Presented by:

SMILIN MARY JOE

14mee11015.

Guided by:

Mrs.MINU V S

Asst . Professor EEE

MES college of Engineering

Kuttippuram.

OUTLINE

Introduction.

Pneumatic muscle actuator.

Components and properties of PMAs

Conventional PID

AN-PID

Fundamental components of AN-PID

Conclusion

References

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INTRODUCTION

• Advanced Nonlinear PID control is a model-less control

mainly preferred in industrial control applications.

• They are used to achieve

reference tracking.

disturbance cancellation.

• Nonlinearities in the system will lead to significant

increase in modeling complexities so we prefer

AN-PID.

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s.p e u y

SIMPLE BLOCK DIAGRAM OF A PROCESS WITH AN-PID

CONTROLLER

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AN-PID Plant

Nonlinearadjustments

PNEUMATIC MUSCLE ACTUATORS

• Pneumatic Muscle Actuator PMA

• It is a tube like actuator.

• They are characterized by decrease in actuating length

when pressurized.

• PMA is a device that mimics behaviour of skeletal muscle

• It generate force in a nonlinear manner when activated

(pressurized).

• It replaced pneumatic cylinders.

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PMA

PMA in normal state Pressurised PMA

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ADVANTAGES OF PMAs OVER PNEUMATIC

CYLINDERS:

High force-to-weight ratio.

No mechanical parts.

Lower compressed air consumption.

Low cost

Light weight

faster

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COMPONENTS AND POPERTIES OF

PMA

• The basic PMA component is Festo muscle(test

PMA).

• Two Festo muscles having same properties of test

PMA are used form antagonist setup.

• They are clamped together and are connected with test

PMA via a pulley.

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PMA Setup Cross section of PMA tube

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• All three PMAs are on vertical position and their upper end is

clamped.

• Pressure regulators → to control and measure the compressed

air supplied to PMAs.

• A pressure sensor is integrated inside pressure regulator to

provide measurement accuracy.

• A distance sensor is used to measure the displacement of PMA

in the vertical axis.

• A load cell is used to measure force produced from PMA.

• Data acquisition →national instruments USB-6251 DAC .

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NON LINEAR PROPERTIES OF PMA:-

• PMA is having double helix aramid netting, it is covered

by a neoprene threaded coating → tube like formation.

• Aluminium bearing are properly attached at the ends of

the aramid-neoprene fibre wrapping.

• Cross-sectional view of the PMA is shown in figure.

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• The dual material leads to a non-linear characteristics:-

Viscoelastic properties of the neoprene wrapping

Friction phenomena between the aramid threads and

neoprene coating .

Irregular deformation of the tubes.

• These properties result in complex hysteretic phenomena.

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CONVENTIONAL PID

• It is the most utilised controller.

• It features a feedback control action u(t).

• u(t) weighted sum of three control parameters

* Proportional term

* Integral term

* Derivative term

• They are mathematically formulated as:-

u(t)=𝑲𝑷 𝒆 𝒕 +𝟏

𝑻𝑰 𝟎

𝒕𝒆 𝒕 𝒅𝒕 + 𝑻𝑫

𝒅𝒆(𝒕)

𝒅𝒕………….(1)

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Cont…• Where

𝐾𝑃 Proportional gain

𝑇𝐼 Reset time

𝑇𝐷 Rate time

e(t) Error signal

e(t) =𝒙𝒅(t)-x(t) ……………………………..(2)

𝑥𝑑(t) : Set point value

x(t) : Process value

• Controllers goal is to

* adjust the manipulated variable u(t)

* minimise the process error signal e(t)

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Contd…

• Due to the positioning control problem in PMA actuated

applications different PID controllers were used.

• Apart from this a more efficient type of PID controller is

used here.

• That is Advanced nonlinear PID .

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AN-PID

• Conventional PID control is considered as ideal.

• In cases of highly nonlinear processes like PMA, there is a

need of modifying the conventional PID.

• This is to achieve advanced performance.

• For this AN-PID was formulated.

• Additional degrees of freedom and tuning parameters was

incorporated with conventional PID.

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FEATURES OF AN-PID

Increased flexibility

Advanced customizable properties of overall control behaviour

Trapezoidal integration and partial derivative action

Nonlinear adjustment of the integral action by anti-windup

switch function

Gain scheduling mechanism

Bumpless transition mechanism

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FUNDAMENTAL COMPONENTS OF

AN-PID

DERIVATIVE KICK CANCELLATION & NONLINEAR INTEGRAL ADJUSTMENT

• Sudden alteration in ‛ 𝑥𝑑 ’ value results in spikes in PID

output.

• This is due to response of the derivative term Derivative

kick

• To avoid the derivative kick derivative term is posed on the

process value ‛x’ instead of e(t).

• So derivative term 𝑢𝑑(t) is expressed as 𝑢𝐷(t)

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Contd….

