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AN1213/D

SEMICONDUCTOR

MOTOROLA

APPLICATION NOTE

16-Bit DSP Servo Control With the MC68HC16Z1

By David Wilson

INTRODUCTION

This application note discusses digital filter implementation of Proportional, Integral, Differential (PID) con-

trol algorithms. The implementation takes advantage of the control-oriented digital signal processing capa-

bilities of the Motorola M68HC16 family of modular microcontrollers.

Microcontrollers have come a long way in the past two decades. Once relegated strictly to computer appli-

cations, these devices have steadily encroached on domains previously dominated by analog technology.

Closed-loop control systems are among the most recent bastions to fall. Control systems based on digital

processing of measured values are inherently less sensitive to changes in temperature and to aging than

systems implemented with analog circuitry. In addition, digital system performance can be changed by de-

veloping new software rather than by physically altering a PC board. In fact, many emerging controller tech-

nologies, such as adaptive control, would be economically unattainable if not for digital processing

capabilities.

MICROCONTROLLERS AND DIGITAL SIGNAL PROCESSORS

After the decision to use a digital solution has been made, a designer must evaluate system requirements

to determine what type of device is best suited for the job. The decision often comes down to a choice be-

tween a standard microcontroller or a digital signal processor. Although design constraints vary, all digital

signal processors are designed specifically to perform algebraic sum of products calculations at high

speeds.

Standard microcontrollers are best suited for applications that require relatively little real-time control, and

also require the controller to perform other tasks, such as running an operating system or user interface.

Digital signal processors, on the other hand, are generally used when a control algorithm is real-time inten-

sive, and other system tasks can be handled by a master processor. There is thus a price-performance gap

between general-purpose controllers and specialized, dedicated DSP engines.

THE M68HC16 FAMILY

The M68HC16 family of modular microcontrollers bridges the gap between standard microcontrollers and

digital signal processors. The CPU16 module provides a rich instruction set as well as dedicated control-

oriented DSP capability, while other system modules provide a variety of interfacing options. The high level

of functional integration in M68HC16 devices reduces the amount of external hardware necessary to

achieve a complete system solution.

The M68HC16 family bridges another gap by providing a migration path from the M68HC11 family of 8-bit

controllers to the M68300 family of 32-bit modular controllers. Many M68HC16 and M68300 modules, such

as the general-purpose timer (GPT), queued serial module (QSM), and system integration module (SIM),

are identical. Use of the SIM provides both families with a common external bus interface.

MOTOROLA AN1213/D

The CPU16 programming model is similar to that of the M68HC11 CPU, and the CPU16 instruction set is

upwardly code-compatible with that of the M68HC11 CPU. However, the CPU16 also provides significant

additional capabilities. With dedicated multiply and accumulate registers and 18 instructions added specif-

ically for DSP support, M68HC16 family devices are general-purpose microcontrollers capable of perform-

ing DSP operations, not just DSP engines with a few additional embedded-control features. This is an

important distinction because most digital signal processors do not have bit manipulation capability, multiple

interrupt vectors, or a flexible software stack. Although M68HC16 devices do not perform multiply and ac-

cumulate operations as rapidly as some dedicated digital signal processors, they are ideally suited for ap-

plications such as motion control systems.

PID CONTROLLER BASICS

PID controllers offer some distinct advantages over other control topologies; but nothing is free —as in all

design processes, there must be trade-offs.

Figure 1

is a block diagram of an analog PID control structure.

Figure 1 PID Controller Block Diagram

PID TRANSFER FUNCTION

The transfer function (as a function of s) is :

(EQ 1)

where:

C(s) is the output of the PID section

E(s) is the input to the PID section (usually servo error)

P is the multiplier for the servo error

I is the multiplier for the integral of the servo error

D is the multiplier for the derivative of the servo error

s is the Laplace complex frequency variable.

The previous equation shows that the PID controller has a pole at s = 0, and two zeros :

(EQ 2)

The two zeros are real-valued when 4DI

≥

. A Bode plot of the PID transfer function with real-valued zeros

reveals that one of the zeros is used to brake the 20 dB/decade descent associated with the integrator, and

the other is used to provide a 20 dB/decade rise and positive phase lead required to stabilize the system.

INPUT

E (S)

SOUTPUT

C (S)

PID CONTROLLER BLOCK

AN1215

C(s)

E(s)

----------- Ps + I + Ds2

--------------------------------=

s– P P24DI–±2D

---------------------------------------=

AN1213/D MOTOROLA

TRANSFER FUNCTION TERMS

Each of the transfer function terms affects system performance.

