Alciatore D.G., Histand M.B. Introduction to Mechatronics and Measurement Systems

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Table 11.1 Ziegler-Nichols recommended gains

Controller

0.5 K

Infinity 0

0.45 K

/1.2

PID

0.6 K

/2 0.125 P

11.3 Introduction to Control Theory 491

11.3.4 Controller Empirical Design

In cases where it is difficult or impossible to model a system analytically, there

are techniques to empirically design a controller by performing tests on an actual

system. The procedure described in the previous section for simulation is one such

approach, where the gains are adjusted iteratively. There are also software tools

available that can perform system identification automatically, where a model can

be approximated by analyzing the system’s response to various inputs. A control-

ler can then be designed, possibly with the help of other software tools. Video

Demo 8.8 shows a demonstration of how an example set of software tools can be

used to develop a speed controller for a simple DC motor system. Video Demo 8.9

provides much more background and detailed demonstrations of the individual

steps in the process.

A simple empirical method for tuning a PID controller that is sometimes used in

industry is called the Ziegler-Nichols (Z-N) method (see Palm in the bibliography).

The Z-N method is applied by observing the step response of the system under con-

trolled conditions. From the observations, PID gains can then be selected to provide

a fast system response with minimal overshoot and oscillation.

A PID controller expressed in the s domain can be written as

controller

s() K

-----

s++=

(11.10)

where K

, K

, and K

are the proportional, integral, and derivative gains. Using the

Ziegler-Nichols method, the controller is usually expressed as

controller

s() K

------- T

s)++=

(11.11)

where T

is called the reset time and T

is the derivative time.

To apply the Z-N method, start by using proportional control action alone

( T

⫽ infinity, T

⫽ 0) and increase K

from zero until the observed output shows

sustained (undamped) oscillation. The resulting period of the oscillations is observed

and labeled P

, and the corresponding gain value is called the critical gain K

. Then

is reduced by a factor, and K

( T

) and K

( T

) are selected based on the propor-

tions in Table 11.1 . Ziegler and Nichols showed that these proportions result in a

good system response for the selected type of controller. Note that K

is lower for a

PI controller than a P controller and higher for a PID controller because the I compo-

nent increases the order of the system and may destabilize it, and the D component

tends to stabilize the system, so K

can be increased a little.

Video Demo

8.8National

Instruments DC

motor demo

8.9National

Instruments

LabVIEW DC

motor controller

design

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Figure 11.12 Analog PID controller constructed from op amp circuits.

command

signal

sensor

feedback

error

signal

e(t)

d/dt

–

PID controller

output

signal to

physical

plant

∫

492 CHAPTER 11 Mechatronic Systems—Control Architectures and Case Studies

Often, the Z-N gains will serve only as a starting design, and you may need to

tune the gains (i.e., tweak the K

, K

, and K

parameters) to achieve your desired

design specifications. This usually requires some trial and error.

11.3.5 Controller Implementation

In previous sections, everything was done in simulation, where the physical sys-

tem was represented by a mathematical model. To implement a PID controller in an

actual physical system, the model is replaced by actual hardware, and the controller

must be built as an analog circuit or with a microprocessor-based system running

digital software. In Chapter 5, we learned how to construct proportional gain, inte-

grator, differentiator, summer, and difference circuits using operational amplifiers.

These circuits can serve as the building blocks for an analog controller. Figure 11.12

shows how the various circuits can be combined, in schematic form, to create an ana-

log PID controller. Each control action has a gain ( K

, K

, or K

) created by appropri-

ate choices of component values in the op amp circuits.

An alternative to an op-amp-based analog controller is a digital controller

created with software in a microprocessor-based system (e.g., a microcontroller).

A digital control system is different from an analog controller because it requires a

discrete amount of time to perform control updates. During each update cycle, the

sensor signal is acquired, the controller output is calculated, and the controller signal

is output. The time delay corresponding to the control loop cycle affects the response

of the system. This effect must be accounted for in the mathematical model of the

system to be able to predict system response accurately and to choose control param-

eters intelligently. The concept of the z -transform, where the continuous s -domain

is transformed into a discrete representation, enables us to model and analyze such

systems. Please refer to a book on modern control theory (e.g., Ogata or Palm in the

bibliography at the end of this chapter) if you want to pursue this topic.