𝑢𝐷(t) = 𝐾𝑃𝑇𝐷𝑑𝑥(𝑡)

𝑑𝑡…………………. (3)

• To avoid the overshoot a nonlinear term ‛ h(t) ’ was

added for adjusting the integral term 𝑢𝑖(t).

• Then 𝑢𝑖(t) is denoted as 𝑢𝐼(t).

• Where 𝑢𝐼(t) = 𝐾𝑃ℎ(𝑡)

𝑇𝐼 0

𝑡𝑒 𝑡 𝑑𝑡 ………………….(4)

• With h(t) = (𝑥2𝑑,𝑟𝑎𝑛𝑔𝑒 ( 𝑥2

𝑑,𝑟𝑎𝑛𝑔𝑒+ 10𝑒2(t)))

𝑥𝑑,𝑟𝑎𝑛𝑔𝑒 - Range of set-point value

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Contd…

TWO DEGREE FREEDOM ERROR MODIFICATION

• Additional modes were introduced for the PID tuning

parameters.

• The modes selectors are f , q € R.

• They are posed on proportional and derivative term is, whereas

integral term is remained unaffected to avoid steady state

error.

• The error signals are chosen as:-

𝑒𝑃(t) = f𝑥𝑑(t) - x(t)

𝑒𝐼(t) = 𝑥𝑑 𝑡 - x(t)

𝑒𝐷(t) = q𝑥𝑑(t) - x(t) ....(5)

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Contd…

• In conventional PID multiple control demands were

satisfied by using the error mechanism in one- degree of-

freedom manner.

• Equation (5) formulates a two-degree-of-freedom for

AN-PID.

• This provided advanced flexibility for control design

helped in disturbance rejection.

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• Mode selector f € [0,1] trade-off between noise rejection and

set-point tracking.

• f=1 → error effected action → control emphasis on tracking

reference signal.

• f = 0 → measurement effected action → emphasis on disturbance

cancellation.

• Mode selector q € [0,1].

• q = 1→ differentiation on error

• q = 0→ differentiation on measurement →reduces derivative

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Contd…..

ADVANCED NONLINEAR ERROR FUNCTION

• To achieve good control behaviour in different error

magnitudes through auto-adjustable gain →nonlinear error

function error squared is used.

𝒆𝒔𝒒𝒖𝒂𝒓𝒆𝒅(t) = 𝒆 𝒕 × 𝒆(𝒕)

𝒙𝒅,𝒓𝒂𝒏𝒈𝒆........... (6)

• This will increase the efficiency of PID algorithm against

low-frequency disturbances which cannot be removed from

the measurement signal.

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• This function drives the ‛𝐾𝑃’ to lower values as error

decreases and vice versa.

• Equation (6) is again modified as

𝑒AN−PID(t) = 𝑒(𝑡)

𝑥𝑑,𝑟𝑎𝑛𝑔𝑒𝑔 × 𝑥𝑑,𝑟𝑎𝑛𝑔𝑒 + (1 − 𝑔) 𝑒(𝑡) ..(7)

𝑔 → linearity factor

• 𝑔 € R+ and is bounded in 𝑔[0,1].

• 𝑔 accounts the increase in 𝐾𝑃 with respect to error.

• Graphical representation between linear error and

modified squared-error is shown in figure.

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𝑔=0 → linear error signal

𝑔=1 → squared error

𝑔=0.3

𝑒AN−PID(t) = 0.3e(t)+0.7𝑒(𝑡)× 𝑒(𝑡)

𝑥𝑑,𝑟𝑎𝑛𝑔𝑒………….(8)

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• In case of small values of e(t) , the effect of the term

𝑒(𝑡) × |𝑒(𝑡)| 𝑥𝑑,𝑟𝑎𝑛𝑔𝑒 will become negligible → result in

minimum value of 𝑒AN−PID(t).

𝑒AN−PID(t) = 0.3 e(t) ........(9)

• Comparing equation (5) and (7) error signals for proportional,

integral and derivative actions are given by

𝑒𝑃AN−PID(t)=

[𝑓𝑥 𝑑 −𝑥 𝑡 ]

𝑥𝑑,𝑟𝑎𝑛𝑔𝑒

× 𝑔𝑥𝑑,𝑟𝑎𝑛𝑔𝑒 + 1 − 𝑔 𝑓𝑥𝑑 𝑡 − 𝑥(𝑡) (10)

𝑒𝐼AN−PID(t)=

𝑥𝑑 𝑡 −𝑥(𝑡)

𝑥𝑑,𝑟𝑎𝑛𝑔𝑒× 𝑔𝑥𝑑,𝑟𝑎𝑛𝑔𝑒 + (1 − 𝑔) 𝑥𝑑 𝑡 − 𝑥(𝑡)

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𝑒𝐷AN−PID(t)=

𝑞𝑥𝑑 𝑡 −𝑥(𝑡)

𝑥𝑑,𝑟𝑎𝑛𝑔𝑒× 𝑔𝑥𝑑,𝑟𝑎𝑛𝑔𝑒 + (1 − 𝑔)|𝑞𝑥𝑑 𝑡 −

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• Discretization of the integral term is by trapezoidal integration.

