Introduction to PID Tuning - What is PID?

This is an introductory document on using the PID control system in MoTeC ECU's.  Whilst it is based on the Hundred series ECU's, the base principles also apply to the M1 series of ECU's as well, with the M1 having extra flexibility in operation.

What is PID?
PID stands for Proportional, Integral, and Derivative and is a type of feedback control system. It compares a measured value (from a sensor, say) against a desired value (the setpoint or aim) and adjusts outputs to reduce the difference (error) between the two.

The controller (or ECU in our case) uses a constantly updating calculation to control a physical system. It looks at the current value of the error, the integral of the error over a recent time interval, and the current derivative of the error signal to determine not only how much of a correction to apply, but for how long.

In the case of a Drive by Wire system the drivers’ pedal position gives the Aim value while the angle of the throttle bodies Throttle Position sensor is the feedback channel. When there is a difference between the two signals, the duty cycle of the ECU outputs are changed to so that the feedback tracks the aim value.

The response time of any system is greatly dependant on the physical components (lag time). E.g.: cam position changes quickly, while fuel cell gas pressure changes much more slowly. A Drive by Wire system uses a servo motor to drive the throttle blade to the Aim position where the response time of the system will be different again.

We can also consider the varying rate at which the driver requests different positions. In practice this can be accounted for when tuning the PID parameters by testing the systems’ response to sudden (or step ) changes in the aim value.

Note that in the real world a PID system will never track exactly* to the setpoint. Instead the tuning parameters include a ‘dead band’ – an area around the setpoint where the controller doesn’t try and drive the system any closer to the setpoint.

The output signal is the sum of the Proportional, Integral and Differential components. We will look at each of these in turn.

Proportional Component
The Proportional component is equal to the Proportional Gain (‘P’) multiplied by the Error. The proportional parameter has an immediate response when there is an Error and it controls the bulk of the response in the system. The proportional component alone will never reduce the error to zero, since as the error decreases, the proportional response also decreases.

If the Proportional Gain is too small, the error will only be reduced by a small amount and response will appear to be slow. Too much proportional gain and the system will be unstable and hunting will occur. Hunting is the rapid over and undershooting of the system around the setpoint.

Integral Component
Integral is a more slowly changing factor there to reduce error over the longer term. The size of the Integral component will keep increasing as long as there Error is not zero. E.g.: boost and idle control valves require some duty cycle to hold a position, with an error value of close to zero, P & D components have little effect, but the I component will hold the valves position. If the control overshoots the setpoint, the error value changes polarity and a ‘negative’ term is added to the Integral component, reducing it.

Large amounts of Integral Gain can sometimes cause problems as well. “Integral Windup” is a situation that occurs when the error is constant, causing the Integral component to keep increasing the output to try to reduce this. If the conditions maintaining the error are removed the system can overshoot the aim value and then the control needs to reverse. Use the lowest Integral Gain that will ensure long term errors are within the dead band.

Some MoTeC PID functions include an ‘Integral Clamp’ parameter that sets the maximum allowable value of the Integral component so that you do not get Integral Windup.

Derivative Component
Derivative Gain has a damping effect on control of the system. It is there to improve the response time of the system. It is based on the rate of change of the Error value, so the derivative component will be larger for sudden changes in error than for gradual changes.

Again, the response time of any system is greatly dependant on the physical components (i.e.: lag time), so the Derivative Gain must be set accordingly. For example, if the Derivative Gain is too large, this will lead to ‘overshoot’ as the response goes past the aim value, and the system must reverse.

If there is high frequency noise on a measured position, a large Derivative gain will cause wild fluctuations. Therefore the size of the Derivative gain is dependant on the noise of the physical system. For a filter to be used on the feedback channel, the response time of the system must be of a lower frequency than any noise.

The derivative term tends to come into operation during the initial transient change in the system. It should have the effect of ‘flattening’ the response curve, reducing overshoot from the proportional response.

Feed Forward
Also known as “Linearization”. Some systems will always require a certain output duty cycle for operation, e.g.: where there is a known resistance in the system such as from the spring in a DBW throttle body. Feed-Forward is a predicted output value based on knowledge of how much output is needed to control a system to a certain Aim. This value can be used as a starting point for the systems control.

E.g.: feed forward is used as the Average Position for the PD and PID Boost Control function. The Average Position sets a starting value duty cycle the valve works from. If you need roughly a known duty cycle to achieve your aim boost you would set this as your Average Position so the control loop has a close starting point.

A Real World Analogy
Think of a driver with no brakes wishes to stop a car at a set of lights. The driver is using the accelerator pedal to give the car forward movement to get to the lights. The closer the car gets the less the driver pushes on the accelerator pedal. The amount of throttle is the Proportional Gain. The Driver is relying on the car to slow down because of rolling friction between the tires and the road. If the driver is trying to get to the lights quickly, more throttle will be used. 

The problem is that if the driver relies solely on the rolling friction to stop the car, they may roll straight past the lights and then need to put the car into reverse and head back. This could happen several times before the car comes to rest at the lights and the faster the driver tries to get there, (better system response) the worse the over/undershooting problem becomes.

Now consider if the driver also has a braking system. When approaching the lights they can reduce the amount of throttle to slow the car and also apply the brakes to reduce the speed. The brakes act as the Derivative component of the system. It is logical to suggest that with the throttle and brakes the driver can now get to and stop at the lights with greater ease and generally more quickly, with less over/undershoot.

Now consider the driver has to do this when the lights are on a slight upward sloping hill. The driver can perform the stopping exercise using the throttle and brakes but the car will start rolling backwards when it is stopped. The driver now needs to apply a little bit of throttle (assume the brakes are ONLY for reducing speed and not to stop movement) to hold the car at the stopping point so it does not roll backwards, this is the Integral component of the system.

It can be seen that if the same driver has a very powerful car, the amount of throttle and brake needed to get to the set of lights is different to the amount of throttle and brake needed for a less powerful car. Obviously the high powered car will get the job done quicker but with more energy needed and therefore more stress on the equipment.