Iteration dependent interval based open‐closed‐loop iterative learning control for time varying systems with vector relative degree

Abstract

For linear time varying (LTV) multiple input multiple output (MIMO) systems with vector relative degree, an open‐closed‐loop iterative learning control (ILC) strategy is developed in this article, where the time interval of operation is iteration dependent. To compensate the missing tracking signal caused by iteration dependent interval, the feedback control is introduced in ILC design. As the tracking signal of many continuous iterations is lost in a certain interval, the feedback control part can employ the tracking signal of current iteration for compensation. Under the assumption that the initial state vibrates around the desired initial state uniformly in mathematical expectation sense, the expectation of ILC tracking error can converge to zero as the number of iteration tends to infinity. Under the circumstance that the initial state varies around the desired initial state with a bound, as the number of iteration tends to infinity, the expectation of ILC tracking error can be driven to a bounded range, whose upper bound is proportional to the fluctuation. It is revealed that the convergence condition is dependent on the feedforward control gains, while the feedback control can accelerate convergence speed by selecting appropriate feedback control gains. As a special case, the controlled system with integrated high relative degree is also addressed by proposing a simplified iteration dependent interval based open‐closed‐loop ILC method. Finally, the effectiveness of the developed iteration dependent interval based open‐closed‐loop ILC is illustrated by a simulation example with two cases on initial state.

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