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

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.