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# Vehicle Model with Power as Input

## Vehicle Model with Power as Input

(OP)
Hi I'm working on a simple Simulink model of a vehicle with power as input and speed as output as can be seen in the picture:
When input is constant, there are no problems but when trying to have an input from the signal builder there are problems.

The point with the model is also to be able to experiment with acceleration times. I want to see what speed I can reach after accelerating for 10 seconds in a certain slope.
Any experts out there with some tips?

### RE: Vehicle Model with Power as Input

(OP)
Trying to post the picture again...

### RE: Vehicle Model with Power as Input

A quick unit analysis indicates a problem, so something is wrong. I'm not exactly sure what, though, so I recommend restarting from the beginning.

First, write your equation in differential form, e.g., dv/dt = f(v, P, m, Ka, Kr, Ki), where v is velocity, P is power, m is mass, Ka is the air drag, Kr is the rolling resistance, and Ki is the inclination. Then, put an integral block down in a new model. Next, you want the dv/dt term to go into the integrator so that the v term will come out of it. Since you have the equation in differential form, use signals passing through blocks into a sum block to create the right side of the function f(v, P, m, Ka, Kr, Ki), and wire that into the input of the integrator. Put a scope on the output of the integrator, and you will be viewing the velocity.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
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### RE: Vehicle Model with Power as Input

When I try it the issue appears to be with lack of initial conditions rendering the derivative block ineffective. Even with constant power input the results were suspect.

At first I tried adding random noise but just got lots of Inf/NaN simulation errors. I then tried adding a step function to the denominator that is initially very large and falls to nothing. That introduced a nasty transient at the start, but from then on the results appeared to behave realistically.

I'm no expert though - this is the first time I've constructed a model in Simulink, but that's what I tried and it seems to work. What have you tried?

### RE: Vehicle Model with Power as Input

Post a link to an image with your differential equation written out, and I'll show you what I meant.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

### RE: Vehicle Model with Power as Input

(OP)

The equations i have been using as a ground for this models are the following:

m*dv/dt = F - .5*rho*cd*A*v^2 - m*g*fr - m*g*sin(alfa) --> F = m*dv/dt + m*g*fr+ m*g*sin(alfa) + .5*rho*cd*A*v^2
where fr is the rolling resistance

and P = F*v

that should make F = P/v ?

I.e. v = P/(m*dv/dt + m*g*fr+ m*g*sin(alfa) + .5*rho*cd*A*v^2)

### RE: Vehicle Model with Power as Input

Here is a sketch of what I was describing - I don't currently have access to Simulink. You should check the math, though, as I didn't, but it should be mostly correct.

You never want to have a derivative block in a model if you can help it, since derivative blocks will amplify any high frequency signals, and step signals have an infinite derivative. Always rewrite your equations so that you can use integrator blocks as I did in the sketch.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

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