First things first, which exact tire characteristics do you mean? Second, what is your objective function? It is unclear so far what you want to optimize.

Tire characterstics : Pacejka Coefficients from a Tire test rig.

Objective : Generate reference tire longitudinal slip value to follow a velocity profile imposed by the driver through throttle demand.

Objective function: I am not so sure about it but one function could be to minimize the summation of all the Fx of the tires such that the error between demanded velocity and actual velocity is zero.

There could be a better objective function but at this stage I don't have a clear idea as to what it could be.

And why do you want to control slip then? Your controlled variable is the ground speed. Slip is a function of the ground speed (and wheel rotation frequency). Such an indirect method of controlling the ground speed is at least peculiar, when not senseless.

So consider this, the tire slip dynamics are very fast as compared to the vehicle longitudinal speed dynamics. If you control just the speed and not the tire slip, the slip will become very high and due to the non-linear tire properties, the maximum acceleration will not be obtained. If you do the reverse, you can control both the slip and the velocity. Imagine a drag race between a Nissan GT-R with launch control and a 69 Mustang or Camaro. What will happen when you press full throttle (PI controller based on velocity)?

When you say "tire slip dynamics are very fast as compared to the vehicle longitudinal speed dynamics" you effectively mean wheel rotation frequency. Yes indeed it's faster. What you say after that is incomprehensible. Can you precisely formulate what exactly you try to achieve using formulas?

Hi guys,

Not quiet sure what your trying to achieve with the electric vehicle. It sounds like it has a shit load of torque which keeps producing enough power to keep spinning the wheels when you accelerate, is this correct?

So, what is the vehicle configuration, Automotive or special purpose?

If it is for an automotive design, I would probably use a LSD or Limited Slip Differential type design, this is assuming that the electric motor is driving the input shaft of the differential, the LSD will limited the wheel slip automatically internally via the clutch mechanism.

Now that you have the ACTUAL wheel speed under control, you now need to fit a ground speed sensor or rear facing radar under the vehicle (usually at about 30 to 45 degree angle, (this will depend on the type of radar being used). This sensor will give the controller the ACTUAL GROUND SPEED. the controller will measure this against the ACTUAL WHEEL SPEED and then adjust the voltage accordingly so that the wheels slow down slightly to reduce slip, without loosing traction torque or power.

This two sensor method is simple to use and with some work and fine tuning you will have it sorted in no time

It would interesting to see the configuration of the unit, for example the drive train layout, differential or direct drive etc; using a direct drive will create a lot more torque but you will need to set up the controller to be able to read the feed back from both wheel speed sensors.

Cornering is important, as you may know that the inside wheel will travel slower than the outside wheel. This speed variation will also depend on the a couple of things as well such as wheel track width, Radius of the corner, tyre diameter etc;

The controller can be alerted to cornering via a steering wheel motion sensor. This will feed back the amount of turn being done, hence then the wheel slip at the drive wheels can be worked out given the info listed in the last paragraph.

So, I suppose my information will depend on how good your controller is, as it will be relying on feed back from two wheel speed sensors, steering sensor, ground speed sensor, throttle sensor , and probably a torque control module for heavy or light duty work, all working together to control the voltage to the drive motor or motors.

Good luck with the venture, let me know if the information was of any use or no good at all to you....

Cheers for now.

Joe Hayes.

regards

Joe.

I believe he tries to calculate some "optimal" wheel slip to reduce tracking error between actual and desired ground speed assuming knowledge of Pacejka formula parameters and thus wheel longitudinal forces. What exactly it means I have no idea unfortunately as OP did not provide a clear formulation of the optimization problem.

Hi Pavel,

Sorry for using automotive jargon. It was too specific. I believe after seeing your last reply, that you have understood my problem  but not the motivation behind it. Let me try to elaborate in a more general way.

Firstly, lets forget the word optimal. We will come to the optimization aspect later.

The global problem: To find a function that will take as input the throttle demand from driver and give as output the motor torque.

