Bichop R.H. (Ed.) Mechatronic Systems, Sensors, and Actuators: Fundamentals and Modeling

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12-30 Mechatronic Systems, Sensors, and Actuators

TABLE 12.7

Otto, Diesel, and Dual Cycles

(a) Otto Cycle

(b) Diesel Cycle

s = c

v = c

p = c

s = c

--------

–()

--------

---- ---

–=

---- ----

–=

--------

–=

---------

–()

--------

–=

–

----------------–

–

----------------–

–

–()

–()+

-----------------------------------------------

–

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Engineering Thermodynamics 12-31

As all processes are internally reversible, areas on the p–v and T–s diagrams of Table 12.7 can be

interpreted, respectively, as work and heat transfer. Invoking Equation 12.23 and referring to the p–v

diagrams, the areas under process 3-4 of the Otto cycle, process 2-3-4 of the Diesel cycle, and process x-

3-4 of the Dual cycle represent the work done by the gas during the power stroke, per unit of mass. For

each cycle, the area under the isentropic process 1-2 represents the work done on the gas during the

compression stroke, per unit of mass. The enclosed area of each cycle represents the net work done per

unit mass. With Equation 12.25 and referring to the T–s diagrams, the areas under process 2-3 of the

Otto and Diesel cycles and under process 2-x-3 of the Dual cycle represent the heat added per unit of

mass. For each cycle, the area under the process 4-1 represents the heat rejected per unit of mass. The

enclosed area of each cycle represents the net heat added, which equals the net work done, each per unit

of mass.

References

ASHRAE Handbook 1993 Fundamentals. 1993. American Society of Heating, Refrigerating, and Air

Conditioning Engineers, Atlanta.

ASME Steam Tables, 6th ed., 1993. ASME Press, Fairfield, NJ.

Bejan, A., Tsatsaronis, G., and Moran, M. 1996. Thermal Design and Optimization, John Wiley & Sons,

New York.

Bird, R.B., Stewart, W.E., and Lightfoot, E.N. 1960. Transport Phenomena, John Wiley & Sons, New York.

Bolz, R.E. and Tuve, G.L. (Eds.). 1973. Handbook of Tables for Applied Engineering Science, 2nd ed., CRC

Press, Boca Raton, FL.

Bornakke, C. and Sonntag, R.E. 1996. Tables of Thermodynamic and Transport Properties, John Wiley &

Sons, New York.

Gray, D.E. (Ed.). 1972. American Institute of Physics Handbook, McGraw-Hill, New York.

Haar, L., Gallagher, J.S., and Kell, G.S. 1984. NBS/NRC Steam Tables, Hemisphere, New York.

Handbook of Chemistry and Physics, annual editions, CRC Press, Boca Raton, FL.

JANAF Thermochemical Tables, 3rd ed., 1986. American Chemical Society and the American Institute of

Physics for the National Bureau of Standards.

Jones, J.B. and Dugan, R.E. 1996. Engineering Thermodynamics, Prentice-Hall, Englewood Cliffs, NJ.

Keenan, J.H., Keyes, F.G., Hill, P.G., and Moore, J.G. 1969 and 1978. Steam Tables, John Wiley & Sons,

New York (1969, English Units; 1978, SI Units).

FIGURE 12.8 Thermal efficiency of the cold air-standard Otto and Diesel cycles, k = 1.4.

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12-32 Mechatronic Systems, Sensors, and Actuators

Keenan, J.H., Chao, J., and Kaye, J. 1980 and 1983. Gas Tables—International Version, 2nd ed., John Wiley

& Sons, New York (1980, English Units; 1983, SI Units).

Knacke, O., Kubaschewski, O., and Hesselmann, K. 1991. Thermochemical Properties of Inorganic Sub-

stances, 2nd ed., Springer-Verlag, Berlin.

Kotas, T.J. 1995. The Exergy Method of Thermal Plant Analysis, Krieger, Melbourne, FL.

Liley, P.E. 1987. Thermodynamic Properties of Substances, In Marks’ Standard Handbook for Mechanical

Engineers, E.A. Avallone and T. Baumeister (Eds.), 9th ed., McGraw-Hill, New York, Sec. 4.2.

Liley, P.E., Reid, R.C., and Buck, E. 1984. Physical and chemical data. In Perrys’ Chemical Engineers,

Handbook, R.H. Perry and D.W. Green (Eds.), 6th ed., McGraw-Hill, New York, Sec. 3.

Moran, M.J. 1989. Availability Analysis—A Guide to Efficient Energy Use, ASME Press, New York.

Moran, M.J. 1998. Engineering Thermodynamics. In The CRC Handbook of Mechanical Engineering,

F. Kreith (Ed.), CRC Press, Boca Raton, FL, Chap. 2.

Moran, M.J. and Shapiro, H.N. 2000. Fundamentals of Engineering Thermodynamics, 4th ed., John Wiley

& Sons, New York.

