Project - Position control of mass spring damper system

Obtain the transfer function of a mass spring damper system and use it in the model. Add a PID controller to adjust the force on mass so that its position follows a reference signal.

Take m = 3.6; %kg k = 400; %N/m c = 100; %Ns/m

The reference signal is shown in the following figure.

       AIM :   

                To design the project of position control of mass spring damper system using matlab simulink model of transfer function of a mass spring damper system and use it in the model. Add a PID controller to adjust the force on mass so that its position follows a reference signal.

   OBJECTIVE :

                      transfer function of a mass spring damper system and use it in the model. Add a PID controller to adjust the force on mass so that its position follows a reference signal. the matlab model of the pid control and transfer function pulse wavefrome generator.

      This example shows a controlled mass-spring-damper. A controller adjusts the force on the mass to have its position track a command signal. The initial velocity for the mass is 10 meters per second. The controller adjusts the force applied by the Force Source to track the step changes to the input signal.

 PID controller

         In this project, PID controller has been designed by using Simulink in order to control a mass spring damper system which can move any direction. A transfer function for dc motor was added on the diagram. Response curve of the PID controller were fixed by tuning. The computer interface, different control algorithms can be performed on the system easily; control parameters can be set up online, filter algorithms in various structures can be tried and the reaction of these changeable values to the system can be observed. The effects of controller Proportional Integral Derivative (PID) for developing

   TRANSFER FUNCTION :   

        The numerator coefficient can be a vector or matrix expression. The denominator coefficient must be a vector. The output width equals the number of rows in the numerator coefficient. You should specify the coefficients in descending order of powers of s.

'Parameter tunability' controls the runtime tunability level for numerator and denominator coefficients. 'Auto': Allow Simulink to choose the most appropriate tunability level. 'Optimized': Tunability is optimized for performance. 'Unconstrained': Tunability is unconstrained across the simulation targets.

     Command Window commants :

   some parameter are give in the input value of spring mass dambering system using the matlab commants 

    Take m = 3.6; %kg

            k = 400; %N/m

            c = 100; %Ns/m

          the all the input value using to write the program and calculate the value.

      MATLAB PROGRAM OF POSITION CONTROL OF SPRING_MASS_DAMPER_SYSTEM :

      Matlab Simulink Model Of Position control of mass spring damper system :

To design a closed loop control scheme for a DC motor the following changes need to be done in the model in the previously created model.

• Speed is the controllable parameter, so we will set the reference speed in step block as 10,20, 40 whichever you want. 
• Subtract the actual speed from the reference speed to generate the error signal e(t)
• Add Kp as K(1) and Kd as K(2) parameter determined from place command (K=place(A,B,P)). (use gain block to mention values of Kp, Kd, and Ki)
• The feedback for Kd is provided from the output current of the plant/model (figure 1). OR we can take feedback (error speed signal as input to Kd shown by figure 2)
• Add Ki manually with gain and integrator block and tune different values of Ki and check the impact of it on results. 

To check the location of poles on the s-plane from MATLAB the following command (‘pzmap ’-pole zero placement or mapping) can be used in continuation to the above script. You can see two crosses in red indicate complex poles lying on the left hand of the plane which indicate it is a stable system. 

  To Plot output Wavefrom :

     CONCLUSION :

              To complte the project of Position control of mass spring damper system transfer function of a mass spring damper system and use it in the model. Add a PID controller to adjust the force on mass so that its position follows a reference signal to using matlab and simulink wave from plot.