To implement a digital controller, the differentiation and integration must be

discretized. If successive error signal samples are referred to as e

, e

, . . ., e

i ⫺ 1

, e

i ⫹ 1

, . . ., we can accumulate an approximation to the integral with the following

equation:

= I

i–1

+ Δt e

(11.12)

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11.3 Introduction to Control Theory 493

where I

⫽ 0 and Δ t is the cycle time of the control loop. The derivative can be

approximated with a finite difference approximation. For example,

= (e

– e

i-1

) / Δt

(11.13)

Although, a digital filter usually needs to be applied to this calculation to minimize

the undesirable effects of high-frequency noise in the position signal (see Class

Discussion Item 11.1). Code for an example control loop cycle might look like the

following:

error_previous ⫽ 0

integral ⫽ 0

loop:

Gosub get_set_point_value ' acquire set_point value

Gosub acquire_sensor_ ' acquire sensor_value

error ⫽ sensor – set_point

integral ⫽ integral ⫹ error * DT

derivative ⫽ (error – error_previous)/DT

output ⫽ KP * error ⫹ KI * integral ⫹ KD * derivative

Gosub send_output_to_system ' update command signal

error_previous ⫽ error

Goto loop

Video Demo

8.8National

Instruments DC

motor demo

8.9National

Instruments

LabVIEW DC

motor controller

design

■ CLASS DISCUSSION ITEM 11.1

Derivative Filtering

As mentioned below Equation 11.13 , derivative calculations often need to be

filtered. One approach to doing this is to average a set of previous derivative calcu-

lations (i.e., use a running average). What is the effect of such an approach, and how

can the example code be modified to achieve this?

11.3.6 Conclusion

This section presented a very brief overview of control theory. Although this topic

cannot really be covered adequately in such a small amount of space, you at least now

have a basic understanding of the main concepts. Anyone interested in pursuing this

topic further needs references (and coursework) completely dedicated to this topic.

There are many software tools available to help with modeling, analysis, and

controller design. Above, we used Matlab and Simulink for simulation and design.

The LabVIEW software introduced in Chapter 8 also provides tools to help with

these tasks. Video Demos 8.8 and 8.9 demonstrate the whole process of model-based

controller design with LabVIEW. Many additional control systems video demonstra-

tions can be found at Internet Link 11.7. Please review some or all of these videos to

help improve your level of understanding of the application of control theory.

Internet Lin

11.7Control

system

demonstrations

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Figure 11.13 Project phases.

■ Data Acquisition— Measuring and

digitizing the myoelectric signal

■ Classification— Estimating the mus-

cle force based on the myoelectric

signal

■ Actuation— Moving a robotic arm

to a position corresponding to the

estimated force

494 CHAPTER 11 Mechatronic Systems—Control Architectures and Case Studies

11.4 CASE STUDY 1—MYOELECTRICALLY

CONTROLLED ROBOTIC ARM

This case study is an extension of Design Example 5.1, which dealt with myo-

genic control of a prosthetic limb. Here, more detail is presented, and the control is

applied instead to a robotic arm. The problem is presented in steps according to the

microcontroller-based system design procedure presented in Section 7.9. This case

study is a good example of how to use PIC microcontrollers to interface to and com-

municate with an assortment of devices including analog circuits, desktop com-

puters, and standard serial interfaces. Video Demo 11.6 demonstrates the finished

product in action. You might want to view the video first so you can better relate to

the information presented below.

1. Define the problem

The goal of this project is to design a system that uses myoelectric voltages from

a person’s biceps as a control signal for a robotic arm. As shown in Figure 11.13 ,

this project can be divided into three phases: data acquisition, classification, and

actuation.

