AS-74.3199 Wireless Automation

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AS-74.3199 Wireless Automation

• Implementing PIDPLUS for Halvari system

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Halvari a ball balancing system

• The goal is to keep the ball and the cart in the
  middle.
• Can be controlled by a manual joystick or a
  computer.
• The position of the ball (angle f) and of the
  cart (coordinate y) are measured and their
  derivatives calculated. Thus our system has four
  states from which a control variable (force F)
  can be derived.
• In optimal control force is calculated as a
  linear combination of the states

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Halvari a ball balancing system

• Halvari can be described with two nonlinear
  differential equations

The constants used in the equations
Mass of the cart without the ball
Mass of the ball
Balls moment of inertia
Radius of the arch
Radius of rotation
Acceleration of gravity
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Halvari a ball balancing system
The linearized form is derived by assuming that
the angle f is small. Thus we have the following
assumptions
The linearized equations are
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Traditional PID

• PID controller consists of three terms
  proportional, integral and derivative.
• The input of a PID controller is an error signal
  which is the difference between a reference
  signal and the measured output of the process

P
y
yr
u

e
I
process
S
S
-
D
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PIDPlus

• In wireless automation loss of measurement and
  control data is common
• Traditional PID doesnt handle packet loss that
  well and gives a poor dynamic response
• The solution is to replace PIDs integral part
  with a filter that takes packet loss into account
  ? PIDPlus
• PIDPlus holds on to the last filter output until
  a new measurement is received and after that it
  calculates a new filter output from the last
  controller output and time elapsed since the last
  communication

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PIDPlus integral
Source Addressing Control Applications Using
Wireless Devices, Emerson Global Users Exchange
The filter eguation
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PIDPlus derivative

• The derivative term is described by the equation
• Because the reference signal is 0 there
• is a connection
• A filter has to be added to the derivative
• term. The filter equation is

(angle f or place y)
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Halvari Joystick Control
DAC1
N1 Joystick
N2
N3
N4
ON/OFF
CH 18.
CH 12.
DIR
SYSTEM
SPEED

• Joystick measurement and Joystick ON/OFF

• N2 receives packet and uses external pins to
  relay information to N3
• Range 0,4095 Physical values 0,2.5 V
• Measurements range 1300, 1900 ? 0.79,1.15 V

• N3 calculates control speed and direction and
  sends packet to N4

• N4 assigns external pins for speed and direction
• Signals are amplified from 0-2.5 V to 0-5.0 V.

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Halvari PIDplus controller
ACK CH 18.
N3.5
N4
N3
CH 18.
CH 16.
CART POS.
DIR
SYSTEM
BALL POS.
SPEED

• N3 receives cart and ball position measurements
  from the system
• If control switch is activated, PIDplus control
  used
• Measurements are sent to N3.5

• N3.5 uses PIDplus algorithm to determine control
• Sends control command to N4 and waits for ACK
  packet
• If measurements from N3 not received, old control
  values used

• N4 assigns external pins for speed and direction
• Signals are amplified from 0-2.5 V to 0-5.0 V.

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Some simulations
PIDPlus without any packet loss.
red angle f blue place y green y turquoise
f
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Some simulations
PIDPlus with some packet loss. Sampling packet
loss probability 20 and Actuator packet loss
probability 20
red angle f blue place y green y turquoise
f
The longest time between updates is about 3
times the sampling time.
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Some simulations
PIDPlus with a lot of packet loss. Sampling
packet loss probability 40 and Actuator
packet loss probability 40
red angle f blue place y green y turquoise
f
Time between updates can be even 9 times
the sampling time.
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References

• Addressing Control Applications Using Wireless
  Devices, Emerson Global Users Exchange,
  PowerPoint-show

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