Statefeedback control of the doublemassspringdamper system fall 2012 important. Please check your lab schedule to see which workbench you are assigned to. We would like to look at the response of the system using the scope. A new tuned mass damper design method based on transfer. Mathematically the transfer function is a function of complex variables.
As before, the springmass system can be thought of as representing a single mode of vibration in a real system, whose natural frequency and damping coefficient coincide with that of our springmass system. Springmassdamper system example consider the following springmass system. Vibration free fulltext effective mass of tuned mass. Springmassdamper system example consider the following spring mass system. The transfer function is a convenient representation of a linear time invariant dynamical system. From this transfer function, it can easily be inferred that the system can be simulated by either a single transfer function block or a. Simulink tutorial introduction starting the program. The mass m 2, linear spring of undeformed length l 0 and spring constant k, and the. Most closed loop systems and sensors are designed so that an ideal 2 nd order transfer function describes them accurately.
Finding transfer function of a mass spring damper system youtube. Solving problems in dynamics and vibrations using matlab. A mass, spring, and damper system is depicted in fig. Now using newtons law f m a and the definition of acceleration as a x we can write two second order differential equations. These are the equations of motion for the double spring. For a system with two masses or more generally, two degrees of freedom, m and k are 2x2 matrices. Fay technikonpretoriaandmathematics,universityofsouthernmississippi,box5045, hattiesburg,ms394065045,usa email. In its simplest form, a tmd consists of a small mass on a spring moving in the direction of the vibrations of the main structure, as sketched in figure 1. Position control of chained multiple massspringdamper systems adaptive output feedback control approaches s. Massspring system an overview sciencedirect topics. The system is subject to constraints not shown that confine its motion to the vertical direction only. This example shows how to model a double springmassdamper system with a periodically varying forcing function. Then take laplace transform, output input transfer function. Also shown are free body diagrams for the forces on each mass.
Finding transfer function of a mass spring damper system. Springs and dampers are connected to wheel using a flexible cable without skip on wheel. A nonlinear system has more complicated equations of motion, but these can always be arranged into the standard matrix form by assuming that the displacement of the system is small, and linearizing. Taking the laplace transform of 2 yields the following transfer function from the input to the output 1. Identification of a hybrid spring mass damper via harmonic. Motion of the mass under the applied control, spring, and damping forces is governed by the following. For example, a system consisting of two masses and three springs has two degrees of freedom. Functions operate on variables within their own workspace, separate from the workspace you access at the matlab command prompt. Mathematical models of translating mechanical systems. Say that the forward path has the transfer function. Defined as the ratio of the laplace transform of the output signal to that of the input signal think of it as a gain factor. The scope of state phase variable block representation with. Mass spring dashpot subsystem in falling container a mass spring dashpot subsystem in a falling container of mass m 1 is shown. Draw a free body diagram, showing all forces and their directions write equation of motion and derive transfer function of response x to input u chp3 15.
Springmass systems now consider a horizontal system in the form of masses on springs again solve via decoupling and matrix methods obtain the energy within the system find specific solutions. Find the differential equation of motion for this system. Translational mass with spring and damper the methodology for finding the equation of motion for this is system is described in detail in the tutorial mechanical systems modeling using. Consider a simple system with a mass that is separated from a wall by a spring and a dashpot. This research work applied newton law of motion, differential equations, matlab simulation, and transfer function to model mass spring damper model in phase variable form. Massspringdamper systems the theory the unforced massspring system the diagram shows a mass, m, suspended from a spring of natural length l and modulus of elasticity if the elastic limit of the spring is not exceeded and the mass hangs in equilibrium, the spring will extend by an amount, e, such that by hookes law the tension in the.
Introduction systems that require two indddependent coordinates to dbdescribe their motion are called two degree of freedom systems. In this system, the only sensor is attached to the mass on the left, and the actuator is attached to the mass on the. This is is an extremely important mechanical control system. Autoscale the plot so that you can see the response the autoscale button looks like a pair. A classic strategy for reducing the vibration response of a structure is the introduction of a tuned mass damper tmd. Bs, then masons rule says that the transfer function for the loop as a whole. Secondorder systems with potential oscillatory responses require two different and independent types of energy storage, such as the inductor and the capacitor in rlc filters, or a spring and an inert mass. Dynamics of simple oscillators single degree of freedom. This means that its configuration can be described by two generalized coordinates, which can be chosen to be the displacements of the first. Modeling mechanical systems california state university. This paper reported the research work carried on mass spring damper model in phase variable form. An optimal tmd design method is proposed based on transfer functions. Block diagram models consist of two fundamental objects.
