Abstract
This article provides a representation of the double inverted pendulum system that is shaped and regulated in response to torque application at the top rather than the bottom of the pendulum, given that most researchers have controlled the double inverted pendulum based on the lower part or the base. To achieve this objective, we designed a dynamic Lagrangian conceptualization of the double inverted pendulum and a state feedback representation based on the simple convex polytypic transformation. Finally, we used the fuzzy state feedback approach to linearize the mathematical nonlinear model and to develop a fuzzy controller H ∞ , given its great ability to simplify nonlinear systems in order to reduce the error rate and to increase precision. In our virtual conceptualization of the inverted pendulum, we used MATLAB software to simulate the movement of the system before applying a command on the upper part of the system to check its stability. Concerning the nonlinearities of the system, we have found a state feedback fuzzy control approach. Overall, the simulation results have shown that the fuzzy state feedback model is very efficient and flexible as it can be modified in different positions.
Highlights
A double pendulum is made up of two individual pendulums which mimic a nonlinear and unstable dynamic system [1,2,3,4,5]
Bogdanov [9] tested a combination between the linear quadratic regulator, the neural network, and the Riccati equation in order to reach the overall stability of this model. e key downside of this approach lies in the large number of complex calculations
Stabilizing the model through applying a torque on the second pendulum rather than the first is still a mystery to researchers; eventually, in this study, we aim to surmount such a challenge while making use of the state feedback fuzzy theory to control the double inverted pendulum (DIP) on the upright position. e second part presents a mathematical formulation of the DIP based on the Lagrangian approach, illustrated by a graphical modeling, which is rooted in the virtual reality and MATLAB software, as displayed in the third part. e fourth part provides a general overview of the state feedback fuzzy technique simulation results using MATLAB/Simulink, while the fifth and last part sum up all significant results and perspectives of this study
Summary
A double pendulum is made up of two individual pendulums which mimic a nonlinear and unstable dynamic system [1,2,3,4,5]. It displays a perfect model of nonlinear and chaotic movements. E combination of the double pendulum system with a crane became interesting because of its high utility and applicability in the industry. To provide more details about the functionality of this model, Chen et al [14] presented the dynamics of the double-pendulum crane and proposed a time-optimal trajectory planning approach in order to achieve the control objectives. Jaafar et al [16] employed this system and improved its vibration control by designing the model
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
