First-order D-type iterative learning control for multivariable systems with unknown relative degree

D-type iterative learning control (ILC) law is one of the main laws of ILC. D-type ILC law depends on the relative degree of the controlled system. High order ILC law is difficult to realize, and will enhance the effect of the noise. A design method of first-order D-type ILC is presented for multivariable systems with unknown relative degree. A dummy system with unit vector relative degree can be constructed by series and parallel connected first-order subsystem with the multivariable controlled system with unknown vector relative degree. The dummy system can track the desired trajectory completely under the action of the first-order D-type ILC, and the actual controlled system can realize asymptotic tracking along the desired trajectory within a certain error scope. The gain of the D-type ILC law does not depend on the parameters of the controlled system. The simulation example demonstrates the feasibility and effectiveness of the presented method.