is increased. Different from the above control strategies, iterative learning control [5] is unique in modern control theory because of its concise and efficient learning ability. In the repeated operation processes, ILC adopts the iterative method to make the change trail of the control variable gradually tend to the expected trail according to the previous information.…”