In non-linear system, the control problem has been a hot spot and a difficult issue as well. It is well known that non-linear systems are very difficult to control and the controllers are still difficult to design even based on modern control theory. However, as for repetitive non-linear systems, such as robotic manipulators, iterative learning control (ILC) is a simple and effective approach to solve control problems of such systems. ILC can improve the tracking accuracy between the real output and desired output over a fixed period of interval.In order to improve the robustness of iterative learning control and increase the practicability of its engineering, the D-type iterative learning control method is applied firstly to design learning law. And then it verifies that the iterative learning control is very effective for the planar 2-dof manipulator system which owns property of repetitiveness. What's more, on the base of the D-type learning law and the initial state learning, the D-type learning law with initial state learning is designed. Because the system contains the initial state migration, the influence cannot be eliminated by learning law itself with the increase of iteration times, so the output cannot track the desired trajectory, either. Even though this method can eliminate the effects of the initial state migration, the speed of tracking convergence is badly affected. This also limits its practical application. As a result, considered the advantage of D-type learning law with exponent variable gain in convergence speed and coupled with initial state learning, D-type learning law with exponent variable gain and initial state learning is obtained which can eliminate the impact of the initial state migration on tracking performance and improve the convergence speed of the algorithm.The planar 2-dof manipulator is designed as the controlled object, when improving the learning law. Therefore, we apply the Matlab software to get the simulation analysis. The results show that D-type iterative learning control can reduce the trajectory tracking error gradually along with the increase of the number of iterations until achieves exactly tracking. When set initial state error artificially, output will be stable as a constant value error compared to desired trajectory with the increase of the number of iterations. The D-type iterative learning control with initial state learning can suppress initial state migration perfectly, but the convergence speed is influenced. D-type learning law with exponent variable gain and initial state learning, can not only achieve perfect tracking for expected trajectory in the case of initial state migration, but also accelerate the convergence speed and enhances the robustness of the iterative learning control. |