Question 1: A robot-arm drive system for one joint can be represented by the di erential equation
dv(t)
dt = k1v(t) k2y(t) + k3i(t)
where v(t) = velocity, y(t) = position, and i(t) is the control-motor current (Hint: i(t) = u(t)). Put the equations in state variable form and set up the matrix form for k1 = k2 = 1.
Question 2: The state space representation of a dynamical system is given as
X0 (t) = AX(t) + BU(t)
Y (t) = CX(t) + DU(t)
Prove that:
h Z t i
Y (t) = C (t)X(0) + (t ):B:U( )d + DU(t)
0
where (t) = eAt is the fundamental or state transition matrix.
Following problems are from the text book:
Question 3: 2.1
Question 4: 2.3
Question 5: 2.6
Question 6: 2.14
Question 7: 2.15
Question 8: 2.20
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