Journal of Control Engineering and Applied Informatics
Interpolative-Type Control Solutions for a "Ball and Beam" System
Abstract
Controllers with interpolative blocks can replace fuzzy controllers in control structures.
This is possible because fuzzy controllers belong also to the interpolative-type controller category,
meaning controllers which implements interpolative-type reasoning. That kind of replacement is
not only a formal operation, it is also associated with further corrections that confer to the
structures with interpolative controllers enough flexibility to obtain better performances. The
possibility of performances improvement is the main argument of the present paper. Another
argument is the reduced calculus time, suited for the real-time implementation - it's about "lookup
table" type solutions. In order to illustrate the above affirmations, a case study is developed in
the paper. The controlled plant is an electromechanical one: ball and beam system, driven by the
torque applied in the rotational joint. The model used for the system is a 4th order one. Given the
system complexity, two structural solutions are proposed (TPS-4 -a structure with feedback from
all four states- and TPS-2 -a structure with feedback from only two states-), both of them being
tested - from the robustness point of view - at changes in system parameters. The case study is
conceived also in order to underline the differences between them.
This is possible because fuzzy controllers belong also to the interpolative-type controller category,
meaning controllers which implements interpolative-type reasoning. That kind of replacement is
not only a formal operation, it is also associated with further corrections that confer to the
structures with interpolative controllers enough flexibility to obtain better performances. The
possibility of performances improvement is the main argument of the present paper. Another
argument is the reduced calculus time, suited for the real-time implementation - it's about "lookup
table" type solutions. In order to illustrate the above affirmations, a case study is developed in
the paper. The controlled plant is an electromechanical one: ball and beam system, driven by the
torque applied in the rotational joint. The model used for the system is a 4th order one. Given the
system complexity, two structural solutions are proposed (TPS-4 -a structure with feedback from
all four states- and TPS-2 -a structure with feedback from only two states-), both of them being
tested - from the robustness point of view - at changes in system parameters. The case study is
conceived also in order to underline the differences between them.