# Assuming the closed-loop system is stable, find the steady-state error if… 1 answer below »

Assuming the closed-loop system is stable, find the steady-state error if ????

(??) = 0 and ??(??) = 1(??).

This means that inputs are zero reference displacement and a unit step disturbance, and then

calculate the steady state error ????

(8) = ??(8) – ????

(8) = ??(8) which is caused by the

disturbance signal ??(??) = 1(??) . If the controller ??????(??) is replaced by a PD controller, i.e.,

??????(??) = ????(1 + ??????), what is the steady-state error ????

(8) with ????

(??) = 0 and ??(??) = 1(??)?

Explain why the steady state error is different using PD and PID controller (2 Marks).

2. Determine the values of ????

,??, ?? such that the closed-loop system of the inner attitude control loop,

i.e., the transfer function from T??(??) to T(??) exhibits a undamped natural frequency of ???? = 10

rad/sec and damping ratio at ?? = 0.6. Next, open the Matlab script file ‘AS2_Q2.m’, complete this

file by inputting system parrameters ????

, ???? , ?? and selected ????

, ??, ??, run the code, and plot the

response of the inner attitude tracking loop with respect to a step input. Use the MATLAB ‘bode’

command to obtain the Bode plots of the compensated inner attitude loop. Find the gain margin and

phase margin of the system based on the generated Bode plots. Next, check your results with the

MATLAB ‘margin’ command (5.5 Marks).

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