\r\na cascade control system for an underactuated mechanical system.

\r\nCascade control structures usually include two control algorithms

\r\n(inner and outer). To design such a control system properly, the

\r\nfollowing conflicting objectives should be considered at the same

\r\ntime: 1) the inner closed-loop control must be faster than the outer

\r\none, 2) the inner loop should fast reject any disturbance and prevent

\r\nit from propagating to the outer loop, 3) the controlled system

\r\nshould be insensitive to measurement noise, and 4) the controlled

\r\nsystem should be driven by optimal energy. Such a control problem

\r\ncan be formulated as a multi-objective optimization problem such

\r\nthat the optimal trade-offs among these design goals are found.

\r\nTo authors best knowledge, such a problem has not been studied

\r\nin multi-objective settings so far. In this work, an underactuated

\r\nmechanical system consisting of a rotary servo motor and a ball

\r\nand beam is used for the computer simulations, the setup parameters

\r\nof the inner and outer control systems are tuned by NSGA-II

\r\n(Non-dominated Sorting Genetic Algorithm), and the dominancy

\r\nconcept is used to find the optimal design points. The solution of

\r\nthis problem is not a single optimal cascade control, but rather a set

\r\nof optimal cascade controllers (called Pareto set) which represent the

\r\noptimal trade-offs among the selected design criteria. The function

\r\nevaluation of the Pareto set is called the Pareto front. The solution

\r\nset is introduced to the decision-maker who can choose any point

\r\nto implement. The simulation results in terms of Pareto front and

\r\ntime responses to external signals show the competing nature among

\r\nthe design objectives. The presented study may become the basis for

\r\nmulti-objective optimal design of multi-loop control systems.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 161, 2020"}