Moran, M.J. and Shapiro, H.N. 2000. IT: Interactive Thermodynamics, Computer Software to Accompany

Fundamentals of Engineering Thermodynamics, 4th ed., Intellipro, John Wiley & Sons, New York.

Moran, M.J. and Tsatsaronis, G. 2000. Engineering Thermodynamics. In The CRC Handbook of Thermal

Engineering, F. Kreith (Ed.), CRC Press, Boca Raton, FL, Chap. 1.

Obert, E.F. 1960. Concepts of Thermodynamics, McGraw-Hill, New York.

Preston-Thomas, H. 1990. The International Temperature Scale of 1990 (ITS-90). Metrologia. 27: 3–10.

Reid, R.C. and Sherwood, T.K. 1966. The Properties of Gases and Liquids, 2nd ed., McGraw-Hill, New York.

Reid, R.C., Prausnitz, J.M., and Poling, B.E. 1987. The Properties of Gases and Liquids, 4th ed., McGraw-

Hill, New York.

Reynolds, W.C. 1979. Thermodynamic Properties in SI—Graphs, Tables and Computational Equations for

40 Substances. Department of Mechanical Engineering, Stanford University, Palo Alto, CA.

Stephan, K. 1994. Tables. In Dubbel Handbook of Mechanical Engineering, W. Beitz and K.-H. Kuttner

(Eds.), Springer-Verlag, London, Sec. C11.

Szargut, J., Morris, D.R., and Steward, F.R. 1988. Exergy Analysis of Thermal, Chemical and Metallurgical

Processes, Hemisphere, New York.

Van Wylen, G.J., Sonntag, R.E., and Bornakke, C. 1994. Fundamentals of Classical Thermodynamics,

4th ed., John Wiley & Sons, New York.

Zemansky, M.W. 1972. Thermodynamic Symbols, Definitions, and Equations. In American Institute of

Physics Handbook, D.E. Gray (Ed.), McGraw-Hill, New York, Sec. 4b.

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13-1

Numerical Simulation

13.1 Introduction ................................................................. 13-1

13.2 Common Simulation Blocks ....................................... 13-2

Continuous Linear System Blocks

•

Discrete Linear System

Blocks

•

Nonlinear Blocks and Table Lookup

•

Signal

Generation

13.3 Textual Equations within Simulation Block

Diagrams ..................................................................... 13-3

13.4 Solvers ........................................................................... 13-4

13.5 Simulation Timing ....................................................... 13-4

13.6 Visualization ................................................................. 13-4

13.7 Hybrid System Simulation and Control ..................... 13-5

References .............................................................................. 13-6

13.1 Introduction

Numerical simulation of dynamic systems can be used to help design and analyze mechatronics compo-

nents and systems. There are several dynamic system simulation packages available including National

Instruments LabVIEW®

SimulationModule [1,2], The Math Works Inc. Simulink® [3], and Dymola from

Dynasim [4].

Simulations can be developed to run offline on a desktop PC or they can run in real time on a desktop

or an embedded target. The simulation may involve plant dynamics only or the simulation may include

a control system as well. Figure 13.1 shows a V-diagram that is often used to describe a complete embedded

control design process in the automotive and aerospace industries. In this diagram, offline simulation

would be used in the modeling and design phase. Real-time simulation software would be used to

implement a control system in the rapid prototyping phase and to simulate the plant in the hardware-

in-the-loop testing phase. For the targeting phase, a real-time simulation could be converted into code

that would run on an embedded target.

Numerical simulations of dynamic systems are often implemented in block diagram form with the

ability to represent both feedback and feedforward paths. Figure 13.2 shows an example of a simulation

created with the LabVIEW Control Design and Simulation Module [1]. Hierarchy in the block diagram

may be used to represent dynamics of different subsystems.

Jeannie Sullivan Falcon

National Instruments, Inc.

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13-2 Mechatronic Systems, Sensors, and Actuators

13.2 Common Simulation Blocks

13.2.1 Continuous Linear System Blocks

In a simulation, continuous linear systems are typically represented in either transfer function, state

space, or zero-pole-gain form. In addition, the user may also choose to add in integrator, derivative,

and/or transport delay blocks.

13.2.2 Discrete Linear System Blocks

Discrete linear system blocks are used to represent sampled data systems. Discrete transfer function blocks

are used to represent systems in the z-domain. Discrete state space blocks are used to represent systems

as difference equations. Additional blocks in this category include discrete integrator and unit delay.

Both zero- and first-order hold blocks are used to discretize or resample an input signal. In addition,

these blocks can be used to set up nested, multirate systems within a simulation. Discrete signal processing

may be implemented via the use of a discrete filter block to represent an infinite impulse response (IIR)

or a finite impulse response (FIR) filter.

