Question

The model is shown below mathematics of a pendulum actuated by a motor. This pendulum models the dynamics of a simple optical arm.\\ $\ddot{\theta} + \frac{3g}{2l}sin(\theta) = \frac{3}{ml^2}T$\\ You want to bring the position of the pendulum at the equilibrium point $(\theta, \omega) = (0,0)^T$ by means of a PID controller:\ $C(s) = K_p + \frac{K_I}{s} + K_Ds$\ a) Find the values of the parameters $(K_P, K_I, K_D)$ PID controller that allows to bring the pendulum to the desired position.\ b) Is the PID controller capable of returning the pendulum to the equilibrium point $(\theta, \omega) = (0,0)$ if the initial condition is $(\theta, \omega) = (\pi/2,0)^T$? Justify the answer.\ Values\ Pendulum mass=1Kg\ Pendulum length=1m\ Gravity acceleration=g=9.81m/s^2

          The model is shown below mathematics of a pendulum actuated by a motor. This pendulum models the dynamics of a simple optical arm.\\
$\ddot{\theta} + \frac{3g}{2l}sin(\theta) = \frac{3}{ml^2}T$\\
You want to bring the position of the pendulum at the equilibrium point $(\theta, \omega) = (0,0)^T$ by means of a PID controller:\
$C(s) = K_p + \frac{K_I}{s} + K_Ds$\
a) Find the values of the parameters $(K_P, K_I, K_D)$ PID controller that allows to bring the pendulum to the desired position.\
b) Is the PID controller capable of returning the pendulum to the equilibrium point $(\theta, \omega) = (0,0)$ if the initial condition is $(\theta, \omega) = (\pi/2,0)^T$? Justify the answer.\
Values\
Pendulum mass=1Kg\
Pendulum length=1m\
Gravity acceleration=g=9.81m/s^2

The model is shown below mathematics of a pendulum actuated by a motor. This pendulum models the dynamics of a simple optical arm.

θ̈ + (3g)/(2l)sin(θ) = (3)/(ml^2)T

You want to bring the position of the pendulum at the equilibrium point (θ, ω) = (0,0)^T by means of a PID controller:C(s) = Kp + (KI)/(s) + KDsa) Find the values of the parameters (KP, KI, KD) PID controller that allows to bring the pendulum to the desired position.b) Is the PID controller capable of returning the pendulum to the equilibrium point (θ, ω) = (0,0) if the initial condition is (θ, ω) = (π/2,0)^T? Justify the answer.ValuesPendulum mass=1KgPendulum length=1mGravity acceleration=g=9.81m/s^2

Added by Lorenzo R.

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