It is desired to design a model-based nonlinear controller for the RP manipulator shown in
Figure 1.
(a) Using a Lagrangian approach, derive the equations of motion of the RP manipulator,
and find its mass matrix $M(q)$, where $q = [\theta_1, d_2]^T$.
(b) Assuming perfect knowledge of the kinematic and dynamic properties of the
manipulator, and zero joint disturbances, design a nonlinear controller, which can
achieve zero steady state tracking error, $E_{ss}$. The error equation should not depend on
q. Draw a block diagram showing the structure of your controller.
(c) Assume that the worst constant joint disturbance vector is $\tau_d = [\tau_d^1, f_d^2]^T$. Pick-up
the feedback gains of your controller so as to ensure that the error dynamics are
critically damped, and that the max tracking error $E$ at the steady state does not
exceed $E_{ss,max}$