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Temperature control is required in a wide range of industrial, commercial and domestic applications. This paper presents details of the development of a prototype temperature control experimental module suitable for use in conjunction with automatic control lecture courses in higher institutions of learning. The process consists of a small and fast responding plant which can be controlled in the temperature range from ambient (25oC) to about 60oC. The fast heating and cooling features of the plant permit experimentation within the usual limits of laboratory hours. The plant was modelled as a first order plus dead time process. Its parameters obtained from its open loop step test data with the aid of a Matlab programme developed for the purpose. Simulation of the closed-loop ON-OFF control scheme reveals that it exhibits a limit cycle with frequency of 2 MHz and amplitude of approximately 3oC. A solid state ON-OFF controller was implemented along with a digital display of the process temperature. Obtained experimental results reasonably agree with simulation results. The proposed set up was constructed locally using affordable materials, which serve the same purpose as the modules available at much higher costs.
Keywords: Temperature, heating system, plant and prototype, low-cost devices, laboratory equipment
Temperature measurement and control is a major requirement in most process industries that handle and convert gases, liquids, and bulk solids into products [1, 2]. Chemical, petroleum, petrochemical, polymer, plastic and large segments of metallurgical and food processing industries, are examples. Chemical reactions, material separation, distillation, drying, evaporation, absorption, crystallization, baking, extrusion, and thermal therapies are processes that normally operate at controlled temperatures .
Temperature control is also required in many domestic and commercial applications . These include applications such as, air-conditioning, space heating, grilling, roasting, ironing, baking and water heating. Some applications require temperature to be regulated at a constant value or to follow a prescribed temperature profile.
Typical temperature control loops employ the popular proportional plus integral plus derivative (PID) control algorithm [3, 4] . However, there are many control loops that use the ON-OFF control algorithm. It is well known that ON-OFF control is a simple, time-optimal control strategy whose application is made easier by microcontrollers combined with modern solid-state switching devices such as thyristors, diacs, and triacs . In feedback control, the variable being controlled is measured by a sensor; this measurement is compared to a desired value, and the difference is used as a basis to change the parameter being controlled. A common example of closed-loop control is a thermostat-controlled home heating system. The house temperature is measured by a sensor; this temperature is compared to the desired temperature as set by the thermostat. The furnace is turned on if the measured temperature is below the desired temperature and turned off if the measured temperature is above the desired temperature.Whatever the process or the parameter (temperature, flow, speed for example), the principles of control are similar. Input and output signals are specified as appropriate to the application, usually analog (e.g. thermocouple signal input, solid state output power control) but they may be digital .
The paper describes the development of an ON-OFF temperature control system meant for automatic control laboratories.
Temperature is fundamentally a measure of the kinetic energy of the molecules of a substance and may be defined as the condition of a body which determines the transfer of heat from the body to its environment or even more practically as the degree of hotness (or coldness) of the body . Measurement and control of temperature are fundamental operations in most industrial and domestic processes. While some thermal systems use open-loop control principles (e.g., washing machines and bread toasters), majority of others employ closed-loop control whereby the loop comprises four major subsystems as shown in Fig. 1. This section describes selected temperature control loops, elaborates on some features of the temperature control loop and end with an outline of the theoretical background to the simple but widely used ON-OFF control algorithm.
Fig. 1 Generic temperature control loop
Fig 2 Home heating control loop block diagram
An interesting design from Aristotle university of Thessaloniki where there is work on they the development and effectiveness of testing of a module on the conduction of heat transfer and the thermal properties of materials, the work was carried out within the European project on material science .
A low cost flow trainer has been developed with the support of national science foundation (NSF) instructional laboratory instrumentation (ILI) grant to permit training in basic control concept to multiple student teams.
2.2 Temperature Sensors
All materials are affected by temperature, and thus, it is not surprising that there are many means available of inferring temperature from some physical effect . Early thermometers depended on volumetric changes of gases and liquids with temperature change, and of course, the principle is still exploited, as encountered in industrial gas and liquid filled thermal systems and in the familiar liquid column clinical thermometer. Although these instruments were accepted widely for many years, the liquid filled thermometer has been mostly replaced by other simpler and more convenient approaches, including thermocouples, thermistors, and resistance temperature detectors (RTDs).
A thermistor is an electronic device that exhibits a large change in resistance with change in its body temperature . The word "thermistor" is actually a contraction of the words "thermal resistor". A thermistor may have either a positive temperature coefficient of resistance (PTC devices) or a negative temperature coefficient of resistance (NTC devices). Both types of thermistor (PTC and NTC) have definite features and advantages which make them ideal for certain sensor applications .
This work employs an NTC thermistor.
where RT is the resistance at temperature T, RTo is the resistance at reference temperature To, and Î² is a constant for a specific thermistor and is provided by the manufacturer..
2.3 The ON-OFF Temperature Control Algorithm
In the temperature control loop of Fig 1, the controller compares the set point value with the actual process temperature so that based on the result it generates a control signal in accordance with an algorithm with the overall objective of quickly eliminating the control error [24-31]. As mentioned previously, there are numerous control algorithms being used for temperature control. This work is concerned with the ON-OFF control algorithm. This section outlines theoretical aspects of ON-OFF control. ON-OFF control is also known as two-level control in the sense that the controller output, u, can take on one of two values based on the value of the control error, e:
The ON-OFF control algorithm results in a nonlinear control loop described by nonlinear differential equations. Analysis of nonlinear control systems is fairly difficult, however, many methods have been proposed. An outline of three of them is presented in the following paragraphs.
