state variable controller

- N
- nerendra.devnarain
  
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posted
18 years ago

Mon, Apr 17, 2006 3:01 PM

hi. I am having a problem with the state variable controller.I am tryn to locate closed poles in the left hand plane such that my output graph has no overshoot.I am modeling a spring and dashpot system.It has two masses.m1 and m2.My output of interset is the diplacement of m1(is the bottom mass) calle x.I have modelled the system in simulink and it is workn,but i am having difficulty in the controller part.I have designed the controller but i am getting overshoot on my output graph(x) which i dont want.I have choose poles (-2 -2 -4 -4) and it is stil not working.The follwing are my two state differential equations

m1 x =3D k (y =E2=80=93 x) + b (y =E2=80=93 x) =E2=80=93 (m1 + =E2=88=86 m= ) y . . . . SDE1

m2 y =3D F =E2=80=93 k(y-x) =E2=80=93 B ( y =E2=80=93x) =E2=80=93 m2y. . . = . .SDE 2

I chose B =3D 1,K =3D1. m2 =3D1. m1 =3D1. These equations i have modelled in simulink.please help with the state variable controller part.Thanx in advance

- R
- RRogers
  
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posted
18 years ago

Tue, Apr 18, 2006 2:44 PM

m) y . . . . SDE1

I can't help you with the generic design, but there is a cheat that will work. Diagonalize the state space representation and tune each state variable seperately. Not elegant but you achieve clarity in the tuning. Unfortunatly you are now working on parts of the input, and parts of the output so the physical meaning is not as clear unless you think in modes.

Ray

- P
- Peter Nachtwey
  
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posted
18 years ago

Wed, Apr 19, 2006 6:11 PM

I don't think you have specified your formulas correctly so everyone is confused. I don't see any indication you are using derivatives. Also the (y-x) terms for velocity and acceleration can't be right. Also, what is not going to overshoot. Position, velocity, or acceleration? What is the set point? What is F(t)? What is b? What about gravity? I don't see a mg term. What kind of closed loop controller are you using? What is =E2=88=86 m? Is the mass chaning? I don't see how this can be simulated correctly. Can you model a second order system and control it correctly?