Project - Position control of mass spring damper system
Answer;
The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers. This model is well-suited for modeling objects with complex material properties such as nonlinearity and viscoelasticity. Packages such as MATLAB may be used to run simulations of such models. As well as engineering simulation, these systems have applications in computer graphics and computer animation.
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 con: mass, force equals mass times acceleration.
The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers. This model is well-suited for modeling objects with complex material properties such as nonlinearity and viscoelasticity. Packages such as MATLAB may be used to run simulations of such models. As well as engineering simulation, these systems have applications in computer graphics and computer animation.
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.
Deriving the Mass Spring Damper System based on Newton's second law F=m*a
where
F = Resultant of all the forces
m = Mass
a = Acceleration
k is the spring stiffness
d is the damping coefficient
Applying Laplace Transform to the above equation
The system is in a state of rest. Let's consider a moving Mass Spring Damper System to see forc act during motion. What are the forces acting if the system is moving.
Expression for Spring Force and Damping Force
Fs=k^ * x - - - (1)
Fd=d^ * (dx / d * t) - - - (2)
Applying F=m*a
EF = m*(d^2x/dt^2) (in the positive direction)
- Fs - Fd+ F=m*(d^2x/dt^2)
F = m*(d^2x/dt^2) + Fd + Fs ---- -(3)
Substituting eq(1) and eq(2) in eq(3) F = m*(d^2x/dt^2) + d*(dx/dt) + k*x The above equation is the equation of motion (EOM).
Applying Laplace Transform to the above equation
F(s) =m^ * (s^ ^ 2^ * x(s))+d^ * (s^ * x(s))
+k ^ * x(s)
F(s)=(m^ * s ^ 2 +d^ * s+k)^ * x(s)
x(s) / F * (s) =1/(m^ * s^2+d^ * s+k).......transfer fnc
Response Time is increased manually for the best outcome and the same response is upgraded for the system using the Update Block option.
SCOPE OUTPUT
The Scope Output is the best tracking response of the system. It is achieved with the help of the PID Controller small Overshoot and Undershoot the signal can be seen.