13.2.3 Nonlinear Blocks and Table Lookup

Nonlinear system blocks include backlash, dead zone, friction, quantizer, saturation, rate limiter, relay,

and switches. Custom nonlinear systems may be added through 1D, 2D, or 3D table lookup blocks or

through the addition of textual equations in the block diagram.

13.2.4 Signal Generation

An input signal must always be chosen for the simulation unless an initial condition response is chosen.

Input signal types include sine wave, chirp, pulse, ramp, or step signals. Random noise may be added to

the input signal or may be used as the primary input signal. In addition, custom inputs can be added to

FIGURE 13.1 V-diagram for embedded control system development.

FIGURE 13.2 Example of a simulation block diagram created using the LabVIEW Control Design and Simulation

Module.

Modeling &

design

Rapid

prototyping

Targeting

System test

Hardware-in-

the-loop test

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Numerical Simulation 13-3

the simulation through the use of an array for single-input/single-output (SISO) systems or a matrix for

multi-input/multi-output (MIMO) systems, which is indexed for each time step in the simulation.

13.3 Textual Equations within Simulation

Block Diagrams

Textual equations may be added to the simulation to represent linear or nonlinear equations such as

kinematics calculations or nonlinear control algorithms. Figure 13.3 shows an example of a linear second-

order system simulation for phase plane analysis created using the LabVIEW Control Design and Sim-

ulation Module. Both the block diagram (Figure 13.3a) and front panel (Figure 13.3b) are shown.

The block diagram shows the differential equation for the linear second-order system inside a textual

input node that is called the Formula Node in LabVIEW [5]. The inputs to this node are the position (x),

velocity (xdot), damping (b), and stiffness (k). The output is the acceleration (xdotdot). Integrator blocks

FIGURE 13.3 (a) Block diagram of simulation of a second-order system with textual node for differential equation,

a “for loop” for initial condition variation, and a “while loop” for system parameter variation. This simulation was

developed using the LabVIEW Control Design and Simulation Module. (b) Front panel of second-order system

simulation showing system parameter inputs, time response, and phase plane analysis.

(a)

(b)

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13-4 Mechatronic Systems, Sensors, and Actuators

are used to calculate position and velocity and these are then fed back into the node as inputs. The system

states are saved in collector blocks. The simulation is run for 10 s at each of three initial conditions. The

initial condition values are given by the For Loop in LabVIEW surrounding the simulation loop. An outer

While Loop surrounds the For Loop, and this allows the user to continuously vary the damping and

stiffness parameters while observing the effects on the phase plane on the front panel.

13.4 Solvers

Ordinary differential equation (ODE) solvers are employed when continuous time systems or subsystems

are used in a simulation. These solvers use numerical methods to approximate the solution to a differential

equation over time. Both fixed-step and variable-step solvers are available. Fixed-step solvers maintain a

constant time step over the duration of the simulation. Variable-step solvers take small time steps when

the states vary rapidly and can take larger time steps when the states vary slowly. This ability to change

step sizes can increase computational efficiency.

Variable time-step solvers are appropriate for offline simulations if computational efficiency is a

concern. For real-time applications such as control prototyping or hardware-in-the-loop simulation,

fixed time-step solvers should be used.

Fixed time-step solvers include Runge–Kutta 1 (Euler method), Runge–Kutta 2, Runge–Kutta 3, and

Runge–Kutta 4. Variable time-step solvers can include Runge–Kutta 23, Runge–Kutta 45, BDF,

Adams–Moulton, and Rosenbrock.

In order to improve computational efficiency for real-time applications, the user should consider a

lower-order fixed-step solver if it meets the desired accuracy. Also, increased efficiency can be obtained

by converting the continuous dynamics in the simulation to discrete time. This conversion avoids the

use of a solver altogether but, again, can affect the accuracy of the result.

13.5 Simulation Timing

There are typically many timing options available with simulation packages. The user can slow down

time in the simulation to study fast dynamics in detail, such as a collision between two cars. In addition,

the user can speed up time to study slow dynamics more efficiently. This would be useful in studying

the effects of temperature control for a large water tank. It is also possible to tie the simulation time to

the actual time if the simulation is running on a real-time target.

The user may also change the start time to be negative time and may change the final time to be finite

or infinite. An infinite time for final time allows the simulation to run until the user halts the simulation.

With a user interface wrapped around the simulation, the user may adjust plant parameters and control

gains as the simulation is running to fully explore variations in the design space of the systems.

Parallel, multirate simulations may be developed with varying timing, priorities, and phasing on

simulation loops in the LabVIEW Control Design and Simulation Module [2]. Parallel, multirate simu-

lations are useful for separating out subsystems with critical control tasks from those with less critical

monitoring and data storage tasks.

