Engineering Systems

usefulness.

Discuss the concepts of energy exchange and relate it to fl ow and

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effort exchanges.

Introduce the generalized variables of power and energy.

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Discuss all the basic elements that could occur in a bond graph

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model.

Highlight many of the conventions used and their meanings.

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2.1 Engineering Systems

Real engineering systems are multidisciplinary. Consider any of the many engineering systems that we use in our daily lives. For example, the automatic car window system is a basic feature of most modern automobiles. The pur-pose of this system is to move the glass window up or down as per instruc-tions received from the user in the form of a button push. The power needed to move this reasonably heavy piece of glass is provided by an electric motor.

There is a logic circuit that has to determine the action based on the intention of the user, such as holding the window at a desired height, moving it all the way up or down, and so forth. Although it is not yet available in automatic window systems, a form of safety device using sensors is being developed as well. The safety system would stop the window if a child’s (or an adult’s) hand got caught between the moving window and the door frame. We see, therefore, the system consists of components from at least two disciplines.

The window (and its inertia) is mechanical, the motor is an electrical device, and there is a control system, some possible sensor use, and safety features. To model the behavior of this system, one needs to consider the behavior of all its components, which happen to be from different disciplines of engineering.

In the car window system, at least two domains are involved. In any mechatronic system many other domains may be involved as well.

Examples of physical phenomena (or domains) involved in real engineer-ing systems are

1. Mechanical translation 2. Mechanical rotation 3. Hydraulic

4. Electrical (static and current) and electronics 5. Magnetic

6. Thermal

In a sense all these domains are artifi cial divisions that have been used for ease of operation. In the bond graph and other energy-based approaches in system modeling, it will be apparent that many components in differ-ent domains are quite similar in behavior. In the bond graph technique we will use this similarity to our advantage.

Systems are divided into subsystems, which can be subdivided into com-ponents. For example, an automobile can be considered a system that con-sists of many subsystems such as: drive train, steering, braking, exhaust, and so on. Subsystems are in turn made of components that behave in a predictable manner. Component behavior is determined by its constitu-tive relationship, that is, every component’s behavior follows some basic law of physics. For example, the behavior of a spring (an elastic element) is governed by the simple linear spring equation where the displacement and the force are linearly related to each other through the spring constant:

Force = spring constant * displacement = kx

Or the voltage drop across an electrical resistance in a circuit is equal to the product of the resistance value and the current that is passing through it:

Voltage = Resistance * Current = RI

In these examples the spring or the electrical resistance are components.

These may be part of subsystems that make up more complex systems;

and the spring equation and the Ohm’s law are constitutive equations for these components respectively. Although the examples used here are both linear, constitutive equations can be nonlinear as well, such as the drag force exerted by the wind on a car driving down the highway is propor-tional to the square of the velocity of the car. We will discuss the constitu-tive relationships a little later.

2.2 Ports

As was mentioned earlier, different parts (or subsystems) of an engineering system exchange power. Places at which subsystems can be interconnected are places at which power can fl ow between the subsystems. Such places (or points on the subsystem) are called ports and actual subsystems with one or more ports are called multiports. Figure 2.1 shows a schematic with two ports. Power enters through one of the ports and leaves through the other.

Sometimes the power may be exchanged along one path, which will mean that the subsystem/component has only one port.

A system (or component) with a single port is called a 1-port system (or component). A system (or component) with two ports is called a 2-port system (or component).

Figure 2.2 shows a variety of multiport systems. A motor with electri-cal input at one port and rotational mechanielectri-cal output at a second port is a 2-port system. Similarly, a pump can be considered a 2-port system with mechanical torque and rotation coming in at one port and the pres-sure difference and fl uid fl ow rate exiting at the other port. A slider crank mechanism that converts rotary motion into linear motion (or vice versa) is a 2-port system with rotational power associated with one port and lin-ear power associated with the other.

A separately excited DC motor with two electrical ports and a mechanical port has three ports with power for the magnetic fi eld coming in at one port, power for the armature coming at a second port, and rotational out-put at the third.

In this context it should be understood that the examples mentioned here are relatively simple. In a real system the level of complexity may be signifi cantly higher. One of the fundamental skills necessary in analyzing/

modeling/designing systems is the ability to break down a system into subsystems and components in a way that is useful or understandable for us. This is a skill that has to be acquired through experience, careful obser-vation, and practice in attempting to breakdown real systems into simpler parts. We will offer an example here to illustrate the process.

Figure 2.3 shows a schematic of a system consisting of a motor that is receiving electrical power. The motor rotates a shaft supported on bear-ings. The shaft is connected to a drum that rotates along with the shaft and raises or lowers a mass that is attached by a cable to the drum. If we

Subsystem Power out Power in

FIGURE 2.1

Schematic showing power fl owing in and out of a subsystem.

observe closely we can see that the system can be subdivided into several subsystems. One may list them as:

1. Motor

2. Output shaft and bearings 3. Drum, cable, and mass

FIGURE 2.2

Examples of subsystems that have one or more ports (compressors, motors, dampers, speakers, etc.).

In coming up with this division we consider the system to be made of three things: the power source (motor), the power transmission (shaft), and the power user (mass hoisting device). Further examinations of these sub-systems indicate that these can be divided into individual components. For example, a DC motor can be modeled as a circuit with an electrical source, an armature resistance, and an armature inductance. The shaft may be treated as a torsional spring, the bearings treated as power dissipative

FIGURE 2.3

Schematic of a motor driven system.

Drum

Mass Motor

Bearings FIGURE 2.2

(Continued)

devices or rotational resistances, the drum is an inertia element, and the cable could be treated as rigid or elastic. If it is assumed to be elastic, then it is a linear spring. The mass that is being hoisted is an inertia element as well. The list of all the separate elements that are in the system will be 1. Armature resistance

2. Armature inductance 3. Electrical power source 4. Rotational spring (shaft)

5. Rotational damping (bearing resistance) 6. Drum inertia

7. Cable, linear spring 8. Hoisted mass

9. Gravity effects on the mass

Apart from these components we also need to recognize that there are two locations in the system where power is being transferred from one domain to another. In the motor, power goes from the electrical domain to rotational domain (via the magnetic domain) and at the drum, power is being transferred from rotational motion to linear translation. Figure 2.4 shows the same system with some more details of the system included.

FIGURE 2.4

Schematic of the motor driven system with more details of individual subsystems.

B Armature

resistance Armature

inductance

Supply voltage

−

+

This example illustrates the process of how one can go about dissecting a system to identify all the important subsystems as well as components.

While doing this, one has to also identify locations where power conver-sion from one domain to another happens. This is a critical step in system analysis and modeling and needs to be practiced by students.