{"title":"Multi-Objective Optimal Design of a Cascade Control System for a Class of Underactuated Mechanical Systems","authors":"Yuekun Chen, Yousef Sardahi, Salam Hajjar, Christopher Greer","volume":161,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":231,"pagesEnd":238,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10011222","abstract":"This paper presents a multi-objective optimal design of<br \/>\r\na cascade control system for an underactuated mechanical system.<br \/>\r\nCascade control structures usually include two control algorithms<br \/>\r\n(inner and outer). To design such a control system properly, the<br \/>\r\nfollowing conflicting objectives should be considered at the same<br \/>\r\ntime: 1) the inner closed-loop control must be faster than the outer<br \/>\r\none, 2) the inner loop should fast reject any disturbance and prevent<br \/>\r\nit from propagating to the outer loop, 3) the controlled system<br \/>\r\nshould be insensitive to measurement noise, and 4) the controlled<br \/>\r\nsystem should be driven by optimal energy. Such a control problem<br \/>\r\ncan be formulated as a multi-objective optimization problem such<br \/>\r\nthat the optimal trade-offs among these design goals are found.<br \/>\r\nTo authors best knowledge, such a problem has not been studied<br \/>\r\nin multi-objective settings so far. In this work, an underactuated<br \/>\r\nmechanical system consisting of a rotary servo motor and a ball<br \/>\r\nand beam is used for the computer simulations, the setup parameters<br \/>\r\nof the inner and outer control systems are tuned by NSGA-II<br \/>\r\n(Non-dominated Sorting Genetic Algorithm), and the dominancy<br \/>\r\nconcept is used to find the optimal design points. The solution of<br \/>\r\nthis problem is not a single optimal cascade control, but rather a set<br \/>\r\nof optimal cascade controllers (called Pareto set) which represent the<br \/>\r\noptimal trade-offs among the selected design criteria. The function<br \/>\r\nevaluation of the Pareto set is called the Pareto front. The solution<br \/>\r\nset is introduced to the decision-maker who can choose any point<br \/>\r\nto implement. The simulation results in terms of Pareto front and<br \/>\r\ntime responses to external signals show the competing nature among<br \/>\r\nthe design objectives. 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