Inverted Pendulum Control using Pole Placement Technique
Control Systems Non-Linear Dynamical System Non-Linear System is a system in which the change of the output is not linearly proportional to the change of the input. Non-Linear Dynamical Systems that describe changes in variable over time may often appear unpredictable. The state variables, represented as a vector x , capture the system's memory or variables of interest, while inputs u influence the system. The system's behavior is compactly expressed using the state equation f . x – State, u – Input, x˙ = f(t,x,u) - State Equation of the System The inverted pendulum is a non-linear system because its equations of motion are non-linear due to the presence of trigonometric functions like sin( θ ) and cos(θ), where θ is the angle of the pendulum. The pendulum’s dynamics depend on both the angle θ and its angular velocity θ˙ . Mathematical Modeling of a System The Euler-Lagrange method is used to derive the equations of motion of a given system. Euler-Lagra...