How to test electric power steering (EPS) for stability on adverse road conditions?

Do you know for a fact the system being controlled is linear? If so, you can apply a series of standard techniques to analyze stability. If the system is non-linear then your methods for analyzing stability are more limited. As it is with reliability which you cannot test in, I suspect it is the same with stability in a non-linear system. No amount of testing will be any kind of guarantee. That said, just as it is possible to control an unstable airframe with sufficient computer (fly-by-wire) capability, the same may be said for an automotive vehicle.

I don't envy your position of having to make a promise that you cannot keep.

>> Do you know for a fact the system being controlled is linear? If so, you can apply a series of standard techniques to analyze stability.

A little about our application. It's a commercial truck. The steering system is EPS. I believe the system being controlled has one input, which is torque applied by a motor. I believe it has one output, torque applied to road wheels. We never discussed if this system is linear.

I read in a book that "linear idealization is extremely useful as a tool for system analysis and control system design." But the control system is already designed. It's a PID controller or cascaded PID controller. The output of PID controller drives the motor or output of PID controller is input to system being controlled.

The book also says "With no plant model, an iterative procedure must be used to determine a suitable controller structure and parameter values." Maybe this is another reason as to why PID controller was chosen.

The book talks about developing linear plant model or model of system being controlled. Let's say system being controlled is non-linear. Is it possible to acquire linear model from non-linear system?

Should I try to find out if system being controlled is linear? If it's non-linear, is it possible to linearize it? If yes, how? The motor is connected to system being controlled, which includes reduction gear, pinion gear, rack, tie rods. Basically steering system components that convert rotational motion to linear motion.

What are the series of standard techniques to analyze stability?

The force-feedback on the EPS will be both wheel speed sensitive for normal driving and frequency sensitive for kick-back, or "bump steer" using motion feedback to null the rough road feedback to the driver.

Null will likely be a spec you can meet with the torque available and maybe -3dB at the break frequency and 30 to 40 dB down for 60 MPH step response to road bumps compared to no EPS.

The break frequency depends on the maximum Ts, slew rate from 10 to 90% full swing with f-3dB= 0.35 /Ts

The stability control for wheel slip requires a good Infineon WSS chip for high-resolution wheel speed sensing on each wheel. This must account for steering position and cornering WSS ratio and again use a frequency response corrected error feedback to the electronic brake modulation.

In it's simplest form, power steering reduces the effort needed to turn the steering wheel by a fixed fraction. The only input is the measured torque on the steering column, so at the drivers hands, and the output is to add torque to the steering column, nearer to the driving wheels than to where the torque is measured.

For the simplest power steering there is a fixed gain linking the input torque and the output torque. For example, let's say that is 3. The driver puts in 10 Nm of torque, the system adds 30 Nm, so the total is 40 Nm. The driver still feels the 10 Nm, so if the road wheels turn very easily, and, for example only 20 Nm in total were needed, then the driver would only need to put in 5 Nm and could tell the difference between that and heavier steering loads, for instance when turning the wheels when stationary on dry tarmac.

The only control needed is the dynamics of making sure that the torque is applied in a way that the driver doesn't notice. It's important that there's little lag, so that when the driver applies a steering angle change, the torque from the power steering increases of decreases as fast as the driver would increase or decrease the torque themselves.

Hydraulic power steering has worked on this principal for decades. is from 1955. Most cars with hydraulic steering have the hydraulic cylinder combined with the steering rack.

With electronic control, and the electric power steering, the are all sorts of additional inputs that can be applied.

A power steering system would be unstable if there was a significant delay from the torque being applied on the steering column and the torque being added by the system, as the driver would first add, or notice, torque, and later feel that being reduced by the system, which would be very disconcerting. It's not really possible to analyse stability of a system like that without considering the input from the driver, or even the inertia and stiffness of the driver's arms in response to forces changing at the driving wheels, from bumps etc. That is all stuff that happens in timescales up to about 50 ms, so it's like wheel wobble caused by out of balance or bent wheels.

All of that is completely separate from the stability of the vehicle, where movement of the vehicle on the road comes into play. That is on timescales of 250 ms and longer, and is far, far more complicated. That is to do with vehicle skids and zig-zagging, like when a trailer swings.

