MATLAB to resolve Dynamic model of a single link robot is as follows: =H sin () + I^.. where H =Mgl where H =5 I =5 (1)

1. Assume that the equation (1) is perfectly known model of the robot and design a controller using Feedback Linearization (inverse dynamic) method and show that the resulting closed-loop dynamic is a linearzed dynamic and exponentially stable (use the method described in class).

2. Assume that the approximately known dynamic model of the robot is as:

=H^{^} sin () + I^{^..}

where 5 <=H^{^} <=10 4 <=I <=7 (2)

Using your Matlab code, show that feedback linearization using approximately known dynamic is not perfect by tracking a sinusoidal trajectory instead of step function (see posted lecture note about implementation issues).