The P Term

The

Proportional

term is the most subtle and perhaps most misunderstood term in the PID algorithm. The

P term amplifies the error signal by a constant amount. However, P is not in series, but in parallel with I and

D, which implies that P cannot be used to scale the transfer function amplitude at all frequencies. Instead,

the P term interacts with the I and D terms to determine the placement of the zeros in the controller open-

loop transfer function.

Figure 2

shows a root locus solution to the numerator of Equation 1 as P is varied

with respect to I and D.

Figure 2 Effect of Varying P on Zeros

The I Term

The

Integral

term gives the servo loop that inflexible, stubborn feel. Since the I term adjusts the amount of

integrated error mixed to the output of the filter, any I value other than zero implies that

steady state error

can be tolerated by the servo loop. In other words, given sufficient time, a PID control loop will eventually

servo the output to the exact value of the commanded input.

In the frequency domain, the I term also affects placement of the zeros, as shown in

Figure 3

. For I = 0,

one of the zeros is at s = –P/D, and the other zero is at s = 0, which means that it will cancel the integrator

pole at s = 0. This makes sense intuitively since the integrator is turned off if I equals zero. As I increases,

the servo loop becomes “snappier”, i.e., it responds more quickly to steady state error.

It appears that adding an integrator to the servo loop would be a panacea for motion control headaches.

However, while adding an integrator does address steady state error, it can also have a negative impact on

system dynamics. The effect is most easily seen in the time domain. Consider a linear PID system that per-

forms servo control. Initially, the controlled motor is at rest, with zero position error. Torque is applied to the

motor shaft, changing its position and holding it in the new position. The control system senses a steady-

state error and tries to return the shaft to the commanded position. Since the example system is linear, con-

trol voltage continues to increase as a result of integrated error. While the increasing control voltage could

cause the motor to overheat, this is not the only detrimental effect. If the applied torque is suddenly removed

while integrator output is large, the motor shaft will spin past the desired shaft position while control voltage

is “dumped”. Eventually, a zero steady-state condition is achieved, but in an underdamped (and potentially

unacceptable) manner. Because this situation is similar to winding up a spring and then letting it go, the term

“wind-up” is used to describe it. Techniques to mitigate wind-up are discussed later in this note.

DELTA P ON ZEROS

P = 0

P = ∞

P = 0

(I ÷ D)

P = ∞

P = (4DI)

– j (I ÷ D)

j (I ÷ D)

S PLANE

AN1213

MOTOROLA AN1213/D

Figure 3 Effect of Varying I on Zeros

The D Term

The

Derivative

term has its greatest effect on servo-loop damping and stability. As

Figure 4

shows, in-

creasing the value of D from 0 to P

/4I causes both zeros to move toward –2I/P. As this happens, the higher-

frequency zero takes on a value that can provide useful phase lead to offset the phase lag introduced by

poles elsewhere in the system.

The design of the derivative portion of a PID controller is critical to system performance. In a position servo,

the feedback position signal is differentiated (either directly or indirectly) to create a signal proportional to

the output velocity. In systems that use a digital feedback mechanism (such as shaft encoders), velocity

information is also quantized, typically in encoder tics per sampling interval. At low velocities, the effect of

quantization on system performance is pronounced because each quantization step represents a large por-

tion of velocity signal amplitude. This can cause an audible scraping noise or unnecessary motor heating

at low speeds.

A velocity state observer can be used to mitigate low-speed quantization effects. The state observer uses

a software model of the load to synthesize a higher-resolution velocity signal. Each sample period, PID con-

troller output is input to the model, and the model generates an estimate of output position. The estimate is

compared to actual encoder position to generate an error value, which is used to refine the estimate for the

next sample period.

A simpler way to deal with this problem is to calculate the velocity information at a lower sampling frequency,

thus increasing the number of encoder tics per sampling interval for a given velocity. A similar technique is

discussed in the next section of this note.

The location of the differentiator in the feedback loop also affects performance. In

Figure 1

, the differentiator

input is the error signal. Since the commanded input position signal is a component of the error signal, any

abrupt change in commanded position is differentiated as if it were feedback position, resulting in a “pop-

ping” effect at the filter output. An alternate topology can provide more satisfactory performance, as shown

in the next section.

DELTA I ON ZEROS

I = P2

4D I = 0

–P

I = 0

I = ∞

– P

I = ∞

AN1213

AN1213/D MOTOROLA

Figure 4 Effect of Varying D on Zeros

DESIGNING A PID FILTER

PID TOPOLOGY

To implement a PID control algorithm on any processor, methods of computing the functions specified by

the controller (an integral and a derivative) must be developed. Once these methods are established, the

digital PID controller transfer function is calculated in much the same way as the analog version. Unfortu-

nately, because this is a sampled system, the Laplace transform or the s domain cannot be directly used,

as in analog PID calculations.

