Embedded Control Systems

Dr. Bonnie Heck

School of ECE

Georgia Tech

Introduction

• Goal: Meet design specifications on performance even under varying operating conditions

• Examples: car cruise control, temperature control, flight controls, motor control, robotic manipulator

Feedback Control

System to be controlled

OutputActuator

Sensor

Controller+

-

Reference

Measurement

Disturbance

Embedded Control Components

• Sensors: transducers that convert physical quantities to voltage

• Controller: Analog or digital implementation of the control– Digital controller: DSP board, microcontroller, or

PC with ADC and DAC

• Actuators: physical device that converts controller outputs to system inputs

• Drive Electronics: power, power amplifier, analog filters

Performance

0 2 4 6 8 10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (Sec)

ReferenceOutput

0 2 4 6 8 10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (Sec)

ReferenceOutput

Closed Loop Frequency Response

Frequency (Hz or rad/sec)

Magnitude

ferenceReOutput

DC Value

0

Bandwidth

Design Metrics

• Speed of Response– Speed at which transient decays

(bandwidth)

• Accuracy– Smallness of error (DC value)

• Relative Stability– Amount of error tolerated in model before

system goes unstable

Design Procedure

System to be controlled

OutputActuator

Sensor

Controller+

-

Reference

Measurement

ADC

DACControl D(z)

Error, E(z)

Command, U(z)

From sensor

To actuatorReference+

-

Common Controllers

• Proportional

• Proportional + Derivative (PD)

• Proportional + Integral (PI)

• Proportional + Integral + Derivative (PID)

K=)z(D

z)az(K=)z(D -

azKz=)z(D -

)1z(z)bz)(az(K=)z(D -

--

Desired Responses

Frequency (Hz or rad/sec)

Magnitude

ferenceReOutput

DC Value

0

BandwidthTime Response

Frequency Response

0 2 4 6 8 10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (Sec)

ReferenceOutput

Design Strategy

• Speed of Response– Bandwidth increases as K increases

• Accuracy– DC value approaches 1 as K increases

• Relative Stability– Often relative stability goes down as K

increases

Control Algorithm

212

212

a+za+z)b+zb+z(K

=)z(E)z(U

=)z(D

)z(E)b+zb+z(=)z(U)a+za+z( 212

212

)z(E)zb+zb+1(=)z(U)za+za+1( 22

11

22

11

General Form:

]2n[eb+]1n[eb+]n[e=]2n[ua+]1n[ua+]n[u 2121 ----

]2n[eb+]1n[eb+]n[e+]2n[ua]1n[ua=]n[u 2121 ----

Pseudo-code]2n[eb+]1n[eb+]n[e+]2n[ua]1n[ua=]n[u 2121 ------

//Initializeu_1 = 0;u_2 = 0;e_1 = 0;e_2 = 0;while(1){y = readsensor();

e=r-y;u = -a1*u_1-a2*u_2+e+b1*e_1+b2*e_2;output(u); //pass to actuator driveru_2=u_1;u_1 = u;e_2 = e_1;e_1 = e;wait(sample_time);

} /* a better way is to use a hardware timer to trigger an event, the event handler runs this code */

Sampling Period

• Nyquist: sample at twice the highest frequency

–But, the signal being sampled is not bandlimited

Rule of thumb: sample at 10 to 20 times the bandwidth of the closed loop system, slower reduces performance and may destabilize the system

Summary

• Feedback control adds robustness (good performance even with varying conditions)

• Embedded controls implemented with DSP boards, microcontrollers, PCs, FPGA boards

• Larger gain, K: faster response, better accuracy, possibly lower stability

• Sample at 10-20 times the closed loop bandwidth