An 3318

Freescale Semiconductor Application Note

AN3318 Rev. 1.0, 9/2006

Closed Loop Software Design for the KIT 34929 By: Juan Sahagun RTAC Americas Mexico

1

Introduction

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

This application note demonstrates how to implement a first order Proportional-Integral (PI) closed loop control algorithm using the MC34929 3-phase Brushless DC (BLDC) Motor Driver IC, and an 8-bit MCU MC9S08QG8 to process all the external signals, and provide the correct control to the motor driver. It also gives a guideline to develop the software code implemented on the KIT34929EPEVME. The PI control specifies the procedure to calculate the proportional and integrative constants as well as all the MCU signal processing.

2 Closed Loop Block Diagram . . . . . . . . . . . . . 2 3 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 MC9S08QG8 Features. . . . . . . . . . . . . . . . . . . 3 5 PI Control Basic Theory . . . . . . . . . . . . . . . . . 4 6 Software Flowchart Diagram . . . . . . . . . . . . . 5 7 MC9S08QG8 Signal Processing . . . . . . . . . . 6 8 Control Process Implementation. . . . . . . . . 11

All of these processes are considered to be implemented with an MC9S08QG8 8-bit MCU, so calculations and timing processes could change depending on the selected MCU.

9 Timing Considerations . . . . . . . . . . . . . . . . . 13 10 Practical Results . . . . . . . . . . . . . . . . . . . . . 14 11 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . 15 12 References. . . . . . . . . . . . . . . . . . . . . . . . . . 15

© Freescale Semiconductor, Inc., 2006. All rights reserved.

Closed Loop Block Diagram

2

Closed Loop Block Diagram Reference Signal

MC9SO8QG8 MCU PWM

RUN

CONTROL DIR

MC34929 BLDC DRIVER 3_PHASE

TACH, 3XTACH

3-Hall Effect Sensors Feedback

BLDC MOTOR Figure 1. Closed Loop Block Diagram

Explanation: 1. The MCU first receives an external reference signal. 2. This signal is compared with the actual motor speed measured by Hall Effect sensors. 3. The error between these two signals is computed by a First Order PI closed loop control algorithm. 4. Depending on the error, a new pulse width PWM signal is generated to the BLDC Driver. 5. The BLDC driver automatically interprets the signal and drives a 3-phase BLDC Motor. 6. This process repeats.

3

Features

The MC34929 is a complete BLDC motor driver integrated in one chip. Its main features are: 1. Operation Supply Voltage (8V-28V) 2. 3-Phase Hall Effect sensors interface 3. Two tachometer outputs (TACH and 3XTACH) 4. Adjustable Maximum Current Limit 5. Short Circuit Detection and Protection 6. Overtemperature Detection and Thermal Shutdown 7. Undervoltage Detection and Shutdown

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MC9S08QG8 Features

Figure 2. MC34929 Simplified Application Diagram

4

MC9S08QG8 Features

The MC9S08QG8 is a member of the low-cost, high-performance HCS08 Family of 8-bit microcontroller units (MCUs). All MCUs in the family use the enhanced HCS08 core and are available with a variety of modules, memory sizes, memory types, and package types.

Figure 3. MC9S08QG8 Features

Closed Loop Software Design for the KIT34929, Rev. 1.0 Freescale Semiconductor

3

PI Control Basic Theory

This application note uses the 16 TSSOP packaged MCU, which is contained on the KIT34929EPEVME EVB.

5

PI Control Basic Theory

The use of an Proportional controller algorithm will have the effect of decreasing the time constant of motor speed, in closed loop control, as well as reducing, but not eliminating the steady state error (desired speed - actual speed feedback). However, the use of the Integral control algorithm will eliminate the steady state error. The PI controller transfer function is:

C ( s) = K p +

R(z)

E(z)

+

C(z)

Kp

τi ⋅ s

M(z)

, τi =

Kp Ki

U(z)

G(z)

-

PI Control Transfer Function

To apply the Z Transform to this function, it is necessary to use the following conversions:

Obtaining:

C ( z) = K p +

Kp

τ i ⋅ (1 − z ) −1

, τi =

Kp Ki

–1

( Kp + Ki ) – Kp • z C ( z ) = ------------------------------------------------–1 1–z

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Software Flowchart Diagram

6

Software Flowchart Diagram

The software described in this flow chart is contained in the file "mainWithPI.c", discussed in MC34929EPUG (User Guide).

