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      Mills controls systems        
                   
      5   ON-OFF controllers        
        - This is the easiest and most economical regulation.      
        - It is reduced to a binary 0 or 1.        
        - It is used for systems with high inertia and which do not require high accuracy like:  
          maintaining a temperature of a furnace, a level in a tank, a water temperature in a circuit ...  
        - This type of control uses a final element, such as a valve, which moves from one position to another as soon as
          the controlled variable deviates from the setpoint adjustment.      
        - It is not necessary that the two positions are always extreme (fully closed or fully open), one can also use
          intermediate situations.        
        - This type of control is shown in the following diagram:      
         
     
         
        - We see in the diagram that the controller commands the ON and OFF positions when the value to control reaches
          one of the 2  setting values C1 and -C1.        
        - The value at which the variable can deviate due to the intervention of the final control element, varies
          depending on the controller setting (also called hysteresis or ON-OFF time cycle).  
        - We can therefore conclude that the controlled variable continues to oscillate at the end of the set point.
        - Note that it is not desirable to have a too low hysteresis in order to avoid an excessive frequency of the intervention
          of the final element of the adjustment, which in the case of a remote switch control for example,
          could quickly wear out.        
        - In conclusion, this type of two-positions control is used for its simplicity, where it is acceptable to adjust a variable
          with limited accuracy.        
        - It is certainly not the desired controller for a grinding plant.      
                   
      6   PID controllers (P, PI, PD and PID)        
       6.1   Introduction to PID controllers:        
        - PID controllers are part of the so called continuous regulation.      
        - PID is the acronym of Proportional Integral Derivative.      
        - This is a natural extension of ON-OFF controller.      
        - It is sufficient for many control problems.        
        - More than 95% of the control loops are using a PID      
        - This is a control mode which allows continuous adjustment of an actuator (partially open, intermediate position, ... etc).
        - These types of controllers require more complex implementation and are more expensive.  
        - This results in a good control performance:        
          * Elimination of the steady state error        
          * Minimization of response time        
          * Minimizing of overshoot        
        - What is expected of PID controllers is then: precision, speed and stability.    
        - On the following diagrams, we can see the difference between a good and less good regulator for these three qualities.
        - On a precision point of view:        
         
     
         
        - On a speed point of view:        
         
     
         
        - On a stability point of view:        
         
     
         
        - In addition, they are well suited to transitory states.      
        - PID controllers have three actions as follows:      
          * The Proportional action (P)        
          * The Integral action (I)        
          * The Derivative action (D)        
        - One can combine these three actions together as needed.      
        - Here are some types of possible architectures (in series, parallel or mixed):    
          * (P+I), (P+D), (P.I), (P.D)        
          * (P+I+D), (P.I.D)        
          * (P.I)+D, (P.D)+I        
        - Example of flowsheet of PID and its environment:      
         
     
           
        - We will study the contribution of each of these effects in the following pages.    
                   
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