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## Monday, March 19, 2012

### Types of processes

All physical systems can be categorized in terms of types of energy used in it. Let’s consider the most common of them: electrical, hydraulic, pneumatic and thermal (see Figure 1.3). Generally speaking, a system can be of any physical type. Common among all these types of physical systems is that each has a single capacity and a single resistance. How these systems behave in respect to time?

Let’s examine behaviour of an electrical system shown in Fig.1.3a. Suppose that the circuit is closed and the capacitor starts to charge to the voltage of the battery. Thus we imposed a step upset or step change (a change from one level to another in supposedly zero time) in the input of the system. Now we start examine how the output of the system (voltage of the capacitor) changes with respect to time. Then, if we measure values of a voltage of the capacitor Uc  at various times and plot them vs time, we’ll get the curve shown in Fig.1.3a. To get more accurate picture we present this curve in the scale (see Fig. 1.4).
Figure 1.3. Types of physical systems and their reaction (response) curves.

As the voltage of the capacitor approaches to the voltage of the battery (corresponds to 100%) the charging rate gradually decreases. It was noted that a time interval necessary for the capacitor to charge to the 63.2% of the battery voltage (no matter what is the battery voltage) is constant for any one value of the resistance (R) and the capacitance (C). This time is called the time constant. To get the value of the time constant we must multiply the values of resistance and capacitance.

τ = R*C,                                                                 (1.1)
where:             τ - time constant, s.

The unit for the time constant is second. In the case presented in Fig.1.4 the time constant is equal 20 sec. It means - the voltage of the capacitor will be equal to 63.2% of the battery voltage after 20 sec will have passed from the beginning of a charging process. For example, if the battery voltage is equal to UB = 50V then after 20 sec the voltage of the capacitor will be equal to Uc = 31.6V.
Figure 1.4. Response curve.

The process examined in this case is called transient process. The curve in Fig. 1.4 is called a reaction curve. The form of this curve is exponential, and sometimes the curve is called exponential-transient curve. The capacitor never will charge to the same voltage as the battery, but after t ≈ 4.6 seconds the former will charge to 99% of the battery voltage. This time we can accept as the end of the transient process.

What is common regarding to response curves of all types of physical processes presented in Fig. 1.4 is that they all have exponential character.

Dynamic characteristic of a system defines behaviour of a process in respect to time (see Fig. 1.3 and Fig. 1.4).

Static characteristic of a system defines behaviour of a process which does not involve time or which takes place over a sufficient length of time that dynamic changes become of minor importance. Static characteristics can be of linear and non-linear character.
Figure 1.5. Static characteristic of a thermocouple of Type K.

At temperatures from -300 to 0 °C a static characteristic of a thermocouple (see Fig. 1.5) has non-linear character, whereas at temperatures above 0 °C it is close to linear one.

Article Source: Dr. Alexander Badalyan, University of South Australia

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