SPRUHJ1I User guide

SPRUHJ1I January 2013 – October 2021 TMS320F2802-Q1 , TMS320F28026-Q1 , TMS320F28026F , TMS320F28027-Q1 , TMS320F28027F , TMS320F28027F-Q1 , TMS320F28052-Q1 , TMS320F28052F , TMS320F28052F-Q1 , TMS320F28052M , TMS320F28052M-Q1 , TMS320F28054-Q1 , TMS320F28054F , TMS320F28054F-Q1 , TMS320F28054M , TMS320F28054M-Q1 , TMS320F2806-Q1 , TMS320F28062-Q1 , TMS320F28062F , TMS320F28062F-Q1 , TMS320F28068F , TMS320F28068M , TMS320F28069-Q1 , TMS320F28069F , TMS320F28069F-Q1 , TMS320F28069M , TMS320F28069M-Q1

11.7 Speed PI Controller Considerations: Current Limits, Clamping and Inertia

Up to now, we have only discussed the tuning problem in the context of a linear system. This is because under steady-state conditions when the system settles out, you will most likely find that you are operating in the linear region, and the AC signal content will be very small. Therefore, performing a small-signal (linear) analysis will tell you how stable your system will be when it is not operating in saturation. But in most real-life scenarios, the system will saturate because of limits on your voltage and/or current, especially under large transient conditions. This saturation effect can play an important role in the PI controller; especially the integrator. Since the maximum torque the motor can produce is limited by your current limit, the acceleration of the system is also limited. But the integrator doesn't know this, and it thinks it can make the motor speed up faster by increasing its output. This increased integrator output can't help the situation since the system is already saturated. All it does is create a very large output that will cause the system to overshoot when it does come out of saturation. For this reason, most PI integrator outputs are clamped to keep them from continuing to integrate needlessly when the system is saturated.

A simple static clamping scheme is illustrated in Figure 12-14. The most common scenario is to set the clamp values equal to the PI output limit values. For example, the output limit of a PI controller that regulates speed is usually what sets your current limit value since the speed PI output is the reference input signal for the current PI controller. However, there is nothing that says that the integrator limit must equal the PI output limit, and many designs use different clamp values based on the specific application.

Figure 11-14 PI Controller with Static Integrator Clamping

Figure 12-15 shows a dynamic clamping scheme which provides superior performance over the static scheme. The thinking behind the design of this scheme is based on the rationale that if the system is already saturated by the P gain output, then why continue integrating? Only during conditions where changes in the integrator output would result in changes in the PI controller output is the integrator allowed to continue to integrate error unconstrained.

Figure 11-15 PI Controller with Dynamic Integrator Clamping

The effectiveness of integrator clamping can be seen by the simulated curves in Figure 12-16. Let's stimulate the system we designed in Section 6 with a commanded speed step from zero to a target speed of 1500 RPM. Shown are the effects of system overshoot under the conditions of no clamping, static clamping where the integrator clamp values equal the output clamp values and finally, dynamic clamping. As you can see, no integrator clamping at all is unacceptable as it results in extremely high overshoot which triggers further system saturation and oscillation. Static integrator clamping dramatically improves this situation. However, dynamic clamping improves performance even further, resulting in a 6 times improvement in the overshoot peak value compared to static clamping in this example.

Figure 11-16 Example Comparison of Integrator Clamping Techniques

At this point, let's double-back and talk about a very important part of this whole discussion. Everything we have talked about in these seven sections is not very significant without knowing one critical piece of the system which is the inertia. Without this knowledge, there is no definitive way of stabilizing the speed loop. In many cases, you can calculate the inertia by knowing the form factor and mass distribution of your rotating load. If a gearhead is present on the motor shaft with a big enough gear ratio, the load inertia can often be ignored since transferred inertia is inversely proportional to the square of the turns ratio, and just deal with the motor inertia which is listed on most motor data sheets. If neither of these options is valid, there are several techniques used to measure inertia which usually involve some type of controlled acceleration, deceleration, or both. However, it is not common to see techniques which also take into consideration static torque loading on the motor shaft ("static," loads in this context mean loads which don't change as a function of time, such as friction or an elevator load). The following is a proposed (but at the time of this writing, untested) technique which should yield a better inertia estimate than the techniques mentioned above:

Design the current controller using techniques discussed in the PI tuning sections.
Set the PI coefficients for the speed loop to conservative values that will just allow spinning the motor up to speed (that is, having sluggish dynamic response should not be a concern at this point).
Spin the motor up to a low speed and allow it to settle (so that inertia torque equals zero). Then take a reading of the average motor torque (Figure 12-17).
Repeat step 3 at successively higher speeds, and generate a graph of average torque readings as a function of speed (Graph 1). Record the average current required for the highest speed setting. Then turn off the motor and allow it to stop.
Disable the speed loop and using current mode only, apply about 1.2x to 1.5x the current from step 4 to the motor. As the speed hits each speed for which a torque value was recorded in step 4, record the torque again (Graph 2), and also take a time stamp.
Subtract graph 1 from graph 2 (this should be the acceleration torque only) (Graph 3).
For each point in graph 3, calculate the delta speed and delta time between the points before and after the target point. Divide delta speed by delta time to get the local acceleration value for that point.
For each torque value in graph 3, divide it by the local acceleration for that point from step 7, to create a graph of inertia (J) as a function of speed.
Average the inertia values at different speeds to obtain a single estimate for system inertia.

This process can be done a priori on a bench dynamometer test, or, if there is a way to measure torque in the control algorithm such as the torque output of InstaSPIN-FOC, this can be done as part of the commissioning process of the motor in its target application.

Up to now, we have only discussed PI tuning in generic terms which are independent of the control topology. In the next section, we will focus on some of the subtle points to consider when designing PI controllers for use in a Field-Oriented Control (FOC) system.

Figure 11-17 Average Motor Torque Readings