Algorithm Research Of Iterative Learning Control For A Class Of Singular Systems

ILC (Iterative Learning Control) is a new control algorithm, which does not rely on theaccurate mathematical model of dynamic systems. Its application objects are like industrialrobots controlled systems with the repetitive nature of sports and its aim is achieving aentirely tracking task in a limited time interval. The singular system is a more general systemform, which is a power system with numerous applications. And the singular system model isused to describe many practical systems with more convenient and natural, such as crosslinked system, economic systems, electronic networks, power system and chemicalengineering. So far, however, the majority of ILC research results are based on the regularjustice system, and the application research of ILC method to the singular system is less. Inthis paper, based on the singular value decomposition of singular systems, ILC problem of aclass of singular systems is studied.The main works are shown as follows:1. Based on singular value decomposition, for a class of singular systems, a newopen-loop ILC algorithm for singular system is proposed in this paper, which is a mixture ofD-type algorithm and P-type algorithm and its complete convergence analysis is given.Numerical simulation examples show that, the new algorithm in this paper is effective.2. Based on the open-loop ILC algorithm for singular, a closed-loop ILC algorithm forsingular system is designed.And its convergence conditions are given. Then, its convergenceis proved.3. Based on the thinking of the algorithm with forgetting factor and the research resultsof the open-loop algorithm, for singular system, the thought that the forgetting factor is afunction of the number of iterations is given in this paper, and ILC algorithm with forgettingfactor for singular system is proposed. Simulation results show that, under the reasonablechoice of forgetting factor, the ILC algorithm with forgetting factor for singular system iseffective. Compared to ordinary algorithm, the error tracking curve of the algorithm withforgetting factor which has certain superiorities in iteration error tracking is smoother.4. Taking into the actual industrial engineering, systems with control delay are common.The proposed research results for singular system are applied to a class of singular systems with control delay, and a similar new algorithm is proposed. Furthermore, the result thatunder certain conditions when the iteration numbers gradually increase the system output canasymptotically track the desired output is proved. And the theoretical results are verified withnumerical examples.