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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…
Jiji M
updated on 25 May 2023
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.
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