UM0324 datasheet(86/105 Pages) STMICROELECTRONICS

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Library functions

UM0324

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4.8.3

PID regulator theoretical background

The regulators implemented for Torque, Flux and Speed are actually Proportional Integral

Derivative (PID) regulators (see note below regarding the derivative term). PID regulator

theory and tuning methods are subjects which have been extensively discussed in technical

literature. This section provides a basic reminder of the theory.

PID regulators are useful to maintain a level of torque, flux or speed according to a desired

target.

Figure 45.

PID general equation

Equation 1 corresponds to a classical PID implementation, where:

●

Kp is the proportional coefficient,

●

Ki is the integral coefficient.

●

Kd is the differential coefficient.

Note:

As mentioned in Figure 45, the derivative term of the PID can be disabled independently

(through a compiler option, see 75x_MCconf.h file) for the torque/flux or the speed

regulation; a PI can then be quickly implemented whenever the system doesn’t require a

PID control algorithm.

4.8.4

Regulator sampling time setting

The sampling time needs to be modified to adjust the regulation bandwidth. As an

accumulative term (the integral term) is used in the algorithm, increasing the loop time

decreases its effects (accumulation is slower and the integral action on the output is

delayed). Inversely, decreasing the loop time increases its effects (accumulation is faster

and the integral action on the output is increased). This is why this parameter has to be

adjusted prior to setting up any coefficient of the PID regulator.

In order to keep the CPU load as low as possible and as shown in equation (1) in Figure 45,

the sampling time is directly part of the integral coefficient, thus avoiding an extra

multiplication. Figure 46 describes the link between the time domain and the discrete

system.

torque = f(rotor position)

flux = f(rotor position)

torque = f(rotor speed)

torque and flux regulation for maximum

torque regulation for speed regulation

of the system

system efficiency

Where:

Error of the system observed at time t = T

Error

sys

Error

sys

–

Error of the system observed at time t = T - Tsampling

()

Error

sys

Error

sys

Error

sys

Error

sys

–

()

∑

(1)

Derivative term can be disabled

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