Application of fuzzy control algorithm based on MATLAB in inverted pendulum system
The inverted pendulum system is a classic nonlinear control problem and has important research value in the field of control engineering. Fuzzy control algorithm is a control method based on fuzzy logic that can effectively deal with nonlinear and fuzzy problems. This article will introduce how to use MATLAB to implement an inverted pendulum system based on fuzzy control algorithm, and provide the corresponding source code.
- Inverted pendulum system model
The inverted pendulum system consists of a rod that can rotate and a mass connected at the top of the rod. The goal of the system is to keep the mass point in a vertical position through the rotation of the control rod. The dynamics of the system can be described by the following equation:
ml^2θ'' + bθ' + mgl sin(θ) = u
Among them, m is the mass of the particle, l is the length of the rod, b is the damping coefficient, g is the acceleration of gravity, θ is the inclination angle of the rod, and u is the control force exerted on the rod. Our goal is to design a fuzzy controller to achieve stable control of the inverted pendulum system by adjusting the control force u.
- Fuzzy controller design
The design of fuzzy controller mainly includes four steps: fuzzification, establishment of rule base, fuzzy reasoning and defuzzification.
(1) Fuzzification
Fuzzification converts continuous input signals into fuzzy linguistic variables. In the inverted pendulum system, we can take the tilt angle θ and angular velocity θ' of the rod as input signals. By setting a suitable set of fuzzy sets and membership functions, the input signal is converted into fuzzy language variables.
(2) Establishment of rule base
The rule base is the core part of the fuzzy controller, which contains a series of fuzzy rules that describe the relationship between input signals and output control forces. The establishment of the rule base needs to be adjusted and optimized according to specific control requirements and system characteristics.
(3) Fuzzy reasoning
Fuzzy inference is to perform inference based on input signals and rule bases to obtain fuzzy output. Commonly used inference methods include the minmax method and the fuzzy correlation method. In the inverted pendulum system, fuzzy reasoning can be based on the current tilt angle and