Port Initialization

TRIM Adjust

PWM Register Configuration

MTIM Module Configuration

Keyboard Register Configuration

Enable Interrupts

Channel 1 PWM Interrupt

Loop Cycle

Keyboard Interrupt

MTIM Interrupt

500ms Set new PWM

PI Control Calculation Figure 4. Software Flowchart Diagram

Closed Loop Software Design for the KIT34929, Rev. 1.0 Freescale Semiconductor

5

MC9S08QG8 Signal Processing

The software described below is contained in the file "mainWithPI.c", discussed in MC34929EPUG (User Guide) and is used with KIT34929EPEVME. Description: 1. It is first necessary to initialize the pins data direction and give them an initial value. 2. Fix the MCU’s internal oscillator’s Trim Value to increase the internal clock precision. 3. Configure all the registers to be used as PWM, MTIM and KEYBOARD registers. 4. Enable all the interrupts. 5. A loop cycle is started and the PWM output signal is generated depending on the initial established values. 6. Until reference signal appears, the Keyboard interrupt is activated. 7. At this time the MTIM timer is activated until the reference signal shut down. 8. The pulse width of the reference signal is measured and feedback is given to the PWM. 9. During this process, some TACH feedback values are stored. 10. After 500ms (½ motor turn @ 1 RPS) the stored values begin a PI process control and set a new pulse width value of the PWM. 11. The loop cycle repeats.

7

MC9S08QG8 Signal Processing 1. Reference Signal Characteristics and decoding process. The reference signal is generated every 20ms.

Figure 5. Reference Pulse Control

This reference signal consist of a periodical pulse width, which varies from 0.9ms to 2.1ms with a neutral time of 1.5ms When the pulse width increases from 1.5ms to 2.1ms, the speed of the motor increases from STOP to full speed in CW direction.

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MC9S08QG8 Signal Processing

When the pulse width decreases from 1.5ms to 0.9ms, the speed of the motor increases from STOP to full speed in CCW direction. 2. PWM requirements for the MC34929. MC34929 BLDC driver can operate with a Maximum input frequency of 100 kHz. This driver uses the same input frequency to control the PWM output signal. It’s important to choose an appropriate frequency, because it can change the power consumption of the IC. (For more information regarding this point please refer to the Hardware design application note AN3319) 3. How to generate the PWM signal. For the purposes of this application, the PWM signal is generated by the TPM (Time/Pulse Width Modulator) registers of MC9S08QG8 MCU. The following TPM registers are used to generate the PWM signal to control the Speed of the Motor:

Figure 6. TPMSC (8-bit status and control register)

This register controls the Timer Overflow Flag, Timer Overflow Interrupt Enable, Center-Aligned PWM Select, Clock Source Select and the Prescaler divisor. In this application the TPMSC value is 0x08. Setting the bus rate clock as the TPM clock source for Prescaler input and configuring the TPM channel to operate as input capture, output compare, or edge-aligned depends on the MSnB:MSnA values of the TPMCnSC register.

Closed Loop Software Design for the KIT34929, Rev. 1.0 Freescale Semiconductor

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MC9S08QG8 Signal Processing

Figure 7. TPMMOD (16-bit module register

This read/write module contains the value of the TPM counter. After the TPM counter reaches the module value, the counter starts again and the overflow flag becomes set. In this application, the TMMOD value is 0x190, setting a PWM period of 20 kHz.