To address this problem, a separate frequency space called the “z” domain has been developed just for

sampled systems. Using the z domain, sampled approximations of many common functions can be repre-

sented using the variable “z” just as “s” is used to represent linear analog functions. For the sake of simplic-

ity, assume the following definitions are true:

(EQ 3)

Where:

z is the complex sampled frequency variable

T is the sampling frequency period, in seconds.

This form is derived from a step-invariant analysis —the filter is constructed by dividing the Z transform of

a specified input (a step function) into the Z transform of the desired output for that input (a ramp function).

The differentiator is simply the inverse, or:

(EQ 4)

Although these are not the only z-domain representations of these functions, they are widely used in control

applications. See Reference 1 for more information on this topic.

D = P2

D = 0

–2I

P– I

D = 0 D = ∞

DELTA D ON ZEROS

AN1213

INTEGRATOR Tz

z – 1

-------------=

DIFFERENTIATOR z – 1

-------------=

MOTOROLA AN1213/D

To mitigate encoder velocity quantization noise, the derivative function is followed by an “n-point averager”,

which averages velocity information over a range of samples to provide finer resolution. However, this crude

low-pass filter also introduces phase lag proportional to

that counteracts the desired phase lead generated

by the differentiator. To balance these two constraints,

is set equal to two, which effectively doubles en-

coder resolution per sampling interval. The derivative stage transfer function is :

(EQ 5)

Figure 5

shows the PID controller and transfer functions of parasitic effects found in the system. All items

Figure 5

except the power stage, the motor, and the encoder, are implemented by the M68HC16 device.

Figure 5 System Block Diagram

The differentiator input is the encoder signal, not the error signal, for reasons discussed in the previous sec-

tion. The commanded input signal is not differentiated, and the stability of the system is not affected be-

cause the overall open-loop transfer function remains the same.

The integrator has several associated features that improve system damping. One is a software switch to

enable the integrator only when it is needed. Since this is a position servo, it is assumed that the integrator

is not required when the velocity magnitude increases above a specified threshold. This prevents an error

signal from being integrated over the entire duration of a change in position, which would require overshoot

to dump the error.

Figure 6

, which shows system response to a step function, illustrates the effectiveness

of this technique.

VELOCITY z – 1

-------------





--- 1

------+





PID SYSTEM BLOCK

– D

THRESHOLD

SWITCH

OUTPUT

POSITION

G (S)

4 POINT

AVERAGER

PROFILER

2 POINT

AVERAGER

EXP(– STC)

z – 1

OUT

INTEGERATOR

LIMIT

PWM LIMIT

VOLTS

PWM

RADIANS

VOLT

COUNTS

RADIAN

MOTOR

DIFFERENTIATOR

ENCODER POSITION

DSP

ACCUMULATOR

COMMANDED

POSITION POSITION

ERROR

ON / OFF

CALCULATION

DELAY

INTEGRATOR

SAMPLE AND

HOLD

OUT

AN1213

z – 1

AN1213/D MOTOROLA

Figure 6 Step Response of System With and Without Integrator Switching

Integrator output magnitude is limited to mitigate the wind-up effect associated with PID integrators. The

limit is application-dependent, and should be set to the minimum value required to generate an output suf-

ficient to overcome any anticipated load resistance.

In theory, the sampling process is modeled as a series of impulse functions, which implies a PID filter cal-

culation time of zero. In reality, the amount of time required to execute a digital filter algorithm must be ac-

counted for, since it introduces phase lag into the system. Even though the lag is minuscule at the

frequencies of interest in this note, it is included for the sake of completeness, and is given by :

(EQ 7)

Where T

= Calculation time in seconds

The MC68HC16Z1 GPT module has two PWM ports, one of which is used as an output for the digital filter.

The PWM value is updated every sample period, and is latched until the following sample period. This sam-

ple and hold function introduces phase lag, which must be considered. There are several mathematical

models for a sample and hold; the one selected for this application is :

(EQ 8)

The commanded position input to the digital filter comes from another software routine called a profiler,

which is responsible for generating a series of positions corresponding to a specific velocity profile (a trap-

ezoidal profile is used for this application). Profiler design is beyond the scope of this note, but, because

profiler execution time rivals that of the digital filter, a new commanded position is not calculated at each

digital filter sampling interval (488

s). While the CPU16 could easily perform the extra calculations, a re-

calculation interval equal to four times the sampling interval was judged sufficient. However, lowering the

profiler update rate creates another problem. The commanded position input now has a large step change

PWM STEP RESPONSE (INT)

WITH INTEGRATOR SWITCHING

AN1213

WITHOUT INTEGRATOR SWITCHING

Gcd 2() e

sTc–

GSH s, z() 1

---



z – 1

-------------





MOTOROLA AN1213/D

every fourth filter sample. This introduces a frequency component corresponding to profiler update rate at

the filter output, which is quite audible in the motor windings. To compensate, profiler outputs are shifted

through a 4-point averager running at the same frequency as the PID filter. The averager linearly interpo-

lates or smoothes profiler data at a 4X oversampling rate, which in turn eliminates motor noise. Filter output

waveforms shown in

Figure 7

illustrate the effectiveness of this technique.

