1- For the linearized system design a full state feedback control system to cont

1-
For the linearized system
design a full state feedback control system to control the radius r of the
satellite close to the linearized trajectory. Design an observer as only the angle
theta is measured as output. For a step
input reference such that r_des = r+0.1r where r is the initial radius design
a controller that achieves this trajectory under 1sec with no overshoot. Design the observer such that it has dynamics
thrice as fast as the controller. 2-
a) Design a PD controller using
the output theta to control the radius close to the linearized
trajectory. For a step input reference
such that r_des = r+0.1r where r is the
initial radius design a controller that achieves this trajectory under 1sec
with no overshoot. b) Add a step disturbance
to the system with magnitude %10 of the initial radius r. Make sure using the PID controller that the
steady state error becomes 0. 3-
Model the system using Simulink
and apply the controllers in 1 and 2. Plot the r and theta of the satellite as
well as control and error functions as well as the 2D system motion. Show how
changing controller parameters effects system performance. 4-
Compare the results for the
State Space and PID controllers.
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