Figure 8. TPMCnSC (8-bit status and control register)

This register contains the channel interrupt status flag and control bits that are used to configure the interrupt enable, channel configuration, and pin function. For this application, channel 1 is used to generate the PWM signal, and TPMCnSC becomes TPMC1SC with a value of 0x24. With this value, the PWM generates as Edge-aligned. Closed Loop Software Design for the KIT34929, Rev. 1.0 8

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MC9S08QG8 Signal Processing

During the program, TPMC1SC_CH1IE changes from 0 to 1 allowing the interrupt vector to do the Feedback count.

Figure 9. PWM Period and Pulse Width

Figure 10. TPMCnV (16-bit channel value register)

The PWM duty cycle depends on the 16-bit value charged into this register. This value must be between 0x0000, and the Period value set on TPMMOD (0x0190). This value has to be updated for every reference signal or PI control value. 4. Interpreting the Feedback signal. The TACH feedback is a square signal which indicates the position of the motor, one cycle of this square signal indicates one turn of the motor. In this application, the feedback signal TACH is polled by the MCU every 50ms (Frequency 20kHz) by reading bit 2 of the MCU’s parallel port A. This bit detects every change of state of the pin. Closed Loop Software Design for the KIT34929, Rev. 1.0 Freescale Semiconductor

9

MC9S08QG8 Signal Processing

With this count, it is possible to obtain the feedback speed and in accordingly, the error value. The period of the control process depends on the minimum speed of the motor. For this case we specified a period of 500ms, which indicates that if the motor speed is 60 RPM, we can measure one turn per second or two counts of the MCU port A, bit 2 polling process. To accurately interpret the TACH signal, it is important to know the maximum numbers of counts possible for the polling process, which depends on the maximum speed of the motor. The program code has a function which makes it necessary to set a Max Speed in RPM of the motor to be controlled. The following program code applies: Function where the RPM of the motor has to be set: void InitPorts(UINT16 RPM); The C code to interpret the RPM signal is: RPS=RPM/60;

/*RPS*/

MAXhallcount=RPS/2;

/*MAX value of counts every 500ms*/ /*Time of 1 RPS*/

HallFactor=4000/MAXhallcount; Turns

/*Frequency hall signal sampling */

= HallCount/2;

Feedback = Turns * HallFactor; Feedback = Feedback/10;

First, it is necessary to calculate a multiplicative factor (HallFactor) to get the feedback value and the PWM duty cycle in the same comparison scale. To get this value the numbers of turns at max control speed is needed. As previously mentioned, the process control period is 500ms. The maximum number of counts (MAXhallcount) are determined by dividing the max RPS of the motor by 2. Following that, divide the max value of the duty cycle (0x0190) by the maximum number of counts (MAXhallcount) to obtain the multiplicative factor (HallFactor) HallCount is the value measured from the TACH feedback signal. Divide it by 2 to get the number of motor turns, and then multiply the result and the HallFactor to obtain the scaled Feedback value (Feedback).

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Control Process Implementation

5. Obtaining Error Value. Following the last decoding process, compare the Feedback value and the reference signal value (Speed). Error = Speed - Feedback; (steady state error)

8

Control Process Implementation The motor system to be controlled was considered as a first order system. The actual motor speed is calculated from input capture channels, and the desired speed is generated in the microcontroller.

R(z)

E(z)

+

C(z)

M(z)

G(z)

U(z)

-

System Transfer Function

This system has the following transfer function in the continuous time domain.

Taking the Z transform, and considering the zero order hold of the PWM module, the system’s transfer function becomes: –T ⁄ τ –1 (1 – e )⋅z G ( z ) = ------------------------------------------–T ⁄ τ –1 1–e ⋅z As it was shown in section 5, the PI control’s function is:

Closed Loop Software Design for the KIT34929, Rev. 1.0 Freescale Semiconductor

11

Control Process Implementation

If we join the C(z) and G(z) to have just one block that shows the closed loop system we obtain:

C ( z) ⋅ G( z) 1 + C ( z) ⋅ G( z)

R(z)

U(z)

