Project - Position control of mass spring damper system

• 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.

•   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.

• Pulse Generator:

•    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

•    MATLAB PROGRAM OF POSITION CONTROL OF SPRING_MASS_DAMPER_SYSTEM :

clc;
close all;
% initial conditions Position control of mass spring damper system
m = 3.6; % kg
k = 400; % N/m
c = 100; % Ns/m
% Pole placement design
wn = sqrt(k/m);
fn=wn/(2*pi);

% A & B matrix value
A = [0 1; -k/m -c/m]; % A is using matrix of c ans k dived value of mass
B = [0; 1/m]; % B is the 1 ovear mass value
�sign values
zeta = 0.5; % for an under-damped behavior
�sied poles value
p1 = -zeta*wn+wn*sqrt(zeta^2-1);
p2 = -zeta*wn-wn*sqrt(zeta^2-1);
p= [p1;p2];
% place comment is the Kp and Kd value
K = place(A,B,p);
Kp = K(1);
Kd = K(2);
Ki=1400;
% End

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

• Speed is the controllable parameter, so we will set the reference speed..,
• Subtract the actual speed from the reference speed to generate the error signal..,
• 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/mode..,
• Add Ki manually with gain and integrator block and tune different values(0,700,1000,1400) of Ki and check the impact of it on results. 

•      simulink model

• 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.