Page 7

Step Response 0.5 0.45 0.4 0.35

Amplitude

0.3 0.25 0.2 0.15 0.1 0.05 0

0

1000

2000

3000

4000

5000

6000

7000

8000

Time (sec)

2.8 Consider a pendulum with control Tc and disturbance torque Td whose differential equation is θ + 4θ = Tc + Td . Assume there is a potentiometer at the pin that measures the output angle θ , that is, y =θ . a) Design a lead compensation using frequency response that provides for an PM > 50 degrees and a bandwidth > 1 rad/sec. b) Add an integral term to your controller so that there is no steady-state error in the presence of a constant disturbance, Td, and modify the compensation so that the specifications are still met. The matlab code is: function prob_2_8a() % w = 5; a = w/sqrt(10); b = w*sqrt(10); k = 100; sys1 = tf(1,[1 0 4]); D = k*tf([1 a],[1 b]); sys2 = D*sys1; figure(1) margin(sys1) figure(2) margin(sys2)

Solution for Take Home Exam 1  

, a) Design feedback assuming you have access to all the state elements. Place the closed- loop system poles at s = [-1 +- 1j, -0.5 +- 5j]....