CONTROL PRINCIPLE - EXAMPLE 1

1.         A Proportional Controller is used for controlling temperature in melting process. Temperature set point is 750°C and temperature measuring tool range is 0 - 1000°C .  Proportional space is set  at 15%.  Pressure output range from controller is 20 –100 kN/m² and pressure output rises when temperature increases.  If pressure output is set at 60 kN/m² for temperature set

            point, find

            i)          Temperature for pressure output at 20 kN/m²

            ii)         Temperature for pressure output at  100 kN/m²    

     

  2.     In a process, a Proportional Controller is used to control the liquid level in the boiler. The   

          level is set at 8 meters and the level range is 1 to 14 meters. Proportional band is at 

          20%.  The output current has a range of  5 – 20mA. Determine:-

          i.                    The output level when current is 5 mA.

         ii.                  The output current at a level of 10 meters.

3.     An air to open valve on the inflow controls level in a tank. When the process is at the set point the valve opening is 50%. An increase in outflow results in the valve  opening increasing to a new steady state value of 80%. What is the resulting offset if the controller PB is:

i)                    80%

                                                                                              

ii)                   40%.

                                                                                                                      

4.   A temperature controller has the following characteristic curve below:

 

 

      The controller has a range of 100 ⁰C to 400 ⁰C. The set‐point is 250 ⁰C. Calculate:

                                                                                                                    

                                i.            The controller Proportional Band

                                                                                                                    

                              ii.            The controller Proportional Gain

                                                                                                                     

MARKAH BLOG JM507

CONTENT - JM507

1.0 INTRODUCTION TO CONTROL SYSTEM 

Introduction to Control System; Definition for general terms; Block
diagrams; Open loop and closed loop control system; Standard
symbols; Control system diagram; single variable and
multivariable; general cascade pattern control, schematic diagram
and block diagram; control system quality, definition for damping.

2.0 CONTROLLER PRINCIPLE 

Definition for general terms: Types of lagging process; ON/OFF
control. Superpositioned and unsuperpositioned ON/OFF control;
Characteristics of Proportionate (P), Integral (I), Derivative (D),
P+I, P+D, P+I+D; Controller Output graph caused by the
presence of constant, ramp and sinusoidal difference. At least one
example for each of the controllers above.

3.0 TRANSFER FUNCTIONS 

Definition; Laplace Transformation Concept; signal flow graph for
control system block diagram. Example of Laplace application

4.0 STABILITY AND PERFORMANCE TEST

Use of several testing methods to evaluate system stability; system
stability for sinusoidal, step and ramp shaped errors, simple Bode plot,
Bode stability criteria. State the final value theorem to examine the final
value of a system.

CONTROLLER PRINCIPLE 3

PID Controllers

•A particular control structure that has become almost universally used in industrial 
control.

•It is based on a particular fixed structure controller family, the so-called PID
controller family.

•These controllers have proven to be robust and extremely beneficial in the control of
many important applications.

•PID stands for:

–P (Proportional) 
–I (Integral) 
–D (Derivative)
Proportional Controllers (P)

•Each mode of control has characteristic advantages and limitations. 

•The modes of control are discussed in this and the next several sections of this 
module.

•In the proportional (throttling) mode, there is a continuous linear relation between 
value of the controlled variable and position of the final control element.

•In other words, amount of valve movement is proportional to amount of deviation.

•Three terms commonly used to describe the proportional mode of control are  
proportional band gain and offset. 

•Proportional band, (also called throttling range), is the change in value of the 
controlled variable that causes full travel of the final control element. 

•Gain, also called sensitivity, compares the ratio of amount of change in the final 
control element to amount of change in the controlled variable. 

•Mathematically, gain and sensitivity are reciprocal to proportional band.

•Offset, also called droop, is deviation that remains after a process has stabilized. 
Offset is an inherent characteristic of the proportional mode of control. In other 
words, the proportional mode of control will not necessarily return a controlled 
variable to its set point. 

•Proportional control is also referred to as throttling control.

CONTROLLER PRINCIPLE 2

3 types of controller are
 

•Discontinuous modes

•Multiposition modes

•Continuous modes

Discontinuous modes are controllers that have only two modes or positions; on and off.

•Example - hot water heater.

•When the temperature of the water in the tank falls below setpoint, the burner turns on. When the water temperature reaches setpoint, the burner turns off. Because the water starts cooling again when the burner turns off, it is only a matter of time before the cycle begins again. This type of control doesn’t actually hold the variable at setpoint, but keeps

the variable within proximity of setpoint in what is known as a dead zone.

  

Multiposition modes 

• controllers that have at least one other possible position in addition to on and off.

•operate similarly to discrete controllers, but as set point is approached, the multistep controller takes intermediate steps. 

•Therefore, the oscillation around set point can be less dramatic when multistep controllers are employed than when discrete controllers are used

 

•Continuous modes

Controllers automatically compare the value of the PV to the SP to determine if an error exists. If there is an error, the controller adjusts its output according to the parameters that have been set in the controller.

The tuning parameters essentially determine:

How much correction should be made? 

• The magnitude of the correction( change in controller output) is determined by the proportional mode of the controller.

How long should the correction be applied? 

•The duration of the adjustment to the controller output is determined by the integral mode of the controller 

How fast should the correction be applied? 

•The speed at which a correction is made is determined by the derivative mode of the controller 

Four modes of control commonly used for most applications are:

Proportional (P)

Proportional plus Reset (PI)

Proportional plus Rate (PD)

Proportional plus Reset plus Rate (PID)