lecture XII Basics of feed-back and control

• Define open loop, feed-forward, feed-back (closed loop)

• Understand the fundamentals of control theory

• Explain the PID algorithm

• Describe an application of control theory: controlling the temperature of the human body

���1

Copyright U

niversità degli S

tudi di M

ilano

Our bodies function amazingly well because of constant

feedback and control processes

HOMEOSTASIS: stability of the chemical and physical conditions of the fluid surrounding the body cells

Copyright U

niversità degli S

tudi di M

ilano

Examples• body temperature

• pressure in blood vessels

• oxygen and carbon dioxide concentrations

• pH

• the concentrations of ions, such as Na+, K+, and Ca2+

• volume

• osmolality (water/dissolved particle ratio)

• the organic nutrient concentrations, such as glucose.

• eye iris opening and closing in response to light levels.

• focal length of the crystalline lenses

• force to grasp objects

• .....

Copyright U

niversità degli S

tudi di M

ilano

open-loop/feedforward, closed-loop/feedback,

(a) open loop: - no information is used to ascertain if the output has achieved the desired goal given the input - useful when little is known or relevant about the system- example: irrigation systems, washing machines

(b)closed loop: - it uses the output to adapt the input - more flexible and reacts to a wider range of situations that do not have to be individually pre-considered during design- it might be slower than an open loop but usually it is more precise - example: body temperature control, blood pressure, glucose, etc. etc.

sometimes the human body combines feedback and feedforward examples: walking, moving the arm, etc. etc.

Copyright U

niversità degli S

tudi di M

ilano

13.1 Basics of Feedback and Control 769

Fig. 13.2. Feedback and control in the body, with an example of controlling highblood pressure in parenthesis. (Based on [607])

center, such as the transmission of signals from sensory centers to the brain bynerves. The integration center induces an effect. This response is transmittedby nerves (motor pathways) to an effector control center. There is some effector response of interest, such as changing the heart rate or stroke volumeto change the blood pressure. The success of this control is determined bymeasuring the response, the new blood pressure, which provides feedback forthe control.

Negative feedback reverses the direction of the change of a variation, to keepthe measured parameter near the desired set point. This type of feedback isvery common in the body. There is usually an operating range centered aboutthis set point bounded by allowable values. Figure 13.3a shows that the effectoris activated to correct the parameter when it wanders above the highest valueallowed or below the lowest value allowed. Room thermostats usually operatein the same manner, with a several degree operating range about the set point;our bodies also have thermostats.

Positive feedback causes the effector to produce more of a change in thesame direction that the parameter is already changing, as in Fig. 13.3b. Thistype of feedback is rare in the body. One example is suckling which leads tothe production of more milk in mothers.

Fig. 13.3. (a) Negative and (b) positive feedback. (Based on [607])

feedback is THE controlin parenthesis an example of controlling the blood pressure

START

Copyright U

niversità degli S

tudi di M

ilano

13.1 Basics of Feedback and Control 769

Fig. 13.2. Feedback and control in the body, with an example of controlling highblood pressure in parenthesis. (Based on [607])

center, such as the transmission of signals from sensory centers to the brain bynerves. The integration center induces an effect. This response is transmittedby nerves (motor pathways) to an effector control center. There is some effector response of interest, such as changing the heart rate or stroke volumeto change the blood pressure. The success of this control is determined bymeasuring the response, the new blood pressure, which provides feedback forthe control.

Negative feedback reverses the direction of the change of a variation, to keepthe measured parameter near the desired set point. This type of feedback isvery common in the body. There is usually an operating range centered aboutthis set point bounded by allowable values. Figure 13.3a shows that the effectoris activated to correct the parameter when it wanders above the highest valueallowed or below the lowest value allowed. Room thermostats usually operatein the same manner, with a several degree operating range about the set point;our bodies also have thermostats.

Positive feedback causes the effector to produce more of a change in thesame direction that the parameter is already changing, as in Fig. 13.3b. Thistype of feedback is rare in the body. One example is suckling which leads tothe production of more milk in mothers.

Fig. 13.3. (a) Negative and (b) positive feedback. (Based on [607])

Positive vs negative feedback

Negative feedback: don’t get too far from me boy example: temperature control !

Positive feedback: run boy...faster than you can.... example: suckling causes production of more milk in mothers, defecation, childbirth

Copyright U

niversità degli S

tudi di M

ilano

PID controller

e(t) is the error signal i.e. actual value-setpoint value of the controlled variable

Copyright U

niversità degli S

tudi di M

ilano

on-off control

the simplest feedback system

Copyright U

niversità degli S

tudi di M

ilano

The P control

• output proportional to KP*e(t)

• large KP means prompt reaction toward setpoint

• typically affected by steady state error (offset) due to losses

• example: temperature control of a houseCopyright U

niversità degli S

tudi di M

ilano

The PI control

• output proportional to KP*e(t)+the history

• compensation of the offset

• slower performances

• oscillations (damped, overdamped, critically damped) in analogy with damped oscillatorCopyrig

ht Università

degli Studi d

i Mila

no

The PID control

• output proportional to KP*e(t)+the history+the instantaneous variation

• reacts faster to changes in the environment

• more subject to external noise

Copyright U

niversità degli S

tudi di M

ilano

PID tuningHow do the PID parameters affect systemdynamics?

The effects of increasing each of the controller parameters KP ,KI and KD can be summarized as

Response Rise Time Overshoot Settling Time S-S ErrorKP Decrease Increase NT DecreaseKI Decrease Increase Increase EliminateKD NT Decrease Decrease NT

NT: No definite trend. Minor change.You may want to take notes of this table. It will be useful inthe later part of the lesson.Remember: combining feed-forward and feedback can

improve performance, especially rise and settling time

Copyright U

niversità degli S

tudi di M

ilano

Whiteboard graphical commented example of a PID controlled

signal

���13

Copyright U

niversità degli S

tudi di M

ilano