13.6 Visualization

The single-body or multibody dynamics in a numerical simulation may be tied to a two- or three

dimensional picture display. This is useful for both offline simulations and for providing a display for a

real-time simulation or control system. Figure 13.4 shows the front panel from a LabVIEW Control

Design and Simulation Module example for the F14 Tomcat fighter. The three-dimensional display was

created through the importation of a VRML (virtual reality markup language). Other three-dimensional

models may be created through the importation of different file formats or through the creation of

OpenGL (open graphics language) objects.

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Numerical Simulation 13-5

13.7 Hybrid System Simulation and Control

A continuous or discrete time simulation may be combined with discrete event programming to create

a hybrid system or hybrid control approach. This approach is useful in applications such as sequenced

process control problems or in the study of fault tolerant control systems.

Figure 13.5 shows a sequenced process control example developed using the LabVIEW Control Design

and Simulation Module and the LabVIEW State Diagram Toolkit [5,6].

FIGURE 13.4

F14 Tomcat longitudinal simulation example in the LabVIEW Control Design and Simulation Module.

FIGURE 13.5 Hybrid system simulation of a sequenced process control application.

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13-6 Mechatronic Systems, Sensors, and Actuators

References

1. http://www.ni.com/embeddedcontrol: “Embedded Control Engineering—Integrated Software and

Hardware for the Entire Design Process,” National Instruments LabVIEW Embedded Control

portal page, National Instruments, Austin, TX.

2. http://zone.ni.com/reference/en-XX/help/371894A-01/: LabVIEW Control Design and Simulation

Module 8.2 Help html document, National Instruments, Austin, TX.

3. http://www.mathworks.com/products/simulink/: “Simulink—Simulation and Model-Based Design,”

The MathWorks Inc. Simulink product page, The MathWorks, Inc., Natick, MA.

4. http://www.dynasim.com: “Dymola Multi-Engineering Modeling and Simulation,” Home page for

Dynasim, Lund, Sweden.

5. http://www.ni.com/toolkits/lv_state_diagram.htm: NI LabVIEW State Diagram Toolkit informa-

tion page, National Instruments, Austin, TX.

6. http://techteach.no/publications/state_diagrams/index.htm: Introduction to State Diagrams by

Finn Haugen, TechTeach, Norway.

7. http://sine.ni.com/manuals/main/p/sn/n23:4.28.9533 LabVIEW Control Design and Simulation

Module Help html document, National Instruments, Austin, TX.

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14-1

Modeling and

Simulation for MEMS

14.1 Introduction ............................................................... 14-1

14.2 The Digital Circuit Development Process:

Modeling and Simulating Systems with

Micro- (or Nano-) Scale Feature Sizes ..................... 14-2

14.3 Analog and Mixed-Signal Circuit Development:

Modeling and Simulating Systems with Micro-

(or Nano-) Scale Feature Sizes and Mixed Digital

(Discrete) and Analog (Continuous) Input,

Output, and Signals ................................................... 14-7

14.4 Basic Techniques and Available Tools for

MEMS Modeling and Simulation ............................. 14-8

Basic Modeling and Simulation Techniques

•

A Catalog

of Resources for MEMS Modeling and Simulation

14.5 Modeling and Simulating MEMS, That Is, Systems

with Micro- (or Nano-) Scale Feature Sizes,

Mixed Digital (Discrete) and Analog

(Continuous) Input, Output, and Signals,

Two- and Three-Dimensional Phenomena,

and Inclusion and Interaction of Multiple

Domains and Technologies ....................................... 14-13

14.6 A “Recipe” for Successful MEMS Simulation .......... 14-15

14.7 Conclusion: Continuing Progress in MEMS

Modeling and Simulation .......................................... 14-16

References .............................................................................. 14-16

14.1 Introduction

Accurate modeling and efficient simulation, in support of greatly reduced development cycle time and

cost, are well established techniques in the miniaturized world of integrated circuits (ICs). Simulation

accuracies of 5% or less for parameters of interest are achieved fairly regularly [1], although even much

less accurate simulations (e.g., 25–30%) can still be used to obtain valuable information [2]. In the IC

world, simulation can be used to predict the performance of a design, to analyze an already existing

component, or to support automated synthesis of a design. Eventually, MEMS simulation environments

should also be capable of these three modes of operation. The MEMS developer is, of course, most

interested in quick access to particular techniques and tools to support the system currently under

development. In the long run, however, consistently achieving acceptably accurate MEMS simulations will

depend both on the ability of the CAD (computer-aided design) community to develop robust, efficient,

user-friendly tools which will be widely available both to cutting-edge researchers and to production

engineers and on the existence of readily accessible standardized processes. In this chapter we focus on

Carla Purdy

University of Cincinnati

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