Throttle demand is generated by the driver which tries to match the velocity of the vehicle with that of a predefined velocity obtained from timeseries data. Generally, driver models have PID controllers. Lets assume that the driver is modelled with a P controller for the sake of brevity.

Therefore, Throttle demand(t) = K * (Predefined Velocity profile(t) - Actual vehicle velocity(t)); given K is positive .

The local problem : If I write Torque demand of electric motor = Kt* throttle demand, which is a very simple control law where the motor torque is now controlled as an error of the velocity, I will not be able to control the tire slip because of the inherent faster tire slip dynamics as compared to the vehicle velocity dynamics. This is evident in the first figure which shows simulation test of an maximum acceleration on a straight line maneuver. It can be seen that without slip control(for ex. 69 Camaro/Mustang), the wheel slip goes up to 2 which is a really high value(undesired). As a consequence, the longitudinal forces generated are not the maximum and thus the acceleration of the vehicle is much lower than that of the case with slip control(for ex. Nissan GT-R with launch control).

Faster dynamics means a shorter rise time (control theory domain) and not the higher wheel rotation frequency.

The solution to this local problem could be have an intermediate block of control which takes into account the throttle demand and finds out which value of tire slip will allow me to achieve the velocity of the vehicle that the throttle demand is intended for.

Since the tire force vs tire slip characteristic is non linear in nature, maybe this problem could be solved either by an optimization algorithm which has this argument  :

min (Tire_force_required for following velocity profile- Actual tire force)

with the optimisation variable being the tire slip,

where the 'Tire_force_required for following velocity profile' could be a consequnce of the the velocity tracking error.

The burning question now is does anyone know how to find out the optimal/best slip reference value to be input into a slip controller given that we know the throttle demand from the driver?

Hi Joe,

Thanks for the answer. You have indeed mentioned the key aspects to be kept in mind while designing a generic powertrain.

My vehicle has a RWD layout. Each wheel has its own motor. As you suspected, the motors plus the reduction gears are able to generate humongous torque numbers, such that the tires slip very easily (like an F1 car). Thus comes the need of slip control. Unfortunately the dual motor setup renders the use of limited slip diff not feasible.

Hi JG..

Thanks for the feedback. I see know what you mean. I was thinking last evening that it must have heaps of torque, and that is why I asked the layout question.

You obviously have the 'optimum' final drive ratio's worked out thru the planetary drive to give you a good ground speed for motor rpm?

How is cornering achieved with the dual motor drive, do you have any slippage issues there?

I know that you need 'full voltage' to get the vehicle moving which is causing the problem,

I wonder if there is another way around the problem such as an 'over-powered drive release' where when the wheels start to slip with-out sufficient ground speed the voltage is reduced to match? It would mean some redesigning, but you have a lot of torque to tend with going thru the planetary gears.

As another thought, would putting the startup voltage to the drive motors on a 'Timer'. That is, a delayed full throttle application. do you know what I mean?

Have the full throttle response from the pedal delayed thru the controller to a preset percentage to allow the wheels to take up the inertia and when the wheels are moving it increases to maximum throttle. Try varying times to see what works at different throttle settings. ie: standing start, rolling starts, full throttle from cruise speeds etc;

Sorry I could not assist with the algorithm side of things though,

Again let me know how it goes,

Cheers

Joe

I think what the OP tries to achieve is a simple TCS which reduces high wheel slip. It is a known fact that on a rigid surface such as asphalt, the maximum traction force is achieved at a relatively small wheel slip. It is, however, not assumed that parameters of the Pacejka formula are known, but rather they are estimated in some way. Indeed, road conditions vary, how can one rely on a single particular set of parameters? Joseph, I think you go too deep into technical details of realization of a TCS, but I am not sure that the OP is asking for this, rather it seems to me that he tries to understand basic principles of TCS. But I repeat: I do not fully understand what he tries to achieve. The details he provided are rather misleading than explanatory.

