Controle de Servomecanismo

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Problem 7.59PP
Consider a servomechanism for following the data track on a computer-disk memory system. 
Because of various unavoidable mechanical imperfections, the data track is not exactly a 
centered circle, and thus the radial servo must follow a sinusoidal input of radian frequency ojO 
(the spin rate of the disk). The state matrices for a linearized model of such a system are
* - [ ; A ] - - [ ; ] ■ >'■
The sinusoidal reference input satisfies y — —o j^r.
(a) Let (uO = 1, and place the poles of the error system for an internal model design at
ac(s) = (s + 2 ± J2){s + 1 ± y i)
and the pole of the reduced-order estimator at
ae(s) = (s + 6).
and the pole of the reduced-order estimator at 
ae(s) = (s + 6).
(b) Draw a block diagram of the system, and clearly show the presence of the oscillator with 
frequency ojO (the internal model) in the controller. Also verify the presence of the blocking zeros 
at ±j(jjO.
(c) Use Matlab (SImulink) software to plot the time response of the system to a sinusoidal input at 
frequency ojO = 1.
(d) Draw a Bode plot to show how this system will respond to sinusoidal inputs at frequencies 
different from but near wO.
Step-by-step solution
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