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.

Answer:

The spring-mass-damper system consists of a mass with weight (m), a spring with stiffness (k), and a shock absorber with a damping coefficient of (c). This system works based on Newton’s second law, which states that Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.

Given values;

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

Simulink Model of mass spring damper system without PID controller block:

Pole placement in MATLAB code:

In this model we have used the following blocks:

Pulse generator:

Here we have used the pulse generator to create the givem reference signal. 

Integrator block:

For Continuous-time integration of the input signal.

Derivative block:

Gives numerical derivative: Δu/Δt.

Gain blocks for Kp, Ki and Kd:

Transfer function block:

Results:

1. When Ki = 1;

2. When Ki = 100;

Simulink Model of mass spring damper system with PID controller block:

The given parameters are defined in MATLAB code:

The blocks used here are;

Pulse generator: 

Here we have used the pulse generator to create the givem reference signal. 

PID controller:

We have tuned the PID controller, to get the exact values of the Kp, Ki and Kd. After tuning we received the below response.

Results:

The results shows that the system is following the given input reference signal perfectly, when the PID controller is used after tuning to correct values of Kp, Ki and Kd.