Myoelectric signals, or surface electromyograms ( sEMG ) , are produced dur-

ing muscle contraction when ions flow in and out of muscle cells. When a nerve

sends the signal to initiate muscle contraction, an “action potential” of ions travels

along the length of the muscle. This ionic current can be transduced into electronic

current with Ag-AgCl electrodes placed on the surface of the skin above the con-

tracting muscle. Typically, the greater the contraction level, the higher the measured

amplitude of the sEMG signal. However, even if a contraction level is constant, the

sEMG signal can be quite irregular.

Video Demo

11.6Robot

controlled by an

EMG biosignal

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11.4 Case Study 1—Myoelectrically Controlled Robotic Arm 495

Research has shown that a typical sEMG signal has the following characteristics:

Amplitude 0–5 mV

Frequency range 0–500 Hz

Dominant frequency range 50–150 Hz

As can be seen, the sEMG signal is very small, in the millivolt range. In fact,

electrical noise on the surface of the skin can be of greater magnitude than the

signal of interest. There are three main frequency ranges in which noise may be

present:

a. 0–10 Hz: low-frequency motion artifacts (e.g., wire sway)

b. 60 Hz: line noise (e.g., electrical equipment in the room)

c. >500 Hz: high-frequency noise (e.g., random movement between the electrodes

relative to the muscle)

2. Draw a functional diagram

Figure 11.14 shows a block diagram depicting the flow of information between the

system’s required components. Before digitizing the sEMG signal, it must be ampli-

fied to take full advantage of the input range of the A/D converter (see Chapter 8

for more details). However, we cannot simply pass the signal into an op amp; if we

did, the noise would also be amplified, and it would be impossible to distinguish

the sEMG from the noise. Consequently, we need to filter out the noise and amplify

the signal prior to A/D conversion. This stage of data acquisition is called signal

conditioning.

After the signal is amplified and the noise is removed, it is ready for A/D con-

version. The digitized signal is then sent to a PC where the muscle force is estimated

based on analysis of the sEMG data. The estimated force is sent via an interface

circuit to the robotic arm. Then the arm moves to a position that corresponds to the

estimated force. For example, at rest the robotic arm will be at zero degrees; at the

maximum contraction level the robotic arm will be at the maximum angle; and at

intermediate contraction levels the robotic arm will be at corresponding angles in-

between. Although we could build a robotic arm from DC or stepper motors, this

project used an AdeptOne-MV robotic arm. This type of robot is usually used for

industrial purposes (e.g., assembly line work), but it also serves as a good laboratory

model of a prosthetic arm.

3. Identify I/O requirements and 4. Select appropriate

microcontroller models

Although a single microcontroller could probably be used with some creative pro-

gramming, two microcontrollers are used to simplify the problem. One microcon-

troller is dedicated to performing the A/D conversion and sending the digitized

signal to a PC. Another microcontroller serves as the interface between the PC

and the robotic arm. For the A/D microcontroller, the primary constraint is that it

must have an analog input with a sampling rate over 1000 Hz (because the sam-

pling theorem states that we must sample at least two times the highest frequency

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Figure 11.14 System overview.

496 CHAPTER 11 Mechatronic Systems—Control Architectures and Case Studies

component of the signal, which is 500 Hz after it is filtered). A PIC16F819 was

chosen, although any PIC with A/D capability would meet this criterion. The only

salient difference between PICs with analog inputs is their resolution; some are

8 or 12 bit, but most are 10 bit (such as the 16F819). With a 20 MHz oscillator, the

PIC can sample 10 bit values at about 50 kHz. Clearly, this is well above the 1 kHz

required. However, the limiting factor in this process is not the sampling rate but

the time required to transmit the digitized value to a PC. Because of the convenient

functions provided in PicBasic for serial communication, this was chosen as the

communications protocol. The fastest standard serial baud rate for the PIC is 38400

bits per second. Because each byte of data is limited to 8 bits, each 10 bit value is

split up into 2 bytes (plus start and stop bits for each byte). Thus, each 10 bit value

requires 20 bits of data to be sent (2 start bits ⫹ 2 stop bits ⫹ 2 bytes). Consequently,

the PIC can only send digitized values at 1920 Hz (38,400 bits per sec / 20 bits).

