The fields with the red border are required.
    www.thecementgrindingoffice.com                    
    All rights reserved © 2012-2015 The Cement Grinding Office
                   
      Mills controls systems        
                   
      6   PID controllers (P, PI, PD et PID)        
       6.4   PI controller:        
        - The output of the PI controller is given by the following formula:      
         
     
         
               
        - The role of the integral action is to cancel the difference between the measurement and the setpoint.
        - The introduction of a PI controller improves accuracy.      
        - So we keep the qualities of proportional correction while significantly reducing the offset.  
        - At the contrary, this type of corrector has some limitations on improving the speed and may even introduce some
          instability of the closed loop system.        
        - Finally, it is more difficult to tune.        
        - Functional diagram of the PI controller:        
         
     
         
        - Step response:        
         
     
         
        - The PI controller transfer function will be:        
         
     
           
                 
                 
        - Ki influence on the system:        
         
     
           
        - We see that the integral term has worked well and that the static error is zero.    
        - We also note that the higher the gain Ki is, more the system converges quickly.    
        - In contrast, greater Ki is, more the system oscillates and overtaking is great.    
        - It is for this that we will integrate the derivative checker.      
       6.5   D controller:        
        - The derivative term reduces the overshoot and oscillations.      
        - Its role is therefore to balance the effects of the dead time (delay) of the process.  
        - The derivative has a stabilizing effect but excessive value can cause instability.    
        - Note that the derivative action can not be used alone.      
        - The output of the corrector is given by the following formula:      
         
     
           
                 
                 
        - Functional diagram:        
         
     
           
        - The D controller transfer function is:        
         
     
           
                 
       6.6   PD controller:        
        - The derivative action can limit the overshoot of the setpoint generated by the PI controller.  
        - When the system approaches the setpoint, this action brakes the system by applying an action in the opposite
          direction, allowing faster stabilization.        
        - The PD controller transfer function is:        
         
     
           
                 
        - We will not insist further on this architecture, because the controller does not work in pure derivative action
          (too unstable).        
       6.7   PID controller:        
        - The PID controller is the combination of three basic actions P, I and D.    
        - Thanks to the term I, it allows the cancellation of the static error while allowing through the action of D speed
          superior performances than a PI controller.        
        - The introduction of a PID controller brings together the various benefits of each action, however, its setting,
          so the weight to be given to each action is rather tricky.      
        - The PID controller control law is given by:        
         
     
         
               
               
        - Here below, an example of a functional diagram:      
         
     
         
        - The PID controller transfer function is:        
         
     
           
                 
                 
        - Step response:        
         
     
         
        - Here below is a PID simulator.        
        - Just change the values of Kp, Ki and Kd to see the reactions of the output value.    
        - The setpoint is 80 t/h.        
                   
           
         
          Proportional action - value of Kp      
           
         
          Integral action - value of Ki      
           
         
          Derivative action - value of Kd      
                   
         
    Unable to load Flash content. The Charts Control requires Flash Player 9.0.45 or higher. You can download the latest version of Flash Player from the Adobe Flash Player Download Center
     
           
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
    www.thecementgrindingoffice.com
    All rights reserved © 2012-2015 The Cement Grinding Office