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Control Theory

  • Control is the art of keeping a measured variable at a desired level
  • Types of Controllers
    • Open loop controller
    • Feed forward controller
    • Feed back controller
  • The most common control algorithm used is the PID control. PID controllers are a feedback type controller
  • PID controllers have 2 inputs and 1 ouptut: set variable(SV), process/controlled variable(PV) and manipulated variable (MV) (output)
  • PV is usually taken from transmitters and MV is given out to control valves. The MV sent to control valves is a 4-20 mA signal. Setting either reverse or direction action in the controller will tell the controller the actuation direction to the control valve whether increase in mA will open or close the valve. For fail open CVs, giving 20mA will shut the valve instead of opening it.
  • SV are usually set by panel man, some are taken from another controller’s MV (SV = MV) and some are taken from other subsystems such as APC (advance process control)
  • The controller action will be to manipulate the MV till the PV = SV. This is a feedback system because the input is taken in front of the control valve
  • PID control block can be set to normal mode, auto mode, manual mode or cascade mode.
  • Usually, PID block have a set of tracking modes. Tracking in general means to force the output to a certain input. This is to ensure safe transition between manual to auto mode. The most common type of tracking modes are
    • Manual Trackin
    • Auto Tracking
  • PID Controllers too has several types
    • Simple Loop
    • Cascade Loop – This controller is used if another controller (master) who also uses the same final control element gives the set point of the first controller (the slave). Reason why cascaded control is used is usually because the controlled process variable has a slow response. In this case, the master controller sending only set point values to the slave controller will control the controlled process variable. Example of an application is vessel level controls, where the level controller is the master sending out set points to the flowing out flow controller
    • The term open loop and close loop is a state of the controller. For open loop, the input is not fed back, in this case the controller is not used, the input, which is the manipulated variable is manually set and the output flow (which would become the input to the PID controller ) will be observed. Close loops
  • The concept of a PID controller is simple,
    • There are 3 main components, which are :-
      • The input, PV
      • The set value, SV
      • The controller output, MV
    • The aim is to get the SV as close as possible to PV. This is done by creating an output of MV
    • There are 3 elements in the PID controller
      • The first element is P, proportional
      • The second element is I, integral
      • The third element is D, derivative

  • The P Controller
    • The P controller causes a change to the MV by an amount which is proportional to the change in Error or Delta Error. Error is simply calculated as PV – SV.
    • The change in error is then multiplied by the proportional constant P. Some DCS vendors refer to P as proportional band(PB) , in which case P = 100/PB.
    • The higher the change in error, the more the controller output will change
    • The higher the P (Or lower the PB) the faster or more aggressive the controller works. However, this may introduce oscillations
    • The problem with having P alone is that there will always be an offset between the settled PV value and SV. Why? It is due to the nature of the controller that it will try to get as close as possible to the set point value but no too close. If it does gets too close to it, it will force the reading to go further away from it. But if it gets too far it will come back closer. Sooner or later it will settle at a value which is not too close but not too far. Hence, the offset
    • P only is hardly used due to this problem. It is only used for coarse control applications and cheap controllers like previously when they use to have pneumatic controllers
    • The initial setting of PB is typically around
      • For Liquid Flow/Pressure = 50-500
        • PB should be high here because liquid response is typically very fast, so you don’t want to change the MV too fast as it will upset the process
      • For Gas Pressure
        • PB should be 1 to 50, i.e. the gain is high
        • PB should be low here as gas moves and changes very slow.
        • Please note that since P is always larger than 2x (i.e. 100/50 = 2), it means that the adjustment to the controller must be done higher
      • For Liquid Level
        • PB = 1 to 50
        • PB should be low since liquid level moves slow
      • For Temperature
        • PB is typically around 2 to 100 (initial setting)
        • PB should be low as D is very high
      • For Analysers
        • PB is 100 to 2000
        • PB is low since we want a very slow controller response since analyzer readings are always lagging


  • The I Controller
    • To address the issue with the P controller, the I controller is produced.
    • The I controller constantly adds a corrective action to the MV change. This corrective action is proportionate to the error (not change in error like P). The proportional constant is known as I (integral gain). Also known as repeat or Repeat/Min. It simply mean how many time the entire error is integrated into the controller within a 1 second
    • Some DCS vendors also use Integral Time(T) instead of integral gain(I). Integral time is the inverse of integral gain. Integral Time = 1/Integral Gain. It means that how long does it takes for an error to be added into the system. It is also known as Reset or Min/Repeat
    • To disable I,
    • If the DCS defines it as Integral Gain/Rate/Repeat, Put I = 0
    • Id the DCS defines it as Integral Time/Reset, Put TI = As high as possible! This is what we normally do when disabling I in a Yokogawa system, we put I as high as possible like 9999 or something…
    • A high I or Low T means that the error will immediately be added to the corrective controller action. This is suitable for a fast moving control valve where it can react quickly.
    • The problem with the I controller is that it is slow in action since the corrective action builds up slowly. We can add a high I (or small T) but this will result in oscillations. Why?
    • Think about it. When we have I, we are actually adding up errors.
    • The Typical I settings would be
    • For flow control or liquid pressure, TI (integral time) is very small (<10s). This is because liquid changes it pressure or flowrate very fast, since it’s does not has an expansion factor
    • For Gas pressure or liquid level, TI is normally a bit larger (30s). This is because gas pressure changes slowly. Again, this depends on the process but it’s better to start large and slowly go lower
    • For temperature, also start at high TI, i.e. 30
    • For quality, also start at very high TI, i.e. 60

