Reference no: EM131223570
1. Consider the control system shown in the block diagram
where K1(s) = K1 (τns+1) / s; K2(s) = Kq (s2 + ω2n) / (s2 +2ζns+ ωn2) and the UAV dynamics G(s) are described using the model x• = Ax+ Bu , y= Cx , u = δ , y = [A, q]T , with G(s)= C(sI - A)-1B .
a) Derive a state space model for the controller (Ac,Bc,Cc,Dc), with
as the input to the controller and δ as the output from the controller.
b) Describe what effect the transfer function K1 (s) has on the system response.
c) Describe what effect the transfer function K2(s) has on the system response.
2. Consider the following aircraft dynamics.
a) Derive the transfer functions for Az / δ and q / δ.
b) Using the data in the above table, compute the poles and zeros for these transfer functions at α = 6 deg and α = 16 deg.
c) What is the primary difference between the dynamics at α = 6 deg and α = 16 deg? What parameter in the model determines this difference?
3. Consider the following two linear time invariant systems
Find a similarity transformation relating system a) with system b). If no transformation exists, explain why.
4. a) Transform this system to diagonal form:
b) True or false
T F Only the zeroes of the transfer function matrix change when transforming to diagonal form. T F The above (A,B,C) is a minimal realization.
5 Consider the following notch filter
How many states are required to implement this filter? Derive the state space matrices for this transfer function: (A,BC,D)
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