Figure 7 PWM Output Ripple With and Without Profiler Filtration

SELECTING PID COEFFICIENTS

The following points should be taken into consideration when designing a servo.

To assure robust operation and speed, it is generally desirable to have as high a system frequency re-

sponse as possible.

To obtain adequate damping performance, phase margin (180 degrees minus the phase lag of the

open-loop transfer function evaluated at unity gain) should be as large as possible.

To make certain the system can tolerate a large change in gain (e.g., sagging power supply voltage or

drifting load parameters) without loss of stability, gain margin (difference in gain between the open-loop

transfer function gain evaluated at the point of –180 degrees phase shift, and unity gain) should be as

great as possible.

All of these conditions can be observed by generating magnitude and phase frequency plots of the open-

loop transfer function G(s,z)H(s,z). The open-loop function can be calculated by breaking the servo loop

diagram at a convenient point, then multiplying all individual transfer functions encountered around the loop

until arriving back at the break point. However, this procedure yields an equation that is a function of both

s and z. Fortunately, there is a mathematical relationship between z and s that allows representation of the

equation as a function of s alone.

PWM OUTPUT RIPPLE

WITHOUT PROFILER DATA FILTERING

WITH PROFILER DATA FILTERING

AN1213

AN1213/D MOTOROLA

(EQ 9)

Where T is the sampling period in seconds

Assume that the PID controller section is bypassed and calculation delay is zero. By using equation 10 as

the transfer function for the motor, and assigning K1 and K2 (Figure 5) values of 0.1875 and 636.62, an

open-loop transfer equation as a function of s is obtained.

(EQ 10)

Where:

Ke is the back EMF constant (70.61 mV/(rad/second))

is the mechanical time constant (6.2 ms)

is the electrical time constant (1.62 ms)

Open loop unity gain frequency is approximately 74 Hz, but phase margin is about –20 degrees. The system

will oscillate due to poor phase margin —phase compensation is needed.

Figure 8

and

Figure 9

are open-

loop transfer function magnitude and phase plots.

Figure 8 Open-Loop Magnitude Without Compensation

GMOTOR s()

-------

s1 st

+()1st

+()

-------------------------------------------------=

PWM OPEN LOOP MAG

–6

–12

32 4 5 6 7 8 9 10 20 30 40 50 100 200

FREQUENCY (Hz)

AMPLITUDE (dB)

AN1213

MOTOROLA AN1213/D

Figure 9 Open-Loop Phase Without Compensation

Values of P, I, and D are iteratively selected using a computer model of the open-loop transfer function that

includes the PID controller. An initial T

value of 30

s is assumed. Phase margin, gain margin, and frequen-

cy response for several sets of terms are calculated, and working values of P = 0.16, I = 5, and D = 1E–3

are selected. Gain margin is –14.4 dB, and phase margin is improved to about 60 degrees, at the expense

of lowering open-loop frequency response to 41 Hz. At this frequency, the phase lag generated by the 2-

point velocity signal averager is 3.6 degrees. Were a 4-point averager used, phase lag would increase to

10.8 degrees at 41 Hz.

Figure 10

and

Figure 11

are open-loop magnitude and phase plots generated from the working values.

Figure 12

and

Figure 13

are controller transfer function plots generated from the working values. Low-fre-

quency amplification caused by the integrator and high-frequency amplification caused by the differentiator

are apparent. Figure 13 shows the positive phase generated by the PID controller.

PWM OPEN LOOP PHASE

160°

120°

80°

40°

0°

–40°

–80°

–120°

–160°

–200°32 4 5 6 7 8 9 10 20 30 40 50 100 200

FREQUENCY (Hz)

PHASE (DEGREES)

200°

PHASE MARGIN = –19.8°

AN1213

AN1213/D MOTOROLA

Figure 10 Open-Loop Magnitude With Compensation

Figure 11 Open-Loop Phase With Compensation

PWM OPEN LOOP

MAG (COMP)

–6

–12

–18

–24 32 4 5 6 7 8 9 10 20 30 40 50 100 200

PHASE (DEGREES)

FREQUENCY (Hz)

GAIN MARGIN =

146 Hz

–14.4 dB

AN1213

PWM OPEN LOOP

PHASE (COMP)

160°

120°

80°

40°

0°

–40°

–80°

–120°

–160°

–200°32 4 5 6 7 8 9 10 20 30 40 50 100 200

PHASE (DEGREES)