  • The D Controller
    • To address the issue of the I controller acting very slow, the D controller is introduced.
    • The D controller will add an acceleration of error (the rate of error change) to the controller movement. This acceleration is multiplied by a constant called the D or derivative time.
    • By adding the acceleration, controller movement can be faster since the controller will calculate how much difference the rates are changing. If the change in error is constant, the D will have no effect
    • D is usually used for temperature and pH control. This is because due to slow response. Even on cascade, the cascade loop will have a temperature controller
    • Disadvantage of having D is that it will cause oscillation
    • The typical D settings would be
    • D is only used for temperature and quality, which typical values would be 20
    • For gas pressure or liquid level, can use a bit of D but must be very small. Start at 0 D first and gradually increase

  • Yokogawa Centus CS has the following controller function. Delta MVn is the change in MV
    •  clip_image002[8]

    • For P, MV will be adjusted by an amount equal to the rate of change of error. PB is the proportional band
      • As you can see in the Yokogawa system, 100/PB encapsulates the entire equation. This is similar to a Gain (which is = 100/PB). The gain will encapsulate the entire equation
        • Ypid = Yp + Yi + Y
        • = Kp ( e + 1/ Ti ò e dt + Td de/ dt )
    • For I, MV will be adjusted by an amount equal to the error it sel
      • Delta T, is the control period, i.e. the cycle time of the controller. Typically it’s 1 second but there are some controllers that can be set to 1/3 of a secon
      • TI is the integral time, in second
      • As you can see, if TI = 5s, it will take 5 seconds for all the error to be summed u
        • However, if this is not a typical controller with 1 second cycle time, delta T will be the alternative cycle time, hence athe TI will still maintain at 5 seconds even though the cycle time is not 1 secon
        • Then again, you need to remember the proportional band thing. T or I will scale accordingly to PB or P

  • Ziegler Nichols open loop tuning method
    • allows to calculate PID parameters from the process parameters. The procedure:
    • Step 1: Make an open loop plant test (e.g. a step test)
    • Step 2: Determine the process parameters: Process gain, deadtime, time constant (see below: draw a tangent through the
      inflection point and measure L and T as shown. By the way: Today we have better and easier methods).
    • Step 3: Calculate the parameters according to the following formulas:
      • K = time constant / (process gain * deadtime)
      • PI: Proportional gain = 0.9 * K, integral time = 3.3 * deadtime
      • PID: Proportional gain = 1.2 * K, integral time = 2 * deadtime, derivative time = 0.5
        deadtime
        •  clip_image003[8]
        • Process gain = dPV / dOP, deadtime = L, time constant = T

  • How do we know a controller has been tuned?
    • ¼ decay
    • Minimum Overshoot
      • clip_image005[8]

  • Types of controllers
    • Cascade Control
      • Occurs when there are
        • Multiple inputs or PVs
        • 1 controller output
      • The set point of the inner loop (Secondary loop) is controlled by the output of the outer loop (Primary loop).
      • Operators will set the desired controller set point at the outer loop
      • The inner loop is called the slave where the outer loop is called the master
      • The purpose of having an inner loop is to reduce disturbances on the PV to be controlled
      • Typically used for level and temperature control
      • clip_image007[8]


    • Ratio Control
      • Purpose of this controller is to set the ratio of flow between two parameters is constant even if one flow changes
      • Only one of the flow will be controlled
      • The ratio controller block will receive input only from the uncontrolled flow
      • Typically used for blending
      • clip_image009[8]


    • Override/Selective Control
      • Is a controller which shares a same controller output for two controlled PV. At any point of time, the higher priority PV will be selected. The selection of which PV is more important will depend on an algorithm such as larger than or smaller than.
      • Selective control is typically used in furnace FG control and steam heating control
      •  clip_image011[8]

    • Split Range Control
      • Is a controller which has same PV but 2 controller output. The output is selected based on the range of the PV.

    • Feedback Control
      • A Control scheme trying to correct back something that has already happened in the past
      • The disadvantage of using feedback control is that it will provide less stability
      • Example of feedback control is furnace outlet temperature control

    • Feedforward Control
      • A control scheme which tries to prevent the error from happening in the first place
      • A control is called feed forward when the following occurs
      • The output goes to a calculation block which
      • An Input taken from another instrument is fed to the calculation block. This variable is called the DV (Disturbance variable)
      • Feedforward control should be used in any case except when there is process limitation

    • Complex Loop
      • clip_image013[6]
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