Sending data in a constant stream like this, however, can easily cause the data to

be corrupted on the receiving end. If the clocks of the transmitter and receiver are

slightly out of sync, then the receiver (i.e., the PC) may lose track of where the

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11.4 Case Study 1—Myoelectrically Controlled Robotic Arm 497

bytes of data start and stop. To obviate this problem, a small delay is incorporated in

PicBasic before sending each value.

Every 100 msec the PC estimates the muscle force based on the previous 100

msec of data. Also, the estimated force is “binned.” For example, an estimated force

between 0 and 5 lb would be assigned to bin 0, an estimated force between 5 and 10 lb

would be assigned to bin 1, and so on. The bin number directly corresponds to a

position of the robotic arm. Every 100 msec, the PC will send two bytes back out

the serial port: the estimated force and the bin number. A PIC16F876 was chosen as

the microcontroller to interface the PC to the robotic arm and to display information

on an LCD. The primary factor considered when choosing a PIC was the number of

I/Os. One input is needed for the serial communication, six I/O are required for the

LCD interface, five outputs are used to interface to the Adept robot, and one output

is for a status LED. Although many PIC models can handle these 13 I/O, the 22 I/O

16F876 is used in case future upgrades are desired.

5. Identify necessary interface circuits

The signal conditioning circuit must amplify the small sEMG signal and filter out

noise prior to digitization. An instrumentation amplifier is used as the primary ampli-

fication component, as well as noise reduction component. As described in Section

5.9, an instrumentation amplifier is essentially a difference amplifier buffered with

op amps at each of its two inputs. The buffering op amps provide high input imped-

ance, which improves the difference amplifier’s ability to reject noise (i.e., it has a

high CMRR). The voltage difference that we will measure is the difference between

two electrodes placed on the biceps. As a muscle action potential travels down the

biceps, the first electrode will become positive relative to the more distal electrode;

conversely, as the action potential continues down the biceps, the second electrode

will then become more positive (which, of course, means the first electrode will be

negative relative to the second). In theory, ambient noise will reach the electrodes

simultaneously and will not be amplified, because the voltage difference between the

two electrodes, due to noise, will be zero.

To further eliminate noise, high-pass and low-pass filters are implemented.

A high-pass filter of 10 Hz is desired to reduce motion artifacts and DC offsets. A low-

pass filter of about 500 Hz is desired to reduce high-frequency noise. A low-pass

filter is important prior to A/D conversion to prevent aliasing. Unfortunately, 60 Hz

line noise is in the middle of the frequency range of the sEMG signal so it would not

be a good idea to employ a notch filter to remove this frequency range. Hopefully,

the instrumentation amplifier will sufficiently reject the line noise.

A 0–5 V input range is used on the A/D converter. To ensure that the sEMG

amplitude is in this range, two more components are incorporated in the signal con-

ditioning circuit: a full wave rectifier and an adjustable gain. The full wave rectifier

approximates the absolute value of the signal. Because the sEMG signal is bipolar

(i.e., it can be both positive and negative), passing it through a full-wave rectifier

will guarantee that the signal is entirely positive. Finally, an adjustable gain is use-

ful to account for differences in electrode size, geometry, and positioning, as well as

differences among individuals—all of which affect the amplitude of the signal. By

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Figure 11.15 MAX232 level converter.

498 CHAPTER 11 Mechatronic Systems—Control Architectures and Case Studies

adjusting the gain of the signal conditioning circuit, we can attain a maximum ampli-

tude of about 5 V (i.e., during maximum contraction levels).

The protocol that dictates how most serial communication is executed is

called RS-232. This protocol states, for example, that a logic 1 is between ⫺ 3 V and

⫺ 25 V, whereas a logic 0 is between ⫹ 3 V and ⫹ 25 V. Because a PIC cannot output

negative voltage (and because some PC serial ports have trouble reading voltages

less than 5 V), it is a good idea to use an RS-232 level converter chip, such as Max-

im’s MAX232 (see Figure 11.15 ). These chips convert TTL/CMOS level signals to

RS-232 level signals, and vice versa. It is also important to note that they also invert

the signal. For example, when given a ⫹ 5 V input, it will output about ⫺ 8 V; when

given 0 V, it will output about ⫹ 8 V. These chips are able to provide these outputs

using a 5 V power supply and ground. This is made possible using a technique called

charge pumping, which uses capacitors to store and boost voltage.

