Generally, most of the physical processes affected by disturbance or incomplete knowledge are complex and highly nonlinear. To solve these problems, many researches are ongoing in modern control theory recently. Owing to those efforts, several kinds of controllers using different techniques have been proposed. The controllers play major roles in the robotization. For instance, it can increase productivity and sophistication. But the researches need apparatuses, which can verify the controller for being not damaged the plant. In this paper, therefore, a seesaw system is considered one apparatus to analyze and apply the control theory.
A seesaw system consists of a moving cart on the rail and seesaw frame made to demonstrate the effectiveness of the control theory. The system has balancing and positioning problems, and the driving force is applied on the DC motor of cart, but not on the pivot. The purpose of control is to maintain an equilibrium of seesaw frame in spite of an allowable disturbance.
First, the mathematical model of the seesaw system is derived from the Langrange's formulations. Second, a stable feedback loop is constructed for the nonlinear seesaw system, and the parameters of its linearized model are estimated using input-output data, a real-coded genetic algorithm(RCGA) and the model adjustment technique.
Third, the PI-type state feedback controller and the reduced-order observer are designed based on estimated linear model and RCGA. The proposed control system combines the PI-type state feedback controller with the reduced-order observer.
Finally, the proposed methods are applied to the seesaw system and a series of simulation are carried out to verify the effectiveness.