Phase plane analysis  is a graphical method of studying second-order nonlinear systems. The basic idea is to solve a second-order differential equation graphically, instead of seeking an analytical solution. The result is a family of system motion trajectories on a two-dimensional plane, called the 'phase plane', which allows visualization of the motion patterns of the system. While phase plane analysis has a number of important advantages, it has the fundamental disadvantage of being applicable only to systems which can be well approximated by a second-order dynamics. Because of its graphical nature, it is often used to provide intuitive insights about nonlinear effects.
Basic Lyapunov theory  comprises two methods proposed by Lyapunov - the indirect method and the direct method. The indirect method, or linearization method, states that the stability properties of a nonlinear system in the neighbourhood of an equilibrium point are essentially the same as those of its linearized approximation. The method serves as the theoretical justification for using linear control for physical systems, which are always inherently nonlinear. The direct method is a generalization of the energy concepts associated with a mechanical system - the motion of a mechanical system is stable if its total mechanical energy decreases all the time. In using the direct method to analyze the stability of a nonlinear system, the idea is to construct a scalar energy-like function ( a Lyapunov function) for the system, and to see whether it decreases. The power of the method stems from its generality - it is applicable to all kinds of control systems, be the time-varying or time-invariant, finite-dimensional or infinite-dimensional. On the converse, its limitation lies in the fact that it is often difficult to find a Lyapunov function for a given system.
Although the Lyapunov direct method is originally meant for stability analysis, it can be used for other problems in nonlinear control. One important application is the design of nonlinear controllers. The idea is to formulate a scalar positive function of the system states, and then choose a control law to make this function decrease. A nonlinear control system thus designed will be guaranteed to be stable. Such a design approach has been used to solve many complex design problems such as adaptive control  and sliding mode control [35, 36]. The direct method can also be used to estimate control system performance and robustness.
The describing function method is an approximate technique for frequency domain analysis of nonlinear systems . The basic idea of the method is to approximate the nonlinear subsystems in a nonlinear control system by linear "equivalents", and then use frequency domain techniques to analyze the resulting system. The method is mainly used to predict limit cycles in nonlinear systems. Other applications include the prediction of sub harmonic generation and the determination of system response to sinusoidal excitation. The method has several advantages. First, it can deal with low order and high order systems with the same straightforward procedure. Second, because of its similarity to frequency-domain analysis of linear systems, it is conceptually simple and physically appealing, allowing users to exercise their physical and engineering insights about the control system. Third, it can deal with the 'hard nonlinearities' frequently found in control systems without any difficulty. Consequently it is an important tool for practical problems of nonlinear control systems analysis and design. The disadvantages of the method are linked to its approximate nature, and include the possibility of inaccurate predictions and restrictions on the systems to which it applies (e.g. systems with multiple nonlinearities).
The describing function of the relay-type (ON-OFF) nonlinearity is given in fig 3 as 
where A is the amplitude of the sinusoidal signal input to the nonlinearity. The normalized describing function (N/M) is plotted in Fig 10 (b) a function of input amplitude.
Fig. 3 ON-OFF nonlinearity and its describing function
The following two features of the ON-OFF describing function can be observed:
N(A) decreases as the input amplitude decreases - saturation amounts to reduction of the output to the input.
There is no phase shift - the nonlinearity does not cause signal delay.
3.1 Proposed Laboratory Thermal Process
The thermal process components were selected taking into consideration the fact that in higher institutions of learning most laboratory experiments are conducted in three-hour sessions. Consequently the process should be capable of heating up and cooling down quickly. A photograph of the proposed process is shown in Fig. 6. It consists of an un-lagged glass jar containing 500 ml of transformer oil. The heating element for the oil may be a 21W or 40W, 12V dc electric bulb. A bulb holder of the type used in car headlamps was provided. The process' glass jar with a 4mm thick wall weighs 190g when empty. Transformer oil is employed due to its electrical insulating properties since the heater bulb is immersed into it. For the thermal process, the input variable, u, is the voltage (12V dc) applied to the heater while the output variable is the transformer oil temperature. A suitable temperature sensor for the process was designed. For purposes of modelling the process a mercury-in-glass thermometer is used in this work, although a digital thermometer was constructed. A thermistor (the round object beside the bulb and close to the 200ml mark in Fig 6) is provided to monitor the process temperature via the red terminals for display and feedback control purposes. The yellow terminals in Fig 6 are used to apply 12V dc to the heater.
Fig 6 Picture of the proposed thermal plant (glass jar and heating bulb).
Figure 7 Pictorial view of the complete module
OSHA Safety act was observed because of the variety of uses for the construction described in this publication ; those responsible for the application and the use of this control equipment must satisfy themselves that all necessary steps taken to ensure that each application and uses met all performance and safety requirements, including any applicable laws, regulation and standard. Following sound safety procedures while working in the laboratory is mandatory. Students failing to meet the required eye wear and dress codes, or who engage in negligent behaviour, should be dismissed from the laboratory without the opportunity for a make up laboratory. Likewise, no food or drink is allowed in any laboratories.
The temperature control loops considered in this work include: the home heating process, the heat exchanger, the reactor, and hyperthermia therapy. The home heating process was used to introduce control engineering terms such as control objective, control error, manipulated process variable, measured process variable, set point, and disturbances. The work briefly explained the different electrical heaters as thermal process actuators. A discussion on common temperature sensors was presented with particular emphasis on the thermistor. An outline of methods of analysing ON-OFF control loops was presented along with their relative merits and demerits. In particular the use of the describing function method to detect limit cycles in control loops with a single ON-OFF nonlinearity was elaborated.