1. The EPS improves efficiency and improves easy of steering but can degrade driver's sense of direction cornering and rate of change of directional inertia. This feeling is important in judging vehicle stability with momentum challenges that increase with speed. If you eliminate this feeling, then you better have smart feedback to prevent over/undershoot.
2. The goal of any design is to define the specs which are to reduce stress and noise but not lose the feel of cornering, a natural return to centre, a reduced gain in sensitivity with increased speed, a correction for road tilt, a sensitivity to cornering with increased wheel force, integration with ABS for a change in direction and stability control with oil slick wet roads or ice.
3. The test methods are considered at the same time as the design in order to best validate the specs.

What are the design specs? Test specs are easy as they come from this. But you want to consider error margins, test to failure, fault injection. Shock and vibration standards are pretty standard with constant x up to a breakpoint then constant g up to the servo limit. A shock test can include fragility testing which defines the limits for velocity and time with variable g for yield a 2D boundary curve for stability analysis.

Is this for SAE-Level 3 , 4 or both in future?

I assume you may not have any design specs if you are GM (lol, and have to glean some from the BCM MATLAB/Simulink tools and need to bring in a consultant. I have WSS and servo design/test experience.

You may want to build a hydraulic or DC motor-controlled force simulator with the real servo and steering wheel and use sliding scale algorithms to measure response curves with vibration&shock at different speeds and turning radius. ( I know someone who can do that).

You will want a sliding-mode gain Bode plots and force feedback to enhance the realism and the fidelity of the driver to control stability under simulated force excitation defined by real-world field data test with wheel inertia included. This can test each of the driver stability control options for road conditions expected and BCM handling required.

I believe some are using fuzzy logic for smarter non-linear algorithms and include a solution with return-to-centre problems with EPS.

jani12 said:

Please consider commercial vehicle equipped with EPS ECU and other ECUs such as Antilock brake system (ABS), engine, transmission, Body Control Module (BCM), etc.

I would like to come up with tests for testing EPS on adverse road conditions such as wet or icy pavement for vehicle stability.

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The EPS itself is purely a servo system.

Other systems may take information from it, but in itself it is a 1:1 servo where the wheel angle should always duplicate the steering wheel angle, as if it were a rigid system - other than for the tiny rotary lag movement of the feedback sensor in the column, during active rotation of the steering wheel.

The tests would be for servo system stability under steady-state loads and shock loads of different force and duration, up to the maximum mechanical ratings of the overall steering system and and vehicle mechanics.

If the servo gain (stiffness or "feel") is variable with speed, then all tests must be done at all stiffness settings.

It must also avoid oscillation if the driver momentarily lets go of the wheel under any conditions, a problem which has occurred in some vehicles; the elasticity of the torque sensor can cause overshoot and inertial oscillation of the wheel, leading to a build up of oscillation.

The torque sensor (or signal) needs adequate damping to avoid that under any conditions.


Other systems such as lane guidance & traction control etc. may interact with steering, but the steering servo system must be absolutely faultless in isolation before those are considered.

You could use an accelerometer/magnetometer to detect if it is doing something unexpected on ice, gravel or hydroplaning.

But then you would need a serious program to decide what to do about it.

The worst disturbance for driving stability is the hysteresis from an aging steering gearbox under a heavy load. Don't neglect this in your tests.


Here's my thought experiment list of variables to check for stability influenced by design limits.

The test for stability under adverse road and vehicle conditions must include measurement parameters;
- steering wheel torque, Td, 5 Nm is a reasonable limit and max. torque velocity and acceleration.
- steering angular velocity, ωs
- steering wheel angle, φs
- steering wheel moment of inertia, Is .
- driver steering speed 200 ms for full sweep driver time, which depends on the range of steering rotation and variable gain if worm gears if used to reduce highway speed sensitivity.
- mass of the steering rack, m,
- moment of inertia Im of the motor
- moment of inertia of the coupling to wheels Ic
- steering arm torque, Ts
- steering arm torque, Ts
- wheel direction position, error, velocity and max acceleration
- vehicle direction, moment of inertia direction, velocity and acceleration
- wheel speed position, velocity acceleration

The end result is the vehicle position error from the centre of the lane and steering wheel "feel" that someone must define. to edge out the competition.

