The purpose of a control system is to produce a desired output. This output is usually specified by a command input, and is often a function of time. For simple applications in well structured situations, to control, and the controller must have the capability of reacting to disturbance, changes in its environment, and new input commands. The keys element that allows a control system to do this is feedback, which is the process by which a system’s output is used to influence its behaviour. Feedback in the form of the room-temperature measurement is used to control the furnace in a thermostatically controlled heating system. Figure 1.1 shows the feedback loop in the system’s block diagram, which is a graphical representation of the system control system is the pressure regulator shown in fig 1.2.
Feedback has several useful properties. A system whose individual elements are nonlinear can often be modeled as a linear one over a wider range of its variable with the proper use of feedback. This is because feedback tends to keep the system near its reference operating condition. Systems that can maintain the output near it desired value despite changes in the environment are said have good disturbance rejection. Often we do not have accurate values for some system parameters, or these values might change with age. Feedback can be used to minimize the effects of parameters changes and uncertainties. A system that has both good disturbance rejection and low sensitivity of parameter variation of feedback, but we are uncertain of its exact value. We use the resistors R1 and R2 to create a feedback loop around the amplifier, and pick R1 and R2 so that AR2/R1 >>1. Then the input output relation becomes R1ei / R2, which is independent of A as long as A remains large. If R1 and R2 are known accurately, then the system gain is now reliable.
Figure 1.4 shows the block diagram of a closed-loop system which is a system with feedback. An open-loop system, such as a timer, has no feedback. Figure 1.4 serves as a focus for outlining the prerequisites for this chapter. The student should be familiar with the transfer function concept based on the Laplace transforms, the pules-transfer functions based on the z-transform, for digital control and the differential equation modeling techniques needed to obtain them. It is also necessary to understand block diagram algebra, characteristic roots, the final-value theorem, and their use in evaluating system response for common inputs like the step function. Also required are stability analysis techniques, such as the Routh criterion, and transient performance specifications such as the damping ratios, natural frequency dominant time constant T, maximum overshoot, setting time, and bandwidth.
CONTROL SYSTEM STRUCTURE
The electromechanical position control system shown in Fig 1.5 illustrates the structure of a typical control system. A load with an inertia is to be positioned at some desired angle θ. A do motor is provided for this purpose. The system contains viscous damping, and a disturbance torque Td acts on the load, in addition to the motor torque T. Because of the disturbance the angular position θ of the load will not necessarily equal the desire value θ. For this reason a potentiometer is used to measure the displacement θ. The potentiometer voltage representing the controlled position is compared to the voltage generated by the command potent meter. This device enables the operator to dial in the desired angle θ. The amplifier sees the difference between the two potentiometer voltages. The basic functions of the amplifiers is to increase the small error voltage up to the voltage level required by the motor and to supply enough current required by the motor to drive the load. In addition, the amplifier may shape the voltage signal in certain ways to improve the performance of the system.
When two wires of dissimilar metals are joined together, a voltage is generated if the junctions are at different temperatures. If the reference junction is kept at a fixed known temperature, the thermocouple can be calibrated to indicate the temperature at the other junction in terms of the voltage v. Electrical resistance change with temperature. Platinum gives a linear relation between resistance and temperature, while nickel is less expensive and gives a large resistance change for a given temperature changes. Semiconductors designed with this property are called thermistors. Different metals expand at different rates when the temperature is increased. This fact is used in the bimetallic strip transducer found in most home thermostats. Two dissimilar metals are bonded together to form the strip. As the temperature rises the strip curls, breaking contact and shutting off the furnace. The temperature gap can be adjusted by changing the distance between the contacts. The motion also moves a pointer on the temperature scale of the thermostat. Finally, the pressure of a fluid inside a bulb will change as its temperature changes. If the bulb fluid is air, the device is suitable for use in pneumatic temperature controllers. Machine tools are usually controlled for temperature readings using the application of temperature transducer.
Flow rates can be measured by introducing a flow restriction, such as an orifice plate, and measuring the pressure drop across the restriction. The flow- rate- pressure relation is ∆p = Rc2 where R can be found from calibration of the device. The pressure drop can be sensed by converting it into the motion of a diaphragm. Figure 2.1 illustrates a related technique. The venturi- type flow meter measures the static pressures in the constricted and unconstricted flow regions. Bernoulli’s principle relates the pressure difference to the flow rate. This pressure difference is converted into displacement by the diaphragm.
The error detector is simply a device for finding the difference between two signals. The Function is something an integral feature of sensors, such as the synch transmitter- transformer combination. A beam on a pivot provides a way of comparing displacement, forces, or pressures, as was done with the pneumatic level controller (Fig 1.8). A similar concept is used with the diaphragm element shown in fig 2.1 A detector for voltage difference can be obtained as with the position-control system shown in fig. 1.5 An amplifier intended for this purpose is a differential amplifier. Its output is proportional to the difference between the two inputs. In order to detect differences in other types of signals, such as temperature, they are usually converted to a displacement or pressure. One of the detectors mentioned previously can then be used. This is simply applied in the flow systems of flow coolants/ fluids used in lathe, turret lathe, drilling machines etc.
The usual transducer and detector models are static models, and as such imply that the components respond instantaneously to the variable being sensed. Of course, any real component has a dynamic response time must be considered in relation the controlled process when a sensor is selected. For example, the time constant of a thermocouple in air typically is between 10 and 100 sec. if the thermocouple is in a liquid, the thermal resistance is different, and so will be the time constant (it will be smaller). If the controlled process has a time constant at least 10 times greater, we probably would be justified in using a static sensor model.
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