Mathematical modelling of control system mechanical electrical. As an example consider first a simple mechanical system, a springmassdamper. Find the transfer function xs fs for the system given. Jan 08, 2018 translational system inertia force damping force spring force rotational system inertia torque damping torque spring torque. Control systems theory transfer function of physical systems chapter 2.
Rotational mechanical systems are handled the same way as translational mechanical systems. Explain how negative feedback affects dc motor performance. Mathematical modelling of control system mechanical. Write the transfer function for an armature controlled dc motor. 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 newtons and dalembert equations.
Ee c128 me c4 feedback control systems lecture chapter 2 modeling in the frequency domain. Problem on mechanical translational system including friction. The transfer function of a linear system is defined as the ratio of the laplace transform of the output variable to the laplace transform of the input variable, with all initial conditions assumed to be zero. We will apply dalemberts principle to extract the equations which governs the dynamics of lumped parameter mechanical systems. Lecture 5mathematical modeling of mechanical systems gear. Transfer functions of electrical networks with operational amplifiers find the transfer function, gs v osv.
The transfer function method for gear system dynamics applied. Modeling mechanical systems california state university. The transfer function of a system represents the relationship describing the dynamics of the system under consideration. View notes chapter 2d from economic econ2210 at ibs college. Find the transfer function xsfs for the following system, with the understanding that each components transfer function is its impedance z ms, the force from each component is, fs z msxs we can draw the freebody diagram with forces in the freq.
Using the graph, we can estimate the time constant as t 0. Transfer functions represent the system dynamics, as described by the simplified model. There are two types of electrical analogies of translational mechanical systems. Chapter 2 mathematical modeling in transfer function form file. After completing this video tutorial, you will be able to learn various methods and techniques in order to improve the performance of the control systems based on the requirements. Find the transfer function, gs for the translational mechanical network shown in figure p2. A block diagram is a visualization of the control system which uses blocks to represent the transfer function, and arrows which represent the various input and output signals. A mass will be drawn with a coordinate system as in the drawing below. Translational mechanical system transfer function simple system assumption movement to the left is assumed to be positive. Equation of motion in sdomain for mass m 1 is given by.
Write all the modeling equations for translational and rotational motion, and derive the translational motion of x as a function of input motion u. The system has two degrees of freedom, since each mass can be moved in the horizontal direction while the other is held still. Translational mechanical systems purdue university. Block diagrams and computer simulation with matlabsimulink chapter 4 5. Methods for computing bearingsupport force spectra and temporal histories of the total force transmitted. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Models are the mathematical descriptions of realworld systems, simplified by various. Analysis and solution techniques for linear systems chapters 7 and 8 8. Jan 30, 2019 we will derive analogies between mechanical and electrical system only which are most important in understanding the theory of control system. The problem given the mechanical system f t 1 1 2 dashpot mechanical resistance mass output 2 2 m k 3 k 2 b 2 m k 2 2 3 1 b x x 2 0 input force 2 b 1 0 k b 2 spring find the transfer function gs for the system f s g s x 2 s list. The transfer function is a property of a system itself,independent of the magnitude. Translational mechanical system transfer function draw a free body diagram, placing on the body all forces that act on the body either in the direction of motion or opposite to it. Write a transfer function for a dc motor that relates input voltage to shaft position.
Jan 23, 2018 problem on mechanical translational system including friction watch more videos at lecture by. Electrical and electro mechanical system transfer functions. Problem on mechanical translational system including friction watch more videos at lecture by. Mathematically the transfer function is a function of complex variables. Find the transfer function, x 2 s f s, for the system of figure 2. Translational system inertia force damping force spring force rotational system inertia torque damping torque spring torque. Find the transfer function for a single translational mass system with spring and damper. Referring to equation 329, the transfer function gs is given by in this problem, matrices a, b, c, and d are chapter 3 mathematical modeling of dynamic systems.
Transfer functions of translational mechanical systems for the system shown below, nd the transfer function, gs x. Find the transfer function of the mechanical translational system given in the figure. Electrical systems and mechanical systems are two physically different systems. The transfer function of a system can be determined from experiments on a system. Translation mechanical system transfer function laplace. Represent a mechanical load using a mathematical model. Translation mechanical system transfer function free download as pdf file.
