Consider the inverted pendulum system shown below Assume tha

Consider the inverted pendulum system shown below. Assume that M = 3 kg, m = 0.5 kg, l = 1 m. Define state variables as: x1 = q, x2 = q’, x3 = x, and x4 = x’. And output variables as y1 = q = x1, and y2 = x = x3.

Derive the state space equations for this system. Linearize the system about the equilibrium position.

Design a full state feedback control system. It is desired to have closed-loop system poles at s = -4 +/- j4, s = -25, and s = -30

Determine the state-feedback controller gain vector K.

Consider the inverted pendulum system shown below. Assume that M = 3 kg, m = 0.5 kg, 1 = 1 m. Define state variables as: x1 = theta, x2 = theta\', x3 = x, and x4 = x\'. And output variables as y1 = theta = x1, and y2 = x = x3. Derive the state space equations for this system. Linearize the system about the equilibrium position. Design a full state feedback control system. It is desired to have closed-loop system poles at s = -4 +/- j4, s = -25, and s = -30 Determine the state-feedback controller gain vector K.

Solution

1. Calculate the degree of undermines “n”;

2. Choose a rational analysis scheme for method of force

3. Calculate diagrams from unit loads and actual forces;