Parameter optimisation in iterative learning control

International Journal of Control

Owens

2005

104

This paper considers the robustness of an inverse iterative learning control algorithm. A simple learning gain results in robust convergence that is monotonic in the least squares sense provided that the multiplicative plant uncertainty satisfies a matrix positivity requirement. The results are extended to the frequency domain using a simple graphical Nyquist test. The analysis extends naturally to a parameter-optimal control setting. Non-monotone convergence is considered by using a simple weighted norm based on exponential weighting of time series.

Section: The Inverse Model Algorithmmentioning

confidence: 93%

Section: Inverse Type Parameter Optimal Ilcmentioning

confidence: 99%

Discrete-time inverse model-based iterative learning control: stability, monotonicity and robustness

Harte

International Journal of Control

Owens

2005

104

“…This leads to the concept of parameteroptimal ILC, which is discussed in detail in Reference [11]. Note that the analysis here considers monotonic convergence only in the l 2 -norm.…”

mentioning

confidence: 99%

“…0 as t s ! 1: Hence, as is discussed in Reference [11], the matrix G e in (7) becomes diagonal, and positivity is guaranteed if CG > 0: Thus by increasing the sampling time, an originally non-positive definite plant can be conditioned to become positive asymptotically. This result is illustrated experimentally in Section 10 using an aliasing approach, which 'artificially' decreases the sampling rate.…”

mentioning

confidence: 99%

P-type iterative learning control for systems that contain resonance

Ratcliffe

Int. J. Adapt. Control Signal Process.

Lewin

et al. 2005

The effect of iterative learning control (ILC) on a plant containing resonance has been experimentally investigated using an industrial gantry robot. The plant is controlled by a PID controller and a P-type learning controller in a parallel configuration. It is demonstrated that the learning controller can cause the amplitude of resonant frequencies to grow at each trial, leading to instability. The reasons for this growth are analysed both theoretically and experimentally. In order to solve the problem with a resonance, a straightforward aliasing technique is developed which is experimentally shown to suppress the increase of resonant amplitudes. The novel aliasing technique is compared with three filtering methods, the aliasing technique giving the best experimental performance. Finally, it is found that additional velocity feedback combined with the aliasing technique can further help to limit the effect of residual resonance. Due to the straightforward implementation of these algorithms, they should be highly applicable to industrial systems.

“…Without loss of generality (see [6]), it will be assumed that CG > 0 and that system (1) is controllable and observable.…”

Section: Introductionmentioning

confidence: 99%

Robustness analysis of an adjoint optimal iterative learning controller with experimental verification

Ratcliffe

Intl J Robust & Nonlinear

Lewin

et al. 2007

SUMMARYA new modification to the steepest-descent algorithm for discrete-time iterative learning control is developed for plant models with multiplicative uncertainty. A theoretical analysis of the algorithm shows that if a tuning parameter is selected to be sufficiently large, the algorithm will result in monotonic convergence provided the plant uncertainty satisfies a positivity condition. This is a major improvement when compared to the standard version of this algorithm, which lacks a mechanism for finding a balance between convergence speed and robustness. The proposed algorithm has been investigated experimentally on an industrial gantry robot and found to display a high degree of robustness to both plant modelling error and initial state error. The algorithm also exhibits both long-term performance and excellent tracking performance, as demonstrated by experimental tests of up to 4000 iterations. To further examine robustness, the plant has been approximated by simple models including one consisting of an integrator and a gain. A simple tuning rule for this reduced model is proposed, which generates a stable system with a good rate of convergence. The robustness properties of the steepest descent algorithm have then been experimentally verified.