a seminar on "Advanced Nonlinear PID-Based Antagonistic Control for Pneumatic Muscle Actuators" for control enginerring,It involves the control of pneumatic mucle actuators using Advanced nonlinear PID control.It is a model less control.These actuators are mainly used in humanoid robborts.this leads to more easier and robust control.

1. Presented by:
SMILIN MARY JOE
14mee11015.
Guided by:
Mrs.MINU V S
Asst . Professor EEE
MES college of Engineering
Kuttippuram.

2. 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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3. 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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4. s.p e u y
SIMPLE BLOCK DIAGRAM OF A PROCESS WITH AN-PID
CONTROLLER
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AN-PID Plant
Nonlinear
adjustments

5. 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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6. PMA
PMA in normal state Pressurised PMA
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7. 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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8. 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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9. PMA Setup Cross section of PMA tube
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10. • 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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11. 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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12. • 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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13. 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)=𝑲 𝑷 𝒆 𝒕 +
𝟏
𝑻 𝑰 𝟎
𝒕
𝒆 𝒕 𝒅𝒕 + 𝑻 𝑫
𝒅𝒆(𝒕)
𝒅𝒕
………….(1)
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14. Cont…
• Where
𝐾 𝑃  Proportional gain
𝑇𝐼  Reset time
𝑇 𝐷  Rate time
e(t) Error signal
e(t) =𝒙 𝒅(t)-x(t) ……………………………..(2)
𝑥 𝑑(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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15. 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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16. 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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17. 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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18. FUNDAMENTAL COMPONENTS OF
AN-PID
DERIVATIVE KICK CANCELLATION & NONLINEAR
INTEGRAL ADJUSTMENT
• Sudden alteration in ‛ 𝑥 𝑑 ’ 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 𝑢 𝑑(t) is expressed as 𝑢 𝐷(t)
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19. Contd….
𝑢 𝐷(t) = 𝐾 𝑃 𝑇 𝐷
𝑑𝑥(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) = 𝐾 𝑃
ℎ(𝑡)
𝑇 𝐼 0
𝑡
𝑒 𝑡 𝑑𝑡 ………………….(4)
• With h(t) = (𝑥2
𝑑,𝑟𝑎𝑛𝑔𝑒 ( 𝑥2
𝑑,𝑟𝑎𝑛𝑔𝑒+ 10𝑒2(t)))
𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒 - Range of set-point value
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20. 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:-
𝑒 𝑃(t) = f𝑥 𝑑(t) - x(t)
𝑒𝐼(t) = 𝑥 𝑑 𝑡 - x(t)
𝑒 𝐷(t) = q𝑥 𝑑(t) - x(t) ....(5)
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21. 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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22. • 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
kick.
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23. 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.
𝒆 𝒔𝒒𝒖𝒂𝒓𝒆𝒅(t) =
𝒆 𝒕 × 𝒆(𝒕)
𝒙 𝒅,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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24. • This function drives the ‛𝐾 𝑃’ to lower values as error
decreases and vice versa.
• Equation (6) is again modified as
𝑒AN−PID(t) =
𝑒(𝑡)
𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒
𝑔 × 𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒 + (1 − 𝑔) 𝑒(𝑡) ..(7)
𝑔 → linearity factor
• 𝑔 € R+
and is bounded in 𝑔[0,1].
• 𝑔 accounts the increase in 𝐾 𝑃 with respect to error.
• Graphical representation between linear error and
modified squared-error is shown in figure.
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25. 𝑔=0 → linear error signal
𝑔=1 → squared error
𝑔=0.3
𝑒AN−PID(t) = 0.3e(t)+0.7
𝑒(𝑡)× 𝑒(𝑡)
𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒
………….(8)
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26. • In case of small values of e(t) , the effect of the term
𝑒(𝑡) × |𝑒(𝑡)| 𝑥 𝑑,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
𝑒 𝑃
AN−PID(t)=
[𝑓𝑥 𝑑 −𝑥 𝑡 ]
𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒
× 𝑔𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒 + 1 − 𝑔 𝑓𝑥 𝑑 𝑡 − 𝑥(𝑡) (10)
𝑒𝐼
AN−PID
(t)=
𝑥 𝑑 𝑡 −𝑥(𝑡)
𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒
× 𝑔𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒 + (1 − 𝑔) 𝑥 𝑑 𝑡 − 𝑥(𝑡)
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27. 𝑒 𝐷
AN−PID(t)=
𝑞𝑥 𝑑 𝑡 −𝑥(𝑡)
𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒
× 𝑔𝑥 𝑑,𝑟𝑎𝑛𝑔𝑒 + (1 − 𝑔)| 𝑞𝑥 𝑑 𝑡 −
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28. • 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) + 𝐾 𝑃
∆𝑇
𝑇 𝐼
𝑒 𝐼
AN−PID(𝑛)+ 𝑒 𝐼
AN−PID(𝑛−1)
2
h(n) ..(14)
• Discrete equivalent derivative term is
𝑢 𝐷(n) = 𝐾 𝑃
𝑇 𝐷
∆𝑇
𝑒 𝐷
AN−PID 𝑛 − 𝑒 𝐷
AN−PID(𝑛 − 1) ……(15)
• Discrete control output is given by adding (13) (14) (15)
𝒖 𝐀𝐍−𝐏𝐈𝐃(𝒏) = 𝒖 𝑷(n) + 𝒖 𝑰(n) + 𝒖 𝑫(n) .......(16)
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29. • 𝑢 𝐴𝑁−𝑃𝐼𝐷(n) limits between 𝑢 𝑚𝑎𝑥 and 𝑢 𝑚𝑖𝑛 .
• In case of constant error factors integral action drives the
control effort to its extreme values 𝑢 𝑚𝑎𝑥 or 𝑢 𝑚𝑖𝑛 .
• 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 𝐾 𝑝
∆𝑇
𝑇 𝐼
𝑒 𝐼
AN−PID(𝑛)+ 𝑒 𝐼
AN−PID(𝑛−1)
2
h(n) ... (17)
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30.  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 𝐾 𝑃,
𝑇𝐼 and 𝑇 𝐷 → according to region of operation specified
by 𝑥 𝑛 .
• An additional switching signal ‛i’ is introduced.
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31. • Switching signal (i) rules the previous switching values of
gain constants.
•
𝐾 𝑃
𝑇𝐼
𝑇 𝐷
=
𝐾 𝑃,𝑖
𝑇𝐼,𝑖
𝑇 𝐷,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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32. • Here 𝑢 𝑃 + 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) + 𝐾 𝑃(n-1)𝑒 𝑃
AN−PID(n-1) - 𝐾 𝑃(n) 𝑒 𝑃
AN−PID(n)
𝑢AN−PID
Bumpless
(n) = 𝐾 𝑃(n-1)𝑒 𝑃
AN−PID
(n-1) + 𝐾 𝑃(n) ×
[ẟ
∆𝑇
𝑇 𝐼
𝑖=1
𝑛−1
[
𝑒 𝐼
AN−PID(𝑖)+𝑒 𝐼
AN−PID(𝑖−1)
2
]h(i-1)
+
𝑇 𝐷
𝑇 𝐼
[𝑒 𝐷
AN−PID(n) - 𝑒 𝐷
AN−PID(n-1) ] …..(18)
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33. AN-PID STRUCTURE
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34. 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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35. 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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