Abstract
In this paper, iterative learning control (ILC) is combined with an optimal fractional order derivative (BBO-Da-type ILC) and optimal fractional and proportional-derivative (BBO-PDa-type ILC). In the update law of Arimoto's derivative iterative learning control, a first order derivative of tracking error signal is used. In the proposed method, fractional order derivative of the error signal is stated in term of 'sa' where  to update iterative learning control law. Two types of fractional order iterative learning control namely PDa-type ILC and Da-type ILC are gained for different value of a. In order to improve the performance of closed-loop control system, coefficients of both  and  learning law i.e. proportional , derivative  and  are optimized using Biogeography-Based optimization algorithm (BBO). Outcome of the simulation results are compared with those of the conventional fractional order iterative learning control to verify effectiveness of BBO-Da-type ILC and BBO-PDa-type ILC
Highlights
Learning is a characteristic of living creatures, human beings among them
Each suitability index variables (SIVs) of PD -type iterative learning control (ILC) controller consists of three parameters, kP, and kD
A similar result is achieved for PD -type ILC when the maximum convergence speed occurs at iteration 14 (Fig. 11), whereas the Biogeography-Based optimization algorithm (BBO) designed PD -type ILC occurs in 4 iterations (Fig. 14)
Summary
Learning is a characteristic of living creatures, human beings among them. Several endeavors have been made to extend this learning ability to engineering systems in design and construction. Intelligent iterative learning control falls into the intelligent control category This involves new techniques to control iterative processes in certain amounts of time. In such control algorithms, the controller learns from its past experiences (iterations) to update itself to improve the performance of the closed loop system. Iteration-based systems use the ability to learn and appropriate tuning of the input to perform a repetitive operation, the iteration process is time and cost consuming. Various research was performed in the field of fractional calculus and its controllers It is because such controllers are more flexible in comparison with integer order ones. Other applications of biogeography-based optimization can be mentioned as reduction of movement estimation time in video [22], dynamic deployment of wireless sensor networks [23], solving the problem of economic load dispatch [24] and optimal dispatch in the power systems [25]
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