• This is for smoother integral action control during x or 𝑥 𝑑

variation.

𝑢𝐼(n) = 𝑢𝐼(n-1) + 𝐾𝑃∆𝑇

𝑇𝐼

𝑒𝐼AN−PID(𝑛)+ 𝑒𝐼

AN−PID(𝑛−1)

2h(n) ..(14)

• Discrete equivalent derivative term is

𝑢𝐷(n) = 𝐾𝑃𝑇𝐷

∆𝑇𝑒𝐷

AN−PID 𝑛 − 𝑒𝐷AN−PID(𝑛 − 1) ……(15)

• Discrete control output is given by adding (13) (14) (15)

𝒖𝐀𝐍−𝐏𝐈𝐃(𝒏) = 𝒖𝑷(n) + 𝒖𝑰(n) + 𝒖𝑫(n) .......(16)

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• 𝑢𝐴𝑁−𝑃𝐼𝐷(n) limits between 𝑢𝑚𝑎𝑥 and 𝑢𝑚𝑖𝑛 .

• In case of constant error factors integral action drives the

control effort to its extreme values 𝑢𝑚𝑎𝑥 or 𝑢𝑚𝑖𝑛 .

• This results in saturated condition → windup.

• Windup will cause overshoot phenomena ,this is avoided

by a switch function → by using anti-windup switch‛ẟ’.

• ẟ will be enhanced with equation (14).

𝑢𝐼(n) = 𝑢𝐼(n-1) +ẟ 𝐾𝑝∆𝑇

𝑇𝐼

𝑒𝐼AN−PID(𝑛)+ 𝑒𝐼

AN−PID(𝑛−1)

2h(n) ... (17)

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GAIN SCHEDULING

• For highly nonlinear process, efficient control

performance is being required throughout their operating

range → gain scheduler.

• Then gain scheduler must be incorporated AN-PID loop.

• This scheduling has the ability to control parameters 𝐾𝑃,

𝑇𝐼 and 𝑇𝐷 → according to region of operation specified

by 𝑥𝑛 .

• An additional switching signal ‛i’ is introduced.

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• Switching signal (i) rules the previous switching values of

gain constants.

•

𝐾𝑃

𝑇𝐼

𝑇𝐷

=

𝐾𝑃,𝑖

𝑇𝐼,𝑖

𝑇𝐷,𝑖

for i = 1,2,3,…..,N

N → Maximum number of operating regions

BUMPLESS TRANSITION

• Bumpless transition is used for smooth transition between

areas of operation .

• It act as integral sum of adjustment function.

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• Here 𝑢𝑃 + 𝑢𝐼 is kept in kept invariant to parameter

alterations.

• Inorder to ensure the invariance during such changes

integral action 𝑢𝐼(n) is being altered.

𝑢𝐼(n) = 𝑢𝐼(n-1) + 𝐾𝑃(n-1)𝑒𝑃AN−PID(n-1) - 𝐾𝑃(n) 𝑒𝑃

AN−PID(n)

𝑢AN−PIDBumpless(n) = 𝐾𝑃(n-1)𝑒𝑃

AN−PID(n-1) + 𝐾𝑃(n) ×

[ẟ∆𝑇

𝑇𝐼 𝑖=1

𝑛−1[𝑒𝐼

AN−PID(𝑖)+𝑒𝐼AN−PID(𝑖−1)

2]h(i-1)

+ 𝑇𝐷

𝑇𝐼[𝑒𝐷

AN−PID(n) - 𝑒𝐷AN−PID(n-1) ] …..(18)

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AN-PID STRUCTURE

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CONCLUSION

• Presented about the advanced and highly adjustable

performance of AN-PID.

• This control helps for smooth functioning of PAMs.

• In future PMA-actuated applications will be used to

perform various operations (e.g., aligning, pressing,

drilling, gripping, clamping, handling, transporting) .

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REFERENCES

[1] George Andrikopoulos ,‛Advanced Nonlinear PID-Based Antagonistic

Control for Pneumatic Muscle Actuators’ ,IEEE Transactions on industrial

electronics, VOL. 61, NO. 12, DECEMBER 2014.

[2] A. B. Corripio, ‘Tuning of Industrial Control Systems’, 2nd ed. Raleigh,

NC, USA: ISA,Jan 2000

[3] K. J. Åström and T. Hagglund, ‘PID Controllers: Theory, Design and

Tuning’, IEEE Control Engineering USA:ISA Dec 1995

[4] S. Bennett, ‘A History of Control Engineering’,IEEE Control Engineering U.K.: IET Jun.1986

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