LQR BASED TYPE-2 FUZZY CONTROLLER FOR DOUBLE INVERTED PENDULUM

Abstract

The inverted pendulum system, which has been focused by control engineering, is among the most important and classical problems. From a human walking on feet to a flying airplane, a lot of processes in life includes the balanced inverted pendulum phenomenon. When we are trying to control an inverted pendulum, we are also trying to find solution to all those complex processes above mentioned. A Double Inverted Pendulum is a more complex system with more control targets to be controlled. Processes like refueling of aircrafts and stable seats in a turning bullet train uses this phenomenon. There are a lot of control teclmiques to control this type of complex systems. As we know that Fuzzy Controllers are getting a lot of attention now a days due to their advantages on other controller like uncertainty handling and use of human expertise in its operation. Due to such advantages they make a great choice. While designing a fuzzy controller for such system, two main problems are controlled namely "rule number explosion" and "uncertainty" in the system. As remedy to these problems, a fusion function based on LQR control is applied before fuzzy controller that reduces number of inputs and thus the fuzzy rule base that encounters first problem. The second problem "uncertainty" is taken care by type-2 fuzzy controller, as the degree of fuzziness is greater than conventional fuzzy controller. Therefore, both the schemes are combined to make the controller more efficient and robust. MATLAB simulation and comparison to a LQR-Fuzzy controller shows that the control effect is perfect.