The tests may include pothole roads in Winnipeg railroad ties, sand and ice on alternate wheel sides with a steep & shallow bank corner turn with pot holes. The vehicle suspension response has a great influence on the EPS + BCM stability under adverse conditions.

rjenkinsgb said:

Other systems may take information from it, but in itself it is a 1:1 servo where the wheel angle should always duplicate the steering wheel angle, as if it were a rigid system - other than for the tiny rotary lag movement of the feedback sensor in the column, during active rotation of the steering wheel.

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All the systems that I have seen are rigid systems, except for the compliance of the torque measurement systems in the steering column, which is small compared to the compliance of the tyres.

We don't yet have drive-by-wire. Even the automated systems end up spinning the wheel as the car manoeuvres, because they are rigid systems. For the same reason, power steering failure just leaves a non-assisted system, which is generally no problem except on very heavy vehicles or at low speeds.

15 years or so ago, I was involved in testing vehicle stability system, because I was being paid to be used as part of the vehicle's control system.

Some car manufacturer, I don't know which one, was looking at stability systems and wanted to measure the biggest unknown of all, how drivers would react. I was paid to drive an experimental car with various stability control systems. The test course was on the ceramic tiles at MIRA (https://www.vehicletesting.solutions/proving-ground-surfaces/straight-line-wet-grip/) and I think it took the whole 150 m to stop the car from 40 mph on those. They had the sprinklers turned on, obviously.

Even more interesting was stopping from 50 mph with two wheels on the ceramic tiles and two wheels on tarmac. The car was travelling with a steady yaw angle of about 10 degrees between the centre line of the car and the direction of travel. There is no way that I would have managed to stop anything like that fast without ABS in those conditions.

I was paid £25 or so for an hour's work, involving about 6 stops, so maybe 1km of driving that they were interested in. Several other volunteer drivers were there, and I got the impression that they had several sessions. There were two cars, an observer in each one, a cameraman filming, and the hire of the facilities at MIRA and so on. It must have added up to over £10,000 for maybe 20 minutes of driving data.

Whoever wanted to find out what drivers would do in such situations was paying lots of money for information that might not have been that useful. I kept the car on the track each time, but one other driver spun his car. They asked me about how safe I felt after each run, and I wasn't at all frightened, 100+ metres from anything that I could hit. In real-world conditions, oncoming cars can be very close and other drivers and I wouldn't have been so relaxed about a skid, so that limits the usefulness of the data.

My point is that stability control for a vehicle is an extensive and extremely complicated subject to study. As rjenkinsgb points out, oscillation when the wheel is released is a no-no, while having the system too slow can result in overshoot and fighting between the driver and the steering system. However, compared to controlling the vehicle, getting simple power steering working is trivial.

Diver300 said:

All the systems that I have seen are rigid systems, except for the compliance of the torque measurement systems in the steering column, which is small compared to the compliance of the tyres.

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Exactly.

As I see it, the power steering is a totally isolated system.
The only "stability" relating to it is servo stability in the steering servo system.

Overall vehicle stability, steering effects & roadholding in general are totally separate matters relating to mechanical geometry and tyres etc., & irrelevant to power steering or otherwise.

I do not see how the "EPS" part is actually relevant to what the OP is asking? He seems to be confusing it with tracktion control, lane-keeping or who knows what??

OK, in an advanced vehicle the steering may have input from such as a torque motor on the column to control the steering for such as lane keeping or obstacle avoidance - but the result through the steering servo is no different to if the driver had turned the wheel at the same instant & not relevant to the power steering servo operation.

rjenkinsgb said:

OK, in an advanced vehicle the steering may have input from such as a torque motor on the column to control the steering for such as lane keeping or obstacle avoidance - but the result through the steering servo is no different to if the driver had turned the wheel at the same instant & not relevant to the power steering servo operation.

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All the automatic steering systems that I have seen have all been on vehicles with electric power steering. They have used the same motor to apply torque for automatic steering as they use for power steering.