For a neutrally stable system, the inertia and stiffness. Also, how to use the pythoncontrol module to find the response of a transfer function to. Me451 s07 transfer function massspringdamper system. The transfer function of the general secondorder system has two poles in one of three configurations. Im trying to model a system with two masses, two springs, two dampers, and one applied force using transfer functions. It is important to note the similarity between the two differential equations that describe. Especially you are studying or working in mechanical engineering, you would be very familiar with this kind of model. The motion profile of the source is selected in such a way that plotting the displacement of the mass against the displacement provided by the source produces a. As an example consider first a simple mechanical system, a springmassdamper. The massspringdashpot system is the inspiration of the ideal or standard 2 nd order transfer function. In this example, you are going to model a simple mechanical system and observe its behavior under various conditions. For a system with n degrees of freedom, they are nxn matrices the springmass system is linear. Stability of the system can be characterized by calculating poles of the transfer function. This tutorial illustrates the essential steps to building a physical model and makes you familiar with using the basic simscape blocks.
Spring mass problem would be the most common and most important example as the same time in differential equation. What is a transfer function and how can they be used to analyze system responses to different inputs. Pdf an interactive educational tool for double spring. Me451 s07 me451 s07 39 transfer function differential equation replaced by algebraic relation yshsus if us1 then yshs is the impulse response of the system. Mass, spring and dampers are basic components of almost every mechanical systems.
Lab information a date, time, location, and report due. A simple plane pendulum left and a double pendulum right. Mathematical models of dynamic processes are often derived using physical laws such as newtons and kirchhoffs. Using the differential equation of motion from 1, what is the systems transfer function. The mass is driven by an ideal velocity source through a friction element. Write all the modeling equations for translational and rotational motion, and derive the translational motion of x as a function of input motion u find expression for natural frequency and damping ratio. Springmass system with damping solution taking the laplace transform of both sides of the equation of motion gives. Define a new function called hyperbola in a new mfile.
This section will describe how to simulate a transfer function in labview. Springmassdamper freebody diagram 2 2 ky t r t dt dy t b dt d y t m. The tmd is tuned relative to the natural frequency of the main structure. The following example explains the use of functions in more detail. The simulink model uses signal connections, which define how data flows from one block to another. Find the transfer function for a single translational mass system with spring and damper. Two degree of freedom systems equations of motion for forced vibration free vibration analysis of an undamped system. Write this expression in terms of the mass m, damping c, and stiffness k of the system. Secondorder system an overview sciencedirect topics. Associated with the example is an animation function that will automatically open a figure window and display to it.
The stretch of the spring is calculated based on the position of the blocks. We will again use a springmass system as a model of a real engineering system. Modeling a one and twodegree of freedom springcart system. Although the equation describing the springmassdamper system of the previous section was solved in its original form, as a single secondorder ordinary di. However, simulink is commonly used for simulating systems in the frequency domain by creating transfer functions from laplace transforms. Me451 s07 38 massspringdamper system ode assume all initial conditions are zero. As and that the backward path has the transfer function.
The impulse function computes the impulse response in the time domain of the given transfer function. Double click the subsystem and click add or change parameters in the inspector tab. The mass could represent a car, with the spring and dashpot representing the cars bumper. This particular video is about how to find the transfer function of a mass spring damper system. Position control of chained multiple massspringdamper. Furthermore, the mass is allowed to move in only one direction. Position control of chained multiple massspringdamper systems. This research work applied newton law of motion, differential equations, matlab simulation, and transfer function to model massspringdamper model in phase variable form. A system of masses connected by springs is a classical system with several degrees of freedom. Tuned mass damper tmd is an effective passive device in reducing harmful vibrations as long as they are designed correctly.
Creating and simulating a simple model building a simscape diagram. Pdf an interactive educational tool for double spring mass. This paper addresses the issue of position control of a chain of multiple mass. This example shows how to model a double spring mass damper system with a periodically varying forcing function. The transfer function of a linear, timeinvariant system is the ratio of the.
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