NPID-type ILC with two nonlinear integral actions for a class of nonlinear systems

In this paper, we presents a new NPID-type iterative learning control law with two nonlinear integral action for a class of nonlinear systems, denoted NP-D-I^NPD, which is composed by the linear combination of the derivative control mode, nonlinear control mode shaped by a nonlinear function of error, and two nonlinear integral control modes driven by a nonlinear function of error and a nonlinear differential feedback of error, respectively. By using Bellman-Gronwall lemma, the simple explicit conditions on the learning gains to ensure convergence are provided in the sense of Lambda norm. An attractive feature of the new NP-D-I^NPD-type iterative learning law is that it is of faster convergence speed, better flexibility and higher accuracy. The simulation examples demonstrate the effectiveness and advantage of NPID-type iterative learning laws with two nonlinear integral actions.