Nevertheless, I suggest OP to look at the attached paper.

www.ajc.org.tw/pages/PAPER/10.1PD/0067-73.pdf

Dear Pavel,

Thank you for the link to the paper. It seems to be a very rudimentary version of TCS where they are able to fix a slip set point and track it within a second. What I need is  reference slip signal which is not fixed at a set point.

As far as 'misleading' goes, I am not sure if you are familiar with the work done by Prof. Junmin Wang. Kindly take a look at it. Maybe it  will clear the picture.

Anyways I appreciate your time and  effort in helping me try and solve the problem.

Thank you and Best regards :)

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4806119&tag=1

Hi JG, and Pavel,

I see what you are attempting to do. I feel the same as Pavel on this point. What with the myriad variations of tyre designs, road surface types, it would be almost inconceivable to adapt a system that does not have some wheel slip, even a minimum of slippage would be needed to activate the system, and when it is activated you will still have the other variables to content with, I think have a 'spontaneous' response traction control system for all active conditions might be unreachable....

It would be a nice 'Theory' project...

Cheers for now guys, take care...

Joe

Well I didn't want to to make self-advertising, but if you are concerned about optimal set-point adjustment, then it turns to be close to my previous research. Feel free to look at it. It doesn't deal with cars specifically, but it gives some more or less general overview.

I think there are two separate aspects to the problem, and they are both very conventional automotive control problems. The first is to have something that relates the throttle pedal position to the speed of the car. As a general rule, some control system that links the throttle pedal position to the motor torque output is quite usual. The second issue is related to what happens when the demanded torque exceeds the available friction at the ground (i.e. the wheels start to spin). At this point it is usual to invoke a second control system that remove the motor torque from the control of the driver, and places it under the control of a separate controller (the TCS controller). TCS algorithms to identify optimal slip are well researched, and readily available in the literature.

I appreciate that you state you would like to do the speed control via slip control, but this really isn't feasible. The problem is just a practical one, but those practical issues are pretty much impossible to overcome. For instance, you can never know what the true slip between the tyre and the ground really is. It depends on the rolling radius of the tyre, which is not possible to measure. You could do rig tests to measure the rolling radius, but whichever model you try to use to establish the rolling radius, it will always contain errors. The second issue is noise; to know the slip you must know the body speed, the yaw rate, the wheel rotation speeds, etc. All of these measurements will contain noise. So your slip ratio measurement will always be noisy, and controlling to it will be nearly impossible. TCS controllers have to deal with this issue, and they are highly sophisticated adaptive controllers, but even they get it wrong sometimes (bumpy roads are particularly challenging). The next issue is resolution. To drive at constant speed requires a really surprisingly small amount of drive torque, and the consequent tyre slips are very small indeed (actually not even measurable). In these conditions measuring a speed error is achievable, but measuring a slip error is not likely to be possible, so controlling to speed is easy, but controlling to slip is probably unachievable.

But don't let me put you off! Whilst controlling to slip has severe practical difficulties, if you could do it then driving response and performance gains could be possible.

Thanks Peter for the informative post. While I have come across articles in literature that demonstrate methods of slip control, I am sure that the issues related to  practical implementation are never addressed by them. I agree that the effects due to the change in the rolling radius make accurate slip control difficult.

That's right. A TCS is usually aimed at preventing spinning on the spot at take off if too much torque is applied. TCS use during usual driving cycle is senseless in impractical. Only for heavy-duty machines, that constantly operate at high extremely high traction, constant slip control makes sense.

That's not quite what I said, Pavel. TCS is a limit slip controller. It can be invoked at any point during the driving cycle, not only during "take off". My comments were related to the difficulty of using sub-limit slip for your motor torque control target. It's not senseless, it's just very difficult. But isn't that what makes engineering fun....?

Good response Peter,

Cheers mate,

Joe

First you need to model the system in such way that slip is among the inputs, but its hard long way well for me, so other solution they use slip compensation which are basically speed limiters.