Simulation.
(a) Simulate the non-linear model of the Inverted Pendulum in the Simulink/Xcos environment for some different initial conditions and different input signals. Comment on your results.
(b) Derive linear models for small pendulum angles by using approximations as sin(θ) ≈ θ and cos(θ) ≈ 1. You should remove some non-linear terms that contain products of θ and θ while linearizing the nonlinear equations.
(c) Construct two transfer functions X(s) and θ(s) for the horizontal motion of the cart F(s) and the rotational motion of the pendulum, respectively.
(d) Obtain impulse and step responses of these linear models either in MATLAB or Scilab.
(e) In Simulink/Xcos, simulate the linear systems for different initial conditions and different inputs. Compare your results with those of part (a).
Solve these coupled equations for x and i.
Simulation.
(a) Simulate the non-linear model of the Inverted Pendulum in the Simulink/Xcos environment for some different initial conditions and different input signals. Comment on your results.
(b) Derive linear models for small pendulum angles by using approximations as sin(θ) ≈ θ and cos(θ) ≈ 1. You should remove some non-linear terms that contain products of θ and θ while linearizing the nonlinear equations.
(c) Construct two transfer functions X(s) and θ(s) for the horizontal motion of the cart F(s) and the rotational motion of the pendulum, respectively.
(d) Obtain impulse and step responses of these linear models either in MATLAB or Scilab.
(e) In Simulink/Xcos, simulate the linear systems for different initial conditions and different inputs. Compare your results with those of part (a).