Question

The scanning mirror system in a barcode scanner can be simply model as a single DOF system, with a force input as shown in Figure 1. k f(t) 777 x(t) Figure 1. A single DOF system that represents a scan mirror system a) Consider the system has following system equation, derive state space equation for the system. m\ddot{x} + c\dot{x} + kx = f(t) For the problems below, assuming m = 0.1kg, k = 1, c = 0.2Ns/m. 771 b) Is the system stable? Why? c) Is the system controllable? Why? Write down the controllability matrix. d) Is the system observable? Why? Write down the observability matrix. e) Place 3 poles as below and simulate time response of the given dynamic system. P1 = -1 + 1i; P2 = -1 - 1i; P3 = -5; f) Try to change pole position and compare the simulation plot and discuss.

          The scanning mirror system in a barcode scanner can be simply model as a single DOF system, with a force input as shown in
Figure 1.
k
f(t)
777
x(t)
Figure 1. A single DOF system that represents a scan mirror system
a) Consider the system has following system equation, derive state space equation for the system.
m\ddot{x} + c\dot{x} + kx = f(t)
For the problems below, assuming m = 0.1kg, k = 1, c = 0.2Ns/m.
771
b) Is the system stable? Why?
c) Is the system controllable? Why? Write down the controllability matrix.
d) Is the system observable? Why? Write down the observability matrix.
e) Place 3 poles as below and simulate time response of the given dynamic system.
P1 = -1 + 1i; P2 = -1 - 1i; P3 = -5;
f) Try to change pole position and compare the simulation plot and discuss.

The scanning mirror system in a barcode scanner can be simply model as a single DOF system, with a force input as shown in
Figure 1.
k
f(t)
777
x(t)
Figure 1. A single DOF system that represents a scan mirror system
a) Consider the system has following system equation, derive state space equation for the system.
mẍ + cẋ + kx = f(t)
For the problems below, assuming m = 0.1kg, k = 1, c = 0.2Ns/m.
771
b) Is the system stable? Why?
c) Is the system controllable? Why? Write down the controllability matrix.
d) Is the system observable? Why? Write down the observability matrix.
e) Place 3 poles as below and simulate time response of the given dynamic system.
P1 = -1 + 1i; P2 = -1 - 1i; P3 = -5;
f) Try to change pole position and compare the simulation plot and discuss.

Added by Brian M.

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