200°

PHASE MARGIN = 59.3°

41 Hz

FREQUENCY (Hz)

AN1213

MOTOROLA AN1213/D

Figure 12 PID Controller Magnitude

Figure 13 PID Controller Phase

PWM PID MAG

–6

–12

–18

–24 32 4 5 6 7 8 9 10 20 30 40 50 100 200

AMPLITUDE (dB)

FREQUENCY (Hz) AN1213

PWM PID PHASE

48°

36°

24°

12°

0°

–12°

–24°

–36°

–48°

–60°32 4 5 6 7 8 9 10 20 30 40 50 100 200

FREQUENCY (Hz)

PHASE (DEGREES)

60°

AN1213

AN1213/D MOTOROLA

SAMPLED TIME DOMAIN SOLUTION

To realize the controller as a difference equation, solve for the output of each portion of the PID controller.

The P Term

Since P is a constant multiplier, the solution is straightforward :

(EQ 11)

where:

P(z) is the output of the proportional stage of the PID controller

E(z) is the error between the commanded position and the feedback position

Performing the transform to the sampled time domain :

(EQ 12)

The notation “n” is used to represent the present sample. Similarly, n+1 indicates the next or future sample,

n–1 indicates the previous sample.

The I Term

From Equation 3, we obtain:

(EQ 13)

Where :

I(z) is the output of the integrator stage

T is the sample period (488 µs).

This results in:

(EQ 14)

Next, the “Shift of Sequence” theorem of the Z transform is used to obtain a solution in the sampled time

domain. The theorem is stated as follows:

(EQ 15)

Where:

Z indicates the Z transform operation.

Applying this theorem in reverse yields:

(EQ 16)

Now shift the function in time (i.e., n +1 = n) to obtain :

(EQ 17)

Simply stated, “the present sample of the integrator output is equal to the previous sample of the integrator

output plus T times I times the present sample of the error signal.”

Since output feedback is employed to calculate the next output value, this portion of the filter is classified

as an IIR (infinite impulse response) filter.

P(z)

E(z)

-----------P= or P(z) PE(z)=

P(n) PE(n)=

E(z)

----------- ITz

z1–

------------=

zI(z) I(z)–ITz E(z)=

If Z[x(n)] X(z),= Then Z[x(n+a)]

aX(z)=

In 1+()I(n) TIE n 1+()+=

I(n) I n 1–()TIE n()+=

MOTOROLA AN1213/D

The D Term

From Equation 5, derive the transfer function for the derivative term:

(EQ 18)

where:

X(z) is the feedback position signal

D(z) is the output of the derivative stage.

This equation can be reduced to :

(EQ 19)

Performing the transform to the sampled time domain yields :

(EQ 20)

Shifting in time yields :

(EQ 21)

In other words, the velocity information is derived from X(n), the present position feedback sample, and from

X(n–2), the feedback sample made two periods earlier. This yields better quantization results at low speeds.

COMBINING TERMS

From Figure 5, we see that :

(EQ 22)

Where Y(n) is the PID controller output.

Therefore, combining equations 12, 17, and 21 (EQ 23):

Since the proportional term and the integral term both operate directly on E(n), it might appear that these

terms could be combined in Equation 23. However, as Figure 5 shows, the integrator must be gated with

the velocity term and integrator output must be limited to mitigate wind-up. For these reasons, the P and I

terms are kept separate.

Since the terms P, I, D, and T are constants, equation 23 can be rewritten :

(EQ 24)

where:

P = 0.16

a = 0.00244

b = –1.0246

D(z)

X(z)

----------- D (z–1)

-------------------





--- 1

------+





2Tz2D(z) Dz2D–()X(z)=

2TD(n+2) DX n 2+()DX n()–=

Dn 2+()

-------Xn 2+()Xn()–()=

Dn() D

-------Xn() Xn 2–()–()=

Y(n) P(n) I(n) D(n)–+=

Y(n) PE(n) + I(n–1) TIE(n) D

-------Xn() Xn 2–()–()–+=

P Term I Term D Term

Y(n) PE(n) I n 1–()aE(n) b X(n) X n 2–()–()+++=

AN1213/D MOTOROLA

M68HC16 IMPLEMENTATION

CODING THE FILTER

The CPU16 can perform signed and unsigned 16-bit integer multiplication as well as signed and unsigned

16-bit fractional multiplication. Since the PID coefficients are neither all-integer nor all-fraction, the values

must be scaled before calculations can be performed, and the same scaling must also be used to correct

the filter output. Because CPU16 DSP instructions use fractional notation, each coefficient is divided by 2,

so that:

P' = 0.08 or $0A3D

a' = 0.00122 or $0028

b' = –0.5123 or $BE6D

The filter is implemented in an interrupt service routine (ISR) which is called each time the programmable

interrupt timer (PIT) in the SIM times out (every 488 µs). The portion of the ISR associated with the PID

implementation is listed at the end of this application note. The complete code can be downloaded from Mo-

torola Freeware Data Systems. Modem connection at (512) 891-3733. Internet address (ftp): free-

ware@aus.sps.mot.com. World-wide web: http://www.freeware.aus.sps.mot.com.

