AN2388 datasheet(43/54 Pages) STMICROELECTRONICS

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AN2388

Software design

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Figure 40.

Mechanical rotor angle estimation block diagram

4.5.3

The PI regulator

Introduction

PID has a fundamental importance in the industrial controller field due to the simplicity of

approach, the robustness of control and the immediacy of calibration.

In this regulator, the variable “error”, the derivative and the integral errors are performed to

calculate the output variable that has the following representation:

A complete discussion of Proportional Integral Derivative (PID) controllers is beyond the

scope of this application, but this section will provide the basics of PID operation.

A digital PID controller is executed at a periodic sampling interval. It is assumed that the

controller is executed frequently enough so that the system can be properly controlled. The

error signal is formed by subtracting the desired setting of the parameter. The sign of the

error indicates the direction of change required by the control input.

The Proportional term (P) of the controller is formed by multiplying the error signal by a P

gain, causing the PID controller to produce a control response that is a function of the error

magnitude. As the error signal becomes larger, the P term of the controller follows and

grows to provide more correction. The effect of the P term tends to reduce the overall error

as time elapses. In most systems, the error of the controlled parameter gets very close but

does not converge so it remains a small steady state error.

The Integral (I) term of the controller is used to eliminate small steady state errors. The I

term calculates a continuous running total of the error signal. Therefore a small steady state

error accumulates into a large error value over time. This accumulated error signal is

multiplied by an I gain factor and becomes the I output term of the PID controller.

The Differential (D) term of the PID controller is used to enhance the speed of the controller

and responds to the rate of change of the error signal. The D term input is calculated by

subtracting the present error value from a prior value. This delta error value is multiplied by a

D gain factor that becomes the D term of the controller. The D term of the controller

produces more control output the faster when the system error is changing.

This application doesn’t use the D terms due to the relatively slow response time of motor

speed changes. In this case, the D term could cause excessive changes in PWM duty cycle

that could affect the operation of the algorithm and produce over current trips.

The PI (Proportional-Integral) regulators are implemented with output saturation. Keep in

mind that all the variables are in 1.15 format.

Mechanical_Rotor_Angle

Pulses Encoder

T3IN

T3EUD

Channel A

Channel B

ST10F276

Scaling factor

Incremental

Timer

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