Ballbeam System Analysis and Design Based on Root Locus Correction and State Space Correction

Abstract

The ballbeam control system is one of the most perfect and classic experimental equipment for the research and analysis of automatic control theory. Other nonlinear and unstable systems have important dynamic performance, but because the ball bar system is nonlinear and unstable, it is necessary to design a controller to correct it. In this paper, the root locus and the state space theory are used for correction. In the root locus correction, the curve of the root locus is changed by adding open-loop zeros and poles to make the system stable; in the state space, a state feedback observer is designed by using the principle of pole assignment, and the state feedback matrix K is obtained to make the system stable. Using the visual tool Simulink in MATLAB to simulate, we can see the specific control effect of the controller intuitively. The real-time control was carried out on gbb2004, and the results were observed.

Ball and Beam Control: Evaluating Type-1 and Interval Type-2 Fuzzy Techniques with Root Locus Optimization

“…By rearranging the equation, the transfer function from the gear angle (𝛩(𝑠)) to the ball position (𝑅(𝑠)) can be determined. The transfer function is shown in (6).…”

“…Accurate system modeling is crucial for understanding the physical system and facilitating the analysis and design of controllers. This research delves into the performance of three control systems, the Proportional-Integral-Derivative (PID) controller [1], [2], [3], root locus controller [4], [5], [6], and fuzzy logic controller [7], [8], [9], [10], employing type-1 and interval type-2 fuzzy techniques [11], [12], [13]. The study aims to determine the most effective fuzzy techniques in conjunction with root locus controller-based optimization.…”

“…PID control systems for the ball and beam have been extensively explored [17], [18], employing techniques such as quantitative PID controller [19], optimal PID-Like fuzzy logic controller [20], and hybrid optimization-based PID control [21]. The design of the root locus controller [6] serves as another foundation that simplifies the control system design and development, similar to PID control systems.…”