×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Are you an
Engineering professional?
Join Eng-Tips Forums!
• Talk With Other Members
• Be Notified Of Responses
• Keyword Search
Favorite Forums
• Automated Signatures
• Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

#### Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

# what are the equations of state space on open loop active suspension ?

## what are the equations of state space on open loop active suspension ?

(OP)

Hello

So I need to solve a problem on an active suspension .I dont know how to find the equations of state space on open loop

Given information

We apply F(t) force as ypou can see

z(t) is the distance of the upper spring edge from the ground

when spring length (not loaded ) = 1

F (spring) = -kδ^3 (t) δ = displacement of z(t)- z(not loaded)

F ( damper ) = - c dz(t)/dt

### RE: what are the equations of state space on open loop active suspension ?

what are the forces acting on the mass ?

these force create an acceleration of the mass, hence velocity and displacement.

as I remember this stuff (from 40 years ago) you get a differential equation (xdbldot, xdot, x).

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

### RE: what are the equations of state space on open loop active suspension ?

(OP)
F(t) up force

F spring , F damper and weight down force

### RE: what are the equations of state space on open loop active suspension ?

(OP)
i am trying to make these x dot dot ,x dot etc but there is δ^3(t) i dont how to make it to x

### RE: what are the equations of state space on open loop active suspension ?

(OP)
ma= F(t) - mg - Fspring -Fdamper

### RE: what are the equations of state space on open loop active suspension ?

Force in the spring = -k*z
force in the damper =-c*Dz
Net force on mass = -g-k*z+F- c*zD=m*D^2z

Using D notation because this is a typewriter.
There's probably a minus sign or two adrift in that. No D^3

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: what are the equations of state space on open loop active suspension ?

(OP)
δ is just a symbol δ = ( z-1 )^3 nit derivative
And my problem says that F spring = - kδ^3(t)
I dont know how to turn u it to x dot

### RE: what are the equations of state space on open loop active suspension ?

ChE here! So, be gentle! Isn’t u (velocity) = x dot = dx/dt

Good Luck,
Latexman

(OP)
Yes

### RE: what are the equations of state space on open loop active suspension ?

Oh, sorry you are using delta to mean dz, I misread your question

Wow, well you cannot easily solve that algebraically. A quadratic rate curve (ie cubic force curve) for a spring is quite a feasible approximation in real life, but to solve it we use numerical solutions.

so -g-k*z*z*z+F- c*Dz=m*D^2z

where k c m and g are constants and D means d/dt

You could try Wolfram Alpha.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: what are the equations of state space on open loop active suspension ?

How can we find the state-space equations for the active suspension system with this information?

### RE: what are the equations of state space on open loop active suspension ?

(OP)
Thanks for your replies but I have another question
I want to find the equation of damper ratio ζ>1 but including cubic spring
I know that for linear active (non cubic ) suspension is ζ= (c√m)/(2m√k)
but in my case that i have cubic spring do you have any idea how the equation is

#### Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

#### Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Close Box

# Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

• Talk To Other Members
• Notification Of Responses To Questions
• Favorite Forums One Click Access
• Keyword Search Of All Posts, And More...

Register now while it's still free!