22 The Role of Modeling in Mechatronics Design 22.1 Modeling as Part of the Design Process Phase 1 • Phase 2 • Phase 3 • Phase 4 22.2 The Goals of Modeling Documentation and Communication • Hierarchical Framework • Insights • Analogies • Identification of Ignorance 22.3 Modeling of Systems and Signals Analytical vs. Numerical Models • Partial vs. Ordinary Differential Equations • Stochastic vs. Deterministic Models • Linear vs. Nonlinear If mechatronics design is more than just the combination of electronic, software, and mechanical design, the additional feature must lie in the ability of the mechatronic designer to optimize a design solution across these disparate fields. This requires a sufficient understanding of each of these fields to determine which portions of an engineering problem are best solved in each of these domains given the current state of technology. In turn, this requires the ability to model the problem and potential solutions using techniques that are domain independent or at least permit easy comparison of solutions and tools from different domains. For example, the optical inspection system shown in Fig. 22.1 depends on optical components in precise alignment, mechanical elements capable of precise motion, transducers for sensing and providing mechanical power, electrical systems to control motion and filter sensor signals, and software for image analysis and motion control. Only by dividing these tasks appropriately among electronics, mechanical components, and software can the system be optimized. This requires an understanding of all the system requirements and limitations as well as the capabilities of each component in the various domains. Modeling of requirements and systems is crucial in determining whether a proposed solution is acceptable as well as in documenting these determinations for future use. In this article we shall examine the varieties of models used at different points in the design process, the diverse roles of these models and their relative strengths and weaknesses in each of these roles, and finally the specific tradeoffs involved in choosing dynamic models for signals and systems analysis. 22.1 Modeling as Part of the Design Process Models serve different purposes at different points in the design process; so to decide which modeling tools are most effectively employed in different phases we must examine the design process itself. Many descriptions of the design process are available that have been developed by researchers around the world. 1–3 Typically these descriptions serve to systematize the process to improve the productivity of Jeffrey A. Jalkio University of St. Thomas ©2002 CRC Press LLC 22 The Role of Modeling in Mechatronics Design 22.1 Modeling as Part of the Design Process Phase 1 • Phase 2 • Phase 3 • Phase 4 22.2 The Goals of Modeling Documentation and Communication • Hierarchical Framework • Insights • Analogies • Identification of Ignorance 22.3 Modeling of Systems and Signals Analytical vs. Numerical Models • Partial vs. Ordinary Differential Equations • Stochastic vs. Deterministic Models • Linear vs. Nonlinear If mechatronics design is more than just the combination of electronic, software, and mechanical design, the additional feature must lie in the ability of the mechatronic designer to optimize a design solution across these disparate fields. This requires a sufficient understanding of each of these fields to determine which portions of an engineering problem are best solved in each of these domains given the current state of technology. In turn, this requires the ability to model the problem and potential solutions using techniques that are domain independent or at least permit easy comparison of solutions and tools from different domains. For example, the optical inspection system shown in Fig. 22.1 depends on optical components in precise alignment, mechanical elements capable of precise motion, transducers for sensing and providing mechanical power, electrical systems to control motion and filter sensor signals, and software for image analysis and motion control. Only by dividing these tasks appropriately among electronics, mechanical components, and software can the system be optimized. This requires an understanding of all the system requirements and limitations as well as the capabilities of each component in the various domains. Modeling of requirements and systems is crucial in determining whether a proposed solution is acceptable as well as in documenting these determinations for future use. In this article we shall examine the varieties of models used at different points in the design process, the diverse roles of these models and their relative strengths and weaknesses in each of these roles, and finally the specific tradeoffs involved in choosing dynamic models for signals and systems analysis. 22.1 Modeling as Part of the Design Process Models serve different purposes at different points in the design process; so to decide which modeling tools are most effectively employed in different phases we must examine the design process itself. Many descriptions of the design process are available that have been developed by researchers around the world. 1–3 Typically these descriptions serve to systematize the process to improve the productivity of Jeffrey A. Jalkio University of St. Thomas ©2002 CRC Press LLC 23 Signals and Systems 23.1 Continuous- and Discrete-Time Signals Signal Classification 1–4 • Singularity Functions • Basic Continuous-Time Signals • Basic Discrete-Time Signals • Analysis of Continuous-Time Signals • Fourier Analysis of CT Signals • Fourier Transform • Sampled Continuous-Time Signals • Frequency Analysis of Discrete- Time Signals • The Discrete Fourier Transform 6,8,13 23.2 z Transform and Digital Systems The z Transform • Digital Systems and Discretized Data • The Discrete Fourier Transform • The Transfer Function • State-Space Systems • Digital Systems Described by Difference Equations (ARMAX Models) • Prediction and Reconstruction • The Kalman Filter 23.3 Continuous- and Discrete-Time State-Space Models Introduction • States and the State-Space • Relationship Between State Equations and Transfer-Functions • Experimental Modeling Using Frequency-Response • Discrete-Time State-Space Modeling • Summary 23.4 Transfer Functions and Laplace Transforms Transfer Functions • The Laplace Transformation • Transform Properties • Transformation and Solution of a System Equation 23.1 Continuous- and Discrete-Time Signals Signals are physical variables or quantities measured at various parts of a system, which when processed yield the desired information. A wide variety of signals are often encountered in describing many practical systems. Electrical signal, in form of current and voltage, is the most easily measured quantity, hence the need to use sensors and transducers to transform other non-electrical quantity into electrical signals. These signals must be processed by appropriate techniques if desirable results are to be obtained. Several methods of signal representation, suitable for effective signal processing in both time and frequency domains, are discussed in this section. Signal Classification 1–4 Signals are broadly classified as either continuous-time (CT) or discrete-time (DT) signals, and each of these may in turn be categorized as deterministic or random signals. A deterministic signal can always be expressed mathematically, whereas the time of occurrence or value of a random signal cannot be predicted with certainty. A CT signal, x ( t ), has a specified value for every value of time, t , while a DT signal, x ( n ), has specified a value only at discrete points, that is, for integer values of n . Closely related Momoh-Jimoh Eyiomika Salami International Islamic University of Malaysia Rolf Johansson Lund Institute of Technology Kam Leang University of Washington Qingze Zou University of Washington Santosh Devasia University of Washington C. Nelson Dorny University of Pennsylvania ©2002 CRC Press LLC . developed by researchers around the world. 1 3 Typically these descriptions serve to systematize the process to improve the productivity of Jeffrey A. Jalkio University of St. Thomas 2002 CRC. University of St. Thomas 2002 CRC Press LLC 22 The Role of Modeling in Mechatronics Design 22.1 Modeling as Part of the Design Process Phase 1 • Phase 2 • Phase 3 • Phase 4 22.2 The Goals. developed by researchers around the world. 1 3 Typically these descriptions serve to systematize the process to improve the productivity of Jeffrey A. Jalkio University of St. Thomas 2002 CRC