Gd(z) Where: – T ⁄ τd –1 (1 – e )⋅z G d ( z ) = ----------------------------------------------– T ⁄ τd – 1 1–e ⋅z Then the controller is: Gd ( z ) C ( z ) = ---------------------------------------------G ( z ) ⋅ [ 1 – Gd ( z ) ] –1 –T ⁄ τ –1 – T ⁄ τd ( Kp + Ki ) – Kp ⋅ z 1–e ⋅z 1–e C ( z ) = ---------------------------- ⋅ --------------------------------------- = ---------------------------------------------------–1 –1 –T ⁄ τ 1–z 1–z 1–e Solving for Ki and KP: Ki = 1 – e

– T ⁄ τd

–T ⁄ τ Ki • e K p = ---------------------------–T ⁄ τ 1–e Where: T : Controller Period τ : Time constant of motor speed in open loop. τd : Desired time constant of motor speed in closed loop. KP : Proportional Gain of the controller. Ki : Integral Gain of the controller.

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Timing Considerations

9

Timing Considerations

Graphic 1

Graphic 2

In Graphic 1 and Graphic 2 the following signals are shown (Graphic 2 represents a zoom in of a single yellow/green pulse event): a) Reference Signal (Yellow) - top signals b) MTIM Signal (Green) - middle signals c) PWM (Pink) - bottom signals The MTIM Timer is configured with a frequency of 40 KHz, counting the time of the reference design pulse width. The MTIM is activated when the Keyboard detects a reference design rising edge and turns off when the Keyboard detects a falling edge. During all this time the TPM produces a PWM signal. All closed loop calculations are processed once the MTIM is turned off. The time you have available to make this calculation is the result of the difference between the 20ms of reference period and the lost time to execute the MTIM counter (reference signal pulse width). The maximum and the minimum time to execute this calculation are:

Closed Loop Software Design for the KIT34929, Rev. 1.0 Freescale Semiconductor

13

Practical Results

10 Practical Results The implementation of the PI controller using parallel programming are shown in the following graphics:

Ki + E(z)

M(z) +

Ki 1 − z −1

Based on this diagram we obtain the following equations in discrete time domain:

For each motor it is necessary to calculate its corresponding Kp and Ki values: Ki = 1 – e

– T ⁄ τd

–T ⁄ τ Ki • e K p = ---------------------------–T ⁄ τ 1–e For this application, the values used to calculate Ki and Kp were the following: T = 500ms τ = 5.44ms τd = 1s.

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Conclusions

Taking these time values and applying the corresponding formulas for KP and KI we obtained the next results: –T ⁄ τ Ki • e – 38 K p = ---------------------------- = 1.22 × 10 –T ⁄ τ 1–e Ki = 1 – e

– T ⁄ τd

= 0.393

These values are scaled by 256 ( KI = 100, KP ˜ 1) to get a better calculation process. At the end of the operation, the result must be divided by 256: MI = ((signed long)(Error*KI)) + ((signed long)(MI)); MK = ((signed int)(Error*KP)) + ((signed long)(MI)); MK = MK>>8; The MK result can now be added to the output signal to make the closed loop control. Speed = ((signed int)(Speed)) + ((signed int)(MK));Recommended Schematic

11 Conclusions The MC34929 is not only a 3-phase BLDC motor control IC, but also it can interpret Hall Sensor inputs and provide TACH signal outputs required to support a PI closed loop control algorithm. Together with an MCU, the MC34929 provides a complete and intelligent 3-phase BLDC Motor Control Driver solution.

12 References 1. Katsuhiko Ogata, MODERN CONTROL ENGINEERING, Third Edition, Prentice- Hall, 1998. 2. W. Bolton, Control Engineering, 2nd Edition, Alfaomega, 2001. 3. Katsuhiko Ogata, DISCRETE TIME CONTROL SYSTEMS, Second Edition, PrenticeHall, 1996. 4. MC34929 Data Sheet 5. AN3319 - Hardware Design Using the MC34929 6. KIT34929 Software Programming Quickstart User Guide - MC34929EPUG

Closed Loop Software Design for the KIT34929, Rev. 1.0 Freescale Semiconductor

15

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AN3318 Rev. 1.0 9/2006

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