Figure 2 2 Block diagram of design of FLC for Inverted Pendulum
Related Figures (10)
The inverted pendulum control problem[8] is usually presented as a pole balancing task. The system to be controlled consists of a cart and a rigid pole hinged to the top of the cart. The cart can move left or right on a one-dimensional bounded track, whereas the pole can swing in the vertical plane determined by the track. The state of the system is defined by values of four system variables the cart position, cart velocity, pendulum angle and angular velocity of the pendulum pole, respectively. Control force is applied to the system to prevent the pole from falling while keeping the cart within the specified limits. The linearized system equations for this problem in the state space is given below Fig.5 Membership function of cart velocity Fig.4 Membership function of cart position Fig.6 Membership function of angular velocity of pendulum The response of angle of the inverted pendulum is shown in Fig.8. FLC are needed to be tuned by Genetic Algorithm. The functional block diagram is shown in Fig.9. 3.4 Simulation Results: Major steps in combing both fuzzy and Genetic algorithms: Major steps in combing both fuzzy and Genetic algorithms: (a).Initialization of population: Initial population is the random population. here 8 MFs each have 5 bits , 16 rules, each rule have allotted 3 bits. So length of string becomes 88bits .population size is chosen as 10. Fig.10 Response of pendulum angle The Fig.10, shows the pendulum angle position and Fig.11 shows the plot of fitness value & mutation rate Vs generation. All the new generation information is recorded for analysis of results. The graph showing pendulum angle position after optimization, the variation in the fitness value and mutation rate is generated at the end of GA operation. Fig.11 The Plot of Generation Vs Fitness & Mutation
![The inverted pendulum control problem[8] is usually presented as a pole balancing task. The system to be controlled consists of a cart and a rigid pole hinged to the top of the cart. The cart can move left or right on a one-dimensional bounded track, whereas the pole can swing in the vertical plane determined by the track. The state of the system is defined by values of four system variables the cart position, cart velocity, pendulum angle and angular velocity of the pendulum pole, respectively. Control force is applied to the system to prevent the pole from falling while keeping the cart within the specified limits. The linearized system equations for this problem in the state space is given below](https://figures.academia-assets.com/91318291/figure_001.jpg)