SERVO CONTROL HARDWARE

The MC68HC16Z1EVB provides an excellent platform for this application. Use of CPU16 background de-

bugging mode, the QSM serial communication interface, and the EVB 16-bit DAC are particularly helpful.

Figure 14 is a diagram of the hardware used in the servo system.

The logic to motor interface module (available from Motorola) contains a complementary H-bridge driver

(MPM3002) that is used to provide up to 60 volts to a motor load. The board is operated in four-quadrant

mode (inverted PWM) —the PWM signal that drives one diagonal transistor pair is an inverted version of

the signal that drives the other pair. The PWM interface module prevents excessive heating due to shoot-

through current by delaying each enabling PWM edge approximately 2 µs. This provides a switching dead-

band between the time one leg is turned off and the other leg is turned on. The PWM interface module also

uses the current mirror feedback from the MPM3002 to provide cycle-by-cycle current limiting. For further

information about the logic to motor interface module, refer to

Interfacing Microcomputers to Fractional

Horsepower Motors

(AN1300).

Operating with four-quadrant PWM implies that the waveform generated by the MC68HC16Z1 must be bi-

polar (50% PWM corresponds to no voltage on the motor). As the sample ISR code shows, this is accom-

plished by adding a fixed offset to the digital filter output before it is put in the PWM register. Once the value

is in the PWM register, the general-purpose timer (GPT) generates the required PWM signal without further

CPU intervention.

The 1000-slot encoder on the motor shaft is processed by the Hewlett-Packard HCTL-2016 quadrature de-

coder, which accumulates the encoder count on an internal 16-bit up/down counter. One of the 12

MC68HC16Z1 chip-select outputs is programmed to perform the address decoding necessary to access

and read the HCTL-2016 counter data. 16-bit data is read on data bus pins DATA[15:8] as two sequential

8-bit values. The 16-bit data word is then used to synthesize a 32-bit absolute position variable, as shown

in the beginning of the PID ISR listing.

MOTOROLA AN1213/D

Figure 14 Hardware Block Diagram

A user can control the application via a terminal connected to the serial communications interface (SCI) in

the queued serial module (QSM). The MC68HC16Z1 EVB provides a 25-pin D connector for this purpose.

To initiate motor movement, issue a MOVE command, specifying the final position, the maximum profiler

velocity, and the acceleration of the move. The SCI transmits and receives such commands with very little

CPU intervention, even during a move.

The MC68HC16 EVB also provides for installation of a Burr-Brown PCM56P 16-bit serial DAC. If the QSM

Serial Peripheral Interface (SPI) is used to drive the DAC, 16-bit DAC updates can be provided at approxi-

mately 4 µs intervals (SCLK frequency = 4.19 MHz). DAC output can be used to probe portions of the servo

loop that are not readily available in analog form, such as shaft encoder position or integrator stage output.

The oscilloscope plots in this note were generated by transmitting variable values to the DAC and updating

them every pass through the sample ISR (once every 488 µs).

CONCLUSIONS

No matter how thorough the analysis, a working design usually requires some adjustment. The designer

must compare actual system function to theoretical expectations, then tune system coefficients to achieve

optimum performance.

The D term has a dramatic effect on system stability, and should be the first term adjusted when damping

performance is less than satisfactory. Figure 15 shows how varying D affects system damping, and indi-

cates that the original calculated value for D provides for quick settling time with little or no overshoot.

As mentioned earlier, the I term is used to “servo out” steady-state position error. To demonstrate, a fric-

tional load was applied to the motor shaft, and the system step response was measured with the integrator

enabled and disabled. When disabled, the position error was measured to be between 65 –69 encoder

counts (approximately 6 degrees). With I set to its default value of 5, the error did not exceed one encoder

count (0.09 degrees).

