Modelinq and Analisys of Dynamic Systems (original) (raw)
Related papers
System Modeling And Control For Mechanical Engineers
2020
Traditional courses in systems modeling focus on linear analysis techniques for systems using Laplace transforms. This method is highly effective for electrical engineering students who will make use of these techniques throughout their studies. For various reasons, such as non-linearity, Laplace transforms are used less frequently in mechanical engineering. In recognition of this difference, the Dynamic Systems Modeling and Control course (EGR 345) at Grand Valley State University was redesigned. EGR 345 examines systems that contain translational, rotational and electrical components, as well as permanent magnet DC motors. These systems are modeled with differential equations. The students are shown how to solve these systems of equations using explicit integration, numerical integration, and recognition of the canonical forms. Students are then shown how to manipulate equations containing the differential operator, and how to put these into transfer function form. Once in this form it is possible to utilize most of the techniques of classical linear control, such as block diagrams, Bode plots and root-locus diagrams. The course includes a major laboratory component. In the first half of the semester the laboratories focus on modeling physical components. The models can then be used to predict the responses of systems to given inputs. As the semester progresses the labs transition to using industrial motor controllers to reinforce the value of the course material. The paper describes the course in detail, including a custom written text book available on the course web page (http://claymore.engineer.gvsu.edu/courses.html).
Mathematical models of control systems are mathematical expressions which describe the relationships among system inputs, outputs and other inner variables. Establishing the mathematical model describing the control system is the foundation for analysis and design of control systems. Systems can be described by differential equations including mechanical systems, electrical systems, thermodynamic systems, hydraulic systems or chemical systems etc. The response to the input (the output of the system) can be obtained by solving the differential equations, and then the characteristic of the system can be analyzed. The mathematical model should reflect the dynamics of a control system and be suitable for analysis of the system. Thus, when we construct the model, we should simplify the problem to obtain the approximate model which satisfies the requirements of accuracy. Mathematical models of control systems can be established by theoretical analysis or practical experiments. The theoretical analysis method is to analyze the system according to physics or chemistry rules (such as Kirchhoff's voltage laws for electrical systems, Newton's laws for mechanical systems and Law of Thermodynamics). The experimental method is to approximate the system by the mathematical model according to the outputs of certain test input signals, which is also called system identification. System identification has been developed into an independent subject. In this chapter, the theoretical analysis method is mainly used to establish the mathematical models of control system. There are a number of forms for mathematical models, for example, the differential equations, difference equations and state equations in time domain, the transfer functions and block diagram models in the complex domain, and the frequency characteristics in the frequency domain. In this chapter, we shall study the differential equation, transfer function and block diagram formulations.
Dynamic Modeling and Control of Engineer Systems Bohdan T. Kulakowski
This page intentionally left blank DYNAMIC MODELING AND CONTROL OF ENGINEERING SYSTEMS THIRD EDITION This textbook is ideal for a course in Engineering System Dynamics and Controls. The work is a comprehensive treatment of the analysis of lumped-parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input-output and statespace models, computer simulation, and modeling methods and techniques in mechanical, electrical, thermal, and fluid domains. Frequency-domain methods, transfer functions, and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lag-lead, root locus), and an introduction to discrete-time systems. This new edition features many new and expanded sections on such topics as Solving Stiff Systems, Operational Amplifiers, Electrohydraulic Servovalves, Using MATLAB ® with Transfer Functions, Using MATLAB with Frequency Response, MATLAB Tutorial, and an expanded Simulink ® Tutorial. The work has 40 percent more end-ofchapter exercises and 30 percent more examples.
AC 2007-2577: TEACHING OF DYNAMIC SYSTEMS WITH INTEGRATED ANALYTICAL AND NUMERICAL TECHNIQUES
Mastering ordinary differential equations is very important and essential to being successful in this course of Dynamics Systems. In order to help the students further explore these new concepts and overcome some of the issues related to these deficiencies in material recall, integrated analytical and numerical techniques are adopted in teaching. One problem can be solved by various different approaches. Analytically, the method of undetermined coefficients and the Laplace transform method are used. Numerically, the transfer function method and the block diagram method in Simulink; LTI models, and symbolic toolbox in Matlab, etc, are used. Numerical approaches, especially with the transfer function method in Simulink, visualize the physics and results behind the seemingly daunting equations. By showing the application of different techniques to the same problem, students are inspired to learn the resulting similarities and differences. The MATLAB graphical user interfaces were developed for second order dynamic systems for both free vibration and forced vibration. The visual interface presents results in a way that students can immediately identify the effects of changing system parameters. Both time response and frequency response are clearly shown in the interface. In the course, a research related project is assigned to identify the dynamic response of a portable telecommunication device. In this project, students are required to use both analytical and numerical approaches to show the insight of the material selection affects the reliability of the portable telecommunication devices.