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In this paper, a new type of iterative learning control systems with fractional order known as iterative learning control with fractional order derivative and iterative learning control with fractional proportional–derivative for linearized systems of single-link robot arm is introduced. First order derivative of classic Arimoto is used for tracking error in updating law of derivative iterative learning control. Suggested method in this paper implement tracking error for updating control law of iterative learning of fractional order. For the first time, nonlinear robot system is linearized by input feedback linearization. Then, convergence analysis of iterative learning control law of type PD^alpha is studied.In the next step, we define a criteria for parameters optimization of proposed controller by using Biogeography-based optimization algorithm. Both updating law of fractional order iterative learning control (D^alpha-type ILC and PD^alpha-type ILC) is applied on linearized robot arm and performance of both controller for different value of alpha is presented. For improving the performance of closed loop system, coefficient of fractional order iterative learning control (proportional and derivative coefficients) is optimized by BBO algorithm. Proposed iterative learning control is compared with common type of system.

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Numerous studies have been devoted to motion control of wheeled mobile robots in recent years. Among them, trajectory tracking has received much attention.. A feed-forward and feedback control structure for trajectory tracking is used to circumvent the limitation of Brockett’s theorem. Feed-forward control is calculated according to the reference trajectory, it can not compensate instrumentation and initial state errors, therefore a feedback controller is utilized as well. In this paper a model predictive controller is used as the feedback controller. Since the initial state is not often matched to the desired trajectory, rapid tracking of the trajectory in early steps is very important. In this paper a model predictive controller with laguerre functions and another one with exponential data weighting is used to reduce tracking error in early steps. According to simulation results, reference trajectory tracking is improved through laguerre functions in model predictive controller.