PID HARDWARE BLOCK

MC68HC16Z1

EVB

PWM

ENABLE

OSCILLOSCOPE

ENCODER

FEEDBACK

HCTL 2016

SCI

INTERFACE

PWM

CURRENT

FEEDBACK

PWM

INTERFACE

MODULE LOGIC TO

MOTOR

INTERFACE

MODULE

CURRENT

LIMIT

USER

INTERFACE

+ 24V

AMPLIFIED

PWM

ENCODER

MOTOR

16-BIT

DAC

AN1213

AN1213/D MOTOROLA

As Equation 5 shows, the PID calculation must be performed quickly, to minimize phase delay introduced

into the loop. Calculation time can be measured by connecting an oscilloscope to an I/O pin and running a

subroutine that drives the pin high just before encoder sampling, then drives it low it just after the PWM reg-

ister is loaded with a new value. Measured in this way, calculation time is roughly 30 µs, which translates

into 0.44 degrees of phase lag at the open-loop unity gain frequency (41 Hz), a minimal contribution to total

system phase lag at that frequency. Also, since less than 10 percent of CPU time is spent controlling axis

motion, multiple axes or more sophisticated control algorithms, including state observers, notch filters, and

adaptive control, could easily be implemented.

The techniques in this application note allow a designer to customize a controller for an application, rather

than be forced to work around pre-packaged servo controls. The capabilities of the M68HC16 family also

enable designers to respond quickly to changes, and permit solution of real-time DSP control problems with-

out loss of the user friendliness provided by a complete microcontroller system.

Figure 15 Effect of Varying D on System Damping

REFERENCES

1. Kuo, B.,

Digital Control Systems,

Holt, Rinehart and Winston, Inc., 1980

2. Oppenheim, A.V., Schafer, R.W.,

Digital Signal Processing,

Prentice-Hall, Inc., 1975

PWM STEP RESPONSE

AN1213

0.61 X 10-3

1 X 10-3

1.586 X 10-3

MOTOROLA AN1213/D

PID INTERRUPT SERVICE ROUTINE LISTING

60 * Here we go!

61 00062E 3908 FA19 bset PORTF0,#test_bit1 ;set test_bit1 output for timing

meas.

63 000632 37F5 0900 ldd enc ;read the encoder.

64 000636 37FA 0004 std Xn+2 ;update lower word of Xn

65 00063A 37F0 0008 subd Xn_1+2 ;subtract old lower word from

new one

66 00063E BB00 bmi enc_neg ;IF delta is positive

67 000640 2775 clre ; sign extend to AccE ($0000)

68 000642 B000 bra add_delta ;ELSE

69 000644 3735 FFFF enc_neg lde #$FFFF ; sign extend to AccE ($FFFF)

70 ;ENDIF

71 add_deltaADDMLONGXn_1

1m +*Adds a 32-bit value in memory at "location" to

2m +*the concatenated value in D and E.

3m 000648 37F1 0008 addd Xn_1+2

4m 00064C 3773 0006 adce Xn_1

72 000650 377A 0002 ste Xn ;Xn now updated.

74 000654 2771 003C lded pcommand

75 SUBMLONGXn

1m +*Subtract a 32-bit variable in memory at "location" from

2m +*the concatenated value of the D and E registers.

3m 000658 37F0 0004 +subd Xn+2

4m 00065C 3772 0002 + sbce Xn

76 000660 37FA 0014 std En ;E(n) = commanded position -

x(n)

78 *E(n) must be limited to a 16-bit number

79 000664 2776 tste ;check whether E(n) is nega-

tive

80 000666 BC10 bge Epositive ;IF E(n) is negative

81 000668 37B1 8000 addd #$8000

82 00066C 3733 0000 adce #$0000 ;add $00008000 to E(n)

83 000670 BC18 bge E_ok ; IF result is negative

84 000672 37B5 8000 ldd #$8000

85 000676 37FA 0014 std En ; E(n) = $8000

86 00067A B00E bra E_ok ;ENDIF

88 00067C Epositive ;ELSE

89 00067C 37B0 8000 subd #$8000

90 000680 3732 0000 sbce #$0000 ; subtract $00008000 from

E(n)

91 000684 BD04 blt E_ok ; IF result is zero or posi-

tive

92 000686 37B5 7FFF ldd #$7FFF

93 00068A 37FA 0014 std En ; En = $7FFF

94 ; ENDIF

95 ;ENDIF

96 00068E E_ok

97 00068E 2771 0002 lded Xn

98 SUBMLONG Xn_2

1m +*Subtract a 32-bit variable in memory at "location" from

2m +*the concatenated value of the D and E registers.

3m 000692 37F0 000C +subd Xn_2+2

4m 000696 3772 000A +sbce Xn_2

99 00069A 37FA 0010 std Xn1 ;x`(n) = x(n) - x(n-2)

100

101 *shift the sampled encoder data

102

103 00069E 2771 0006 lded Xn_1

104 0006A2 2773 000A sted Xn_2

105 0006A6 2771 0002 lded Xn

106 0006AA 2773 0006 sted Xn_1

107

108 * now perform the digital filter

AN1213/D MOTOROLA

109

110 0006AE 37F5 0010 ldd Xn1

111 ABS

1m +*Take the absolute value of the D register.

