Mechanical systems for mechatronics applications 9. These systems mainly consist of three basic elements. This page discusses how the system elements can be included in larger systems, and how a. Lecture notes systems, modeling, and control ii mechanical. Beside block diagram, signal flow graph is another way of illustrating a control system. An ideal mass, depicted schematically in freebody diagram form in fig. Mathematical modeling of dynamic systems mechanical. Improves and lowers the cost of building services by fostering the development and use of more intelligent, integrated, and optimized building mechanical systems and controls.
The basis for all translational motion analysis is newtons second law of motion which states that the net force f acting on a body is related to its mass m and acceleration. State space representation to transfer function find the transfer function and poles of the system represented in state space below. Mechanical system by differential equation model, electrical system by statespace model and hydraulic system by transfer function model. An atlas of engineering dynamic systems, models, and transfer. Mechanical systems 631 a damper is an element that provides resistance in mechanical motion, and, as such, its effect on the dynamic behavior of a mechanical system is similar to that of an electrical resistor on the dynamic behavior of. Translational damper when the viscosity or drag is not negligible in a system. 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. Draw free body diagrams of each mass and junction point. Write all the modeling equations for translational and rotational motion, and derive the translational motion of x as a.
All the materials exhibit the property of damping to some extent. School of mechanical engineering purdue university me375 translation 10 eom of a simple massspringdamper system we want to look at the energy distribution of the system. Determine a set of first order differential equations i. Each part of each problem is worth 3 points and the homework is worth a total of 42 points.
Write all the modeling equations for translational and rotational motion, and. Ec2255 solved problems in control system iv semester ece control systems. 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. The ideal translational motion sensor block represents a device that converts an across variable measured between two mechanical translational nodes into. If a force is applied to a translational mechanical system, then it is opposed by opposing forces due to mass, elasticity and friction of. Modeling translational mechanical systems engineering 5821. This page discusses how the system elements can be included in larger systems, and how a system model can be developed. Rotational mechanical systems gears a rotating body can be considered a system of particles with masses m1,2 3. Pdf ec2255 control system notes solved problems devasena. This section provides an introduction to control system design methods. The roots of the denominator are the system poles and the roots of the numerator are system zeros. Control systems electrical analogies of mechanical systems 16. However, block diagram is more popular for uncomplicated system as it has close.
Mechanical systems 631 a damper is an element that provides resistance in mechanical motion, and, as such, its effect on the dynamic behavior of a mechanical system is similar to that of an electrical resistor on the dynamic behavior of an electrical system. In this course it is aimed to introduce to the students the principles and applications of control systems in every day life. Translational system inertia force damping force spring force rotational system inertia torque damping torque spring torque. Write the differential equations governing the mechanical translational system as. Electrical analogies of mechanical systems tutorialspoint. Well focus on mechanical and electrical systems, but will m ention some others too.
Control systems pdf notes cs notes pdf the control systems pdf notes cs notes pdf cs notes control systems notes. Translational mechanical systems move along a straight line. The system involves one integrator and two delayed integrators. Mechanical, electrical and hydraulic system are represented by mathematical model. Mathematical models of translating mechanical systems.
Mathematical models of above systems are simulated. There are two types of electrical analogies of translational mechanical systems. If damping in the system is not enough then extra elements e. Mechanical translational systems 3 question 4 for the system in figure 4. Those are force voltage analogy and force current analogy. The basic concepts of block diagram reduction, time domain analysis solutions to time. Weight the mechanical system is represented by mass and is assumed to be concentrated at the center of body the elastic deformation of the body can be represented by the spring. Motion sensor in mechanical translational systems matlab. Mathematical modeling of control systems 21 introduction in studying control systems the reader must be able to model dynamic systems in mathematical terms and analyze their dynamic characteristics. Translational mechanical systems purdue university. The mechanical system may be a linear mechanical system or it may be a rotational mechanical type of system. We will derive analogies between mechanical and electrical system only which are most important in understanding the theory of control system.
If a force f is applied to a mass and it is displaced to x meters then the relation bw force and displacements is given by newtons law. Jan 30, 2019 we will derive analogies between mechanical and electrical system only which are most important in understanding the theory of control system. Jan 23, 2018 problem on mechanical translational system including friction watch more videos at lecture by. Find materials for this course in the pages linked along the left. Masspulley system a mechanical system with a rotating wheel of mass m w uniform mass distribution. Module 4b modeling mechanical systems examples duration. A mathematical model of a dynamic system is defined as a set of equations that represents the dynamics of the system. 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. A mass will be drawn with a coordinate system as in the drawing below. While it is convenient to use power and energy in formulating system models for mechanical systems, a motional basis is critical for identifying interconnections and when formulating quanti.
Examples of control systems used in industry control theory is a relatively new field in engineering when compared with core topics, such as statics, dynamics, thermodynamics, etc. You can specify the initial position offset as a block parameter. Mechanical translational systems missouri university of. For many mechanical, translational, and rotational systems, it is suf. Mathematical modelling of control system mechanical. Problem on mechanical translational system youtube. Control system engineeringii 3 10 modulei 10 hours state variable analysis and design. The output of each integrator or delayed integrator can be a state variable. An atlas of engineering dynamic systems, models, and. In translating mechanical systems, the inertia elements are masses. When a force is applied to a translational mechanical system, it is opposed by opposing forces due to mass, friction and elasticity of the system. Analysis of mechanical systems is based on the principles embodied in newton s laws of motion and the principle of compatibility no gaps between connected elements. Problem on mechanical translational system including friction.
Control system and engineering dhanalakshmi srinivasan. School of mechanical engineering purdue university me375 translation 9 in class exercise blood sampler schematic. Early examples of control systems were developed actually before the science was fully understood. The basic elements used for modeling mechanical translational system. Modeling mechanical systems california state university. If a force f is applied to a x t mass and it is displaced to x meters then the relation f t m bw force and displacements is given by newtons law. Springs and dampers are connected to wheel using a flexible cable without skip on wheel. The basic concepts of block diagram reduction, time domain analysis solutions to time invariant systems and also deals with the. Control systems pdf notes cs notes pdf eduhub smartzworld. The basis for all translational motion analysis is newtons second law of motion which states that the net force f acting on a body is related to its mass m. Lecture 2 introduction mathematical modeling mathematical. Electrical systems and mechanical systems are two physically different systems.
Dec 06, 2016 translational and rotational system 1. The term mechanical translation is used to describe motion with a single degree of freedom or motion in a straight line. Translational damper translational damper iii damper opposes the rate of change of motion. The model of mechanical translational systems can obtain by using three basic elements mass, spring and dashpot. 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. Introduction, concepts of state, sate variables and state model, state models for linear continuoustime systems, state variables and linear discretetime. Jan 23, 2018 160 videos play all control system tutorials point india ltd. In force voltage analogy, the mathematical equations of translational mechanical. Rotational mechanical systems are handled the same way as translational mechanical systems, except that torque. Dms6021 dynamics and control of mechanical systems symbol of a damper c power dissipated. Problem on mechanical translational system including friction watch more videos at lecture by. Control is used whenever quantities such as speed, altitude, temperature, or voltage must be made to behave in some desirable way over time.
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