One of the parameters of PicBasic’s Serout command is the mode. Along

with the baud rate, this parameter specifies whether the serial data is driven true

or inverted. Because we are using an RS-232 level converter chip, true is used

because the chip automatically inverts the signal. The MAX232 chip is used to

convert the TTL output of the A/D converter PIC to RS-232 level signals as well

as convert the RS-232 output from the PC to TTL level signals for the robot/LCD

interface.

DB9 serial ports (see Figure 11.16 ) are no longer common on PCs because USB

and other interfaces have made them obsolete; however, one was available on the

computer used for this project. Although the DB9 port has nine pins, only three are

useful for our purpose; the other pins are for handshaking, a method to help regulate

data flow. The only pins necessary for our purposes are listed in Table 11.2. Pin 2 is

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Figure 11.16 Serial port.

Table 11.2 Serial port pins

Pin # Description

2 Receive data

3 Transmit data

5 Ground

11.4 Case Study 1—Myoelectrically Controlled Robotic Arm 499

where the PC will receive the digitized sEMG signal, and Pin 3 is where the PC will

send the estimated force and bin number to the interface PIC (in both cases, via the

MAX232 chip).

6. Decide on a programming language

PicBasic Pro is used. Speed and memory constraints are not primary concerns, so

Assembly language is not required. Also, the serial communication and LCD inter-

face commands provided by PicBasic Pro will be quite useful.

7. Draw the schematic

Figure 11.17 shows a circuit diagram for the conditioning circuit. The first stage is

an instrumentation amplifier with a gain of 939 with the resistor values shown. The

next stage is a simple RC filter followed by a buffer op amp. If the buffer op amp

were not included, then the resistance of the following stage would load the filter

(with impedance) and change its behavior. In other words, it would not act as a sim-

ple RC filter. Next is a two-pole Sallen-Key low-pass filter, a type of active filter

(i.e., it exploits the feedback of an op amp). An entire course can be devoted to ana-

log filter design, but suffice it to say that active filters are more robust than passive

filters (such as an RC filter) and that additional “poles” (an RC filter is a single-pole

filter) are better at attenuating unwanted frequencies. The next stage is an inverting

op amp where the feedback resistor is a potentiometer used to adjust the overall gain

of the system. Finally, the last stage is a precision full-wave rectifier, which requires

no forward bias to turn on the diodes.

After the sEMG signal passes through this circuit, it is amplified by about

1000 ⫻ , depending on the potentiometer setting of the inverting amplifier, bandpass

filtered between 8 and 483 Hz, and full-wave rectified. To make this circuit more

robust, the design was prototyped on a custom-made printed circuit board (PCB),

rather than on a breadboard, using PCB123, a free PCB layout program available

online (see Internet Link 11.8). Figure 11.18 show the traces and soldering pads

Internet Lin

11.8PCB123

software for

designing custom

printed circuit

boards

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Figure 11.18 Conditioning circuit PCB layout.

Figure 11.17 Conditioning circuit diagram.

500 CHAPTER 11 Mechatronic Systems—Control Architectures and Case Studies

created with the software for the PCB. Figure 11.19 shows the assembled PCB after

the components are soldered on. Internet Link 11.9 points to a document that illus-

trates all of the steps necessary to create a PCB. See Section 2.10.3 for more infor-

mation about PCBs and soldering.

The only chips used in this example are two TL074s, quad-package JFET op

amps. These op amps will operate over a fairly large range, about ⫾ 5 to ⫾ 18 V. To

make the system portable, two 9 V batteries can be used. Furthermore, a voltage

regulator can be used to produce the ⫹ 5 V necessary to operate the PICs.

Internet Lin

11.9Example

of steps in the

printed circuit

board process

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