The other control connection needed to the steering system is the steering angle sensor. Those often exist on vehicles without electric power steering or automatic steering. My 2009 Jaguar X-type had a steering angle sensor, which I guess was for the stability / traction control that could apply differential braking and throttle override.

jani12 said:

...

I read in a book that "linear idealization is extremely useful as a tool for system analysis and control system design." But the control system is already designed. It's a PID controller or cascaded PID controller. The output of PID controller drives the motor or output of PID controller is input to system being controlled.

The book also says "With no plant model, an iterative procedure must be used to determine a suitable controller structure and parameter values." Maybe this is another reason as to why PID controller was chosen.

The book talks about developing linear plant model or model of system being controlled. Let's say system being controlled is non-linear. Is it possible to acquire linear model from non-linear system?

Should I try to find out if system being controlled is linear? If it's non-linear, is it possible to linearize it? If yes, how? The motor is connected to system being controlled, which includes reduction gear, pinion gear, rack, tie rods. Basically steering system components that convert rotational motion to linear motion.

What are the series of standard techniques to analyze stability?

Click to expand...

The presence of a PID controller suggest the belief that the "plant" is a linear one or one that can be linearized around an operating point. In non-linear systems the concept of a "transfer function" does not exist. Major problems with non-linear systems include 1. bounded inputs do not guarantee bounded outputs, and 2. the introduction of new frequencies that are not harmonically related to frequencies in the input.

Linearization is possible if the operations are constrained around an operating point. Ability to linearize consists of defining the non-linear differential equations and boundary conditions to see if a possibility exists. Some non-linearities are easier to deal with than others. For example, replacing sin(x) with x for small x. Closed form solutions are rare and numerical methods must be employed to look for solutions and potential linearizations.

Standard techniques for linear systems include Bode plots of magnitude and phase, Nyquist plots, Nichols chart, Root Locus, and Routh-Hurwitz.

There are some tipoffs exhibited by non-linear systems that do not occur in the linear realm:

1. Limit cycles: https://en.wikipedia.org/wiki/Limit_cycle
2. Sensitive dependence on initial conditions
3. Chaotic orbits, eg. the Lorentz attractor and the Rössler attractor

rjenkinsgb said:

but in itself it is a 1:1 servo where the wheel angle should always duplicate the steering wheel angle, as if it were a rigid system

Click to expand...

In our system, 1:20 is the ratio. In one direction, road wheels turn 0° to some small angle. In this same direction, steering wheels turns 0° to some large angle.
Is this still a servo system?

jani12 said:

In our system, 1:20 is the ratio. In one direction, road wheels turn 0° to some small angle. In this same direction, steering wheels turns 0° to some large angle.
Is this still a servo system?

Click to expand...

Apart from on motorbikes, all motor vehicle steering systems have a large gear ratio, so the steering wheel turns much further than the road wheels. On small vehicles, that allows steering without a power steering system.

A power steering system is in addition to that.

Where a "1:1" or "rigid" system was referred to, that means, for a certain angle of the road wheels, the steering wheel needs to turn the same amount, whether or no the power steering is doing anything.

In my EPS system with 1:20 ratio, steering wheel has to turn 20 degrees for every 1 degree turn of road wheel but since it's power steering, partially steering wheel is turned by the driver and partially steering wheel is turned by the system?

The power steering won't alter the 20:1 ratio.

On a system with a 20:1 ratio, and no power steering, there would be just under 20 times the torque available to steer the driving wheels compared to what the driver put in. It will be slightly less than 20 times due to friction, but for now I'll ignore that.

So if the driver applies 15 Nm of torque, the torque shared between steered wheels will be 300 Nm.

If there is power steering, that might have a ratio of 5 times, so each 1 Nm of torque put in by the driver is added to by 4 Nm from the powered system.

If 300 Nm of torque is needed to steer the wheels, that will be 15 Nm of torque on the steering column. Of that, 12 Nm will come from the power system and 3 Nm will come from the driver.

With or without power steering, to steer the road wheels by 10 degrees needs the steering wheel to turn by 200 degrees. The same distance, but less physical effort, is needed with power steering.

>> Do you know for a fact the system being controlled is linear?
Since the steering wheel to road wheel ratio is 20:1, since the road wheels respond proportionally to any steering wheel input, the system (road wheels) being controlled must be linear?