Abstract: This paper presents a multi-objective optimal design of
a cascade control system for an underactuated mechanical system.
Cascade control structures usually include two control algorithms
(inner and outer). To design such a control system properly, the
following conflicting objectives should be considered at the same
time: 1) the inner closed-loop control must be faster than the outer
one, 2) the inner loop should fast reject any disturbance and prevent
it from propagating to the outer loop, 3) the controlled system
should be insensitive to measurement noise, and 4) the controlled
system should be driven by optimal energy. Such a control problem
can be formulated as a multi-objective optimization problem such
that the optimal trade-offs among these design goals are found.
To authors best knowledge, such a problem has not been studied
in multi-objective settings so far. In this work, an underactuated
mechanical system consisting of a rotary servo motor and a ball
and beam is used for the computer simulations, the setup parameters
of the inner and outer control systems are tuned by NSGA-II
(Non-dominated Sorting Genetic Algorithm), and the dominancy
concept is used to find the optimal design points. The solution of
this problem is not a single optimal cascade control, but rather a set
of optimal cascade controllers (called Pareto set) which represent the
optimal trade-offs among the selected design criteria. The function
evaluation of the Pareto set is called the Pareto front. The solution
set is introduced to the decision-maker who can choose any point
to implement. The simulation results in terms of Pareto front and
time responses to external signals show the competing nature among
the design objectives. The presented study may become the basis for
multi-objective optimal design of multi-loop control systems.
Abstract: The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.