2m 0006B2 27F6 +tstd

3m 0006B4 BCFE +bge 1positive

4m 0006B6 27F2 +negd

5m 0006B8 +1positive:

112 0006B8 37B0 0005 subd #$0005

113 0006BC BD06 blt Icalc ;IF ABS(X`n) >= $0005

114

115 0006BE 27F5 clrd

116 0006C0 2775 clre

117 0006C2 2773 0018 sted In_1 ; I(n-1) = 0 (clear "I" term)

118 0006C6 B040 bra I_loaded

119

120 0006C8 Icalc ;ELSE

121 0006C8 2771 0012 lded a ; a ==> AccE , E(n) ==> AccD

122 ; (E(n) follows a in variable

map)

123 0006CC 3727 fmuls

124 ADDMLONG In_1

1m +*Adds a 32-bit value in memory at "location" with

2m +*the concatenated value in D and E.

3m 0006CE 37F1 001A +addd In_1+2

4m 0006D2 3773 0018 +adce In_1

125 0006D6 2773 0018 sted In_1 ; I(n) = I(n-1) + a*E(n)

126 ; Now limit the integrator

127 ; term to 19 bits.

128 0006DA BC10 bge Ipositive ; IF I(n) is negative

129 0006DC FC00 addd #$0000

130 0006DE 3733 0008 adce #$0008 ; add $00080000 to I(n)

131 0006E2 BC20 bge get_I ; IF result is negative

132 0006E4 27F5 clrd

133 0006E6 3735 FFF8 lde #$FFF8

134 0006EA 2773 0018 sted In_1 ; I(n) = $FFF80000

135 0006EE B018 bra I_loaded ; ENDIF

136 ; ELSE

137 0006F0 Ipositive

138 0006F0 37B0 0000 subd #$0000

139 0006F4 3732 0008 sbce #$0008 ; subtract $00080000 from

I(n)

140 0006F8 BD0A blt get_I ; IF result is zero or posi-

tive

141 0006FA 37B5 FFFF ldd #$FFFF

142 0006FE 3735 0007 lde #$0007

143 000702 2773 0018 sted In_1 ; I(n) = $0007FFFF

144 000706 B000 bra I_loaded ; ENDIF

145 ; ENDIF

146 000708 get_I

147 000708 2771 0018 lded In_1

148

149 00070C I_loaded ;ENDIF

150

151 00070C 27B1 tedm ;AM = I(n-1) + a*E(n)

152 00070E 2771 0014 lded En ;E(n) ==> AccE , p ==> AccD

153 ; (p follows E(n) in variable

table)

154 000712 3727 fmuls

155 000714 3723 aced ;AM = I(n-1) + a*E(n) +

p*E(n)

156 000716 2771 000E lded b ;b ==> AccE, X`(n) ==> AccD

(since

157 ;X`(n) follows "b" in vari-

able map)

158 00071A 3727 fmuls

159 00071C 3723 aced ;AM = I(n-1) + a*E(n) +

p*E(n)

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the suitability of its products for any particular purpose, nor does Motorola assume any liability arising out of the application or use of any product or circuit, and

specifically disclaims any and all liability, including without limitation consequential or incidental damages. “Typical” parameters can and do vary in different

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160 ; + b*x`(n)

161

162 00071E 27B6 aslm ;compensate for data scaling

163 ;PID coefficients (multiply

by 2).

164 000720 27B4 tmer ;transfer result to AccE

rounded.

165 000722 377A 001C ste Yn ;Yn is output of filter

166

167 *Now the pwm value must be limited to an 8-bit value.

168

169 000726 27FB ted

170 000728 BC0A bge Ypositive ;IF Y(n) is negative

171 00072A FC7F addd #$007F ; add $007F to Y(n)

172 00072C BC14 bge get_Y ; IF result is negative

173 00072E 37B5 FF81 ldd #$FF81

174 000732 37FA 001C std Yn ; Y(n) = $FF81 (minimum val-

ue—

175 ; PWM interface module always

176 ; needs a PWM edge to do cy-

cle-

177 ; by-cycle current limiting)

178

179 000736 B00E bra Y_loaded ; ENDIF

180 ;ELSE

181 000738 Ypositive

182 000738 37B0 0080 subd #$0080 ; subtract $0080 from Y(n)

183 00073C BD04 blt get_Y ; IF result is zero or posi-

tive

184 00073E 37B5 007F ldd #$007F

185 000742 37FA 001C std Yn ; Y(n) = $007F (maximum PWM

allowed)

186 ; ENDIF

187 ;ENDIF

188 000746 get_Y

189 000746 37F5 001C ldd Yn

190 00074A 37B1 0080 Y_loaded addd #$0080

191 00074E 17FA F926 stab PWMA ;scale PWM so that 50% is

zero volts.

192

193 * We are done with PID filter at this point.