1. State Space circuit model

10. Op Amp circuit example Note: ip1=0, ∴vp1=vo=vA & vB=vp2=0
Let vC1 & vC2 be s.v., vo output.

11. KCL at A:
vo is not s.v. nor input, use
vo=vC2

12. KCL at B:
vo1 not s.v. nor input,
vo1=vA+vC1=vn1+vC1
=vp1+vC1=vo+vC1
=vC2+vC1

13. Output eq:

14. Physical Laws for Mechanical

15. Example: car suspension

16. Car suspension: simplified
Ignore tire deformation.
Suppose y1(t) is measured
from equilibrium position
when gravity has set in.
So gravity is canceled by
spring force at eq. pos.
∴There are two forces on m:
y1(t)
x(t)

17. Newton’s Law: or
num=
den=
T.F.=H(s)=

18. State Space Model For linear motion For angular motion
Define two state variables for each mass
x1=position, x2 = velocity; x1-dot = x2
x2-dot is acc and solve for it from Newton’s
For angular motion
Define two state variables for each rotating inertia
x1= angle, x2 = angular velocity; x1-dot = x2
x2-dot is angular acc and solve for it from Euler’s law

19. Quarter car suspension

20. u

25. Electromechanical systems
Motors
DC motors
Induction motors
Variable reluctance motors
Generators
Angular position sensors
Encoders
Tachometers

27. For field control with constant armature current
For armature control with constant field current

28. Armature controlled motor in feedback

29. Get TF from wd to w and Td to w.