Those are force voltage analogy and force current analogy. The mechanical system may be a linear mechanical system or it may be a rotational mechanical type of system. Finding the transfer function of a physical system youtube. Translational mass translational mass ii translational mass is an inertia element. We will derive analogies between mechanical and electrical system only which are most important in understanding the theory of control system. The frequency response function is the system transfer function evaluated along. We also discussed how to convert from a statespace representation to a transfer function. Find the response in terms of its acceleration, velocity, and position versus time of a 3000lb automobile to a force f i of 500 ib, which is suddenly applied by three members of the football squad i. Find the transfer function, gs system shown in figure p2. In this drawing the coordinate along which the mass translates is x 1, and x 1 is defined relative to a fixed reference the vertical line with hash marks to. Translational mechanical systems move along a straight line. Mathematical models of dynamic processes are often derived using physical laws such as newtons and kirchhoffs. Electrical analogies of mechanical systems tutorialspoint.
Notes 3 translational mechanical system transfer function. The transfer function is a convenient representation of a linear time invariant dynamical system. Lecture 2 introduction mathematical modeling mathematical. Free body diagram fbd first step is to draw the freebody diagram. Transfer function of translational mechanical system 1. Rotational mechanical systems are handled the same way as translational mechanical systems, except that torque. A transfer function represents the relationship between the output signal of a control system and the input signal, for all possible input values. An atlas of engineering dynamic systems, models, and. Craig 21 sinusoidal transfer function m is the amplitude ratio of output over input. A body with mass m is connected through a spring with stiffness k and a damper with damping coefficient c to a fixed wall. Transfer function from unit step response for each of the unit step responses shown below, nd the transfer function of the system. An atlas of engineering dynamic systems, models, and transfer. Notes 3 translational mechanical system transfer function force. Lecture abstract ee c128 me c4 feedback control systems.
An atlas of engineering dynamic systems, models, and transfer functions dr. Begin the solution by drawing the freebody diagram shown in figure 2. In force voltage analogy, the mathematical equations of translational mechanical system are compared. Translation mechanical system watch more videos at comvideotutorialsindex. Chapter 2 mathematical modeling in transfer function form. These systems mainly consist of three basic elements. If a force is applied to a translational mechanical system, then it is opposed by opposing forces due to mass, elasticity and friction of the system. For linear systems the table can be characterized by one 9.
In this analogy, the mathematical equations of the rotational mechanical system are compared with the nodal mesh equations of the electrical system by comparing equation 4 and equation 6, we will get the analogous quantities of. School of mechanical engineering purdue university me375 translation 8 modeling steps understand system function, define problem, and identify inputoutput variables draw simplified schematics using basic elements develop mathematical model diff. Transfer functions of translational mechanical systems for the system shown below, nd the transfer function, gs x 1sfs. Rotational mechanical systems gears a rotating body can be considered a system of particles with masses m1,2 3. While the previous page system elements introduced the fundamental elements of translating mechanical systems, as well as their mathematical models, no actual systems were discussed. Find the transfer function of the mechanical translational system given in figure1. In translating mechanical systems, the inertia elements are masses. Dec 31, 20 translational mechanical system transfer function simple system assumption movement to the left is assumed to be positive. Mathematical models of translating mechanical systems. Forcevelocity, forcedisplacement, and impedance translational relationships for springs, viscous dampers, and mass bayen eecs, ucb feedback control systems september 10, 20 22 34 2modelinginthefrequencydomain2. In this drawing the coordinate along which the mass translates is x 1, and x 1 is defined relative to a fixed reference the vertical line with hash marks to the left. This page discusses how the system elements can be included in larger systems, and how a system model can be developed.
Under the assumption that all initial conditions are zero the transfer function tf from input, ct, to. Similarly, there is a torque current analogy for rotational mechanical systems. Electrical and electromechanical system transfer functions. Springs and dampers are connected to wheel using a flexible cable without skip on wheel. Notes 3 translational mechanical system transfer function free download as word doc. The transfer function of a system is a mathematical model in that it is an operational method of expressing the differential equation that relates the output variable to the input variable. Mechanical systems modeling using newton s and dalembert.
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