Open Loop Control Method For Conveyor Belt Transmission Engineering Essay
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Before the advent of modern automation techniques, factory workers often had to travel from project to project. The cumulative effect of all this physical motion was additional stress and inefficient use of the worker's time. The development of conveyor belts allowed the project to come to the worker, instead of the worker to the project. Parts could then be transported by other conveyor belts to additional workers, and eventually to the shipping docks for delivery.
Many conveyor belts work on the principle of variable speed control. If a particular belt moves too slowly, workers may find themselves waiting for parts. If a conveyor belt moves too quickly, parts may be damaged or workers may become overwhelmed. Much of a factory supervisor's time is spent adjusting conveyor belts for maximum efficiency. This is especially important in food production factories, where conveyor belt speed and proper cooking time work hand in hand.
Modeling of a open-loop control method for conveyor belt transmission
Modeling of a close-loop speed control method for conveyor belt transmission
Research on the performance comparison for variable mass material input
1.2 Organization of thesis
Chapter 2: This chapter thoroughly introduce what conveyor transmission system is and provides a brief history about it. Six categories of typical conveyor transmission system have been introduced. It also explains the sources and types of breakdowns in conveyor belt, as well as the effect of those breakdowns cause in the transmission line. Then, this chapter also discusses about the importance to have speed control for the conveyor belt transmission system.
Chapter 3: This chapter mainly focus on different types of motors. It specifically explains about the AC asynchronous motor which is the most widely used in heavy industry. The different speed control methods of AC asynchronous motors have been compared in several aspects.
Chapter 4: In this chapter, PID controller is discussed in details for process control, including its definition, history, applications, tuning method and implementation. Unlike other kinds of papers concerning PID control approach, the weakness and bad behaviour were brought about as well so that an objective picture of PID method could be completed.
Chapter 5: At the outset, this chapter gives some key modeling process, and then provides the complete models for simulation both of open-loop control and close-loop speed control. With these models, simulation results can be get to make some comparisons. The close-loop results show the performance of different controller parameters on the transmission system with a variable mass material input on several discrete speed value, corresponding to the open-loop curves those seem not to be quite good.
Chapter 6: This chapter summarizes discussion and conclusion about the performance of speed control on the transmission system, and then gives out some recommendations and future works that can be done in speed control for conveyor belt transmission system.
2.0 CONVEYOR BELT TRANSMISSION SYSTEM
Conveyor belts are generally endless loops which move parts or materials from one location to another. Conveyor belts are often driven by variable speed electric motors or by other moving parts in a complex system. They are commonly found in factories, grocery stores, warehouses and public transportation centers.
Further refinement of conveyor belts allowed factory managers to create automated or semi-automated production lines. Individual parts could be moved through automated machinery for routine processing, leaving workers free for quality control tasks or other higher responsibilities. Conveyor belts also proved useful for transporting heavy or hazardous products, reducing worker injuries.
The use of conveyor belts is not restricted to factories. Bakeries and pizza shops often use a slow-moving wire conveyor belt to move their products through an oven. Grocery stores use conveyor belts in their check-out lines to bring items to the clerk and bagger. Airports and other public transportation systems use conveyor belts to deliver checked baggage to customers. Warehouses use long conveyor belts to offload products from incoming trucks or to load outgoing ones. Escalators found in department stores could also be considered conveyor belts, as are 'people movers' in larger airports.
Primitive conveyor belts were used since the 19th century. In 1892, Thomas Robins began a series of inventions which led to the development of a conveyor belt used for carrying coal, ores and other products. In 1901, Sandvik invented and started the production of steel conveyor belts. In 1905 Richard Sutcliffe invented the first conveyor belts for use in coal mines which revolutionized the mining industry. In 1913, Henry Ford introduced conveyor-belt assembly lines at Ford Motor Company's Highland Park, Michigan factory. In 1972, the French society REI created in New Caledonia the then longest straight-belt conveyor in the world, at a length of 13.8 km. Hyacynthe Marcel Bocchetti was the concept designer. In 1957, the B. F. Goodrich Company patented a conveyor belt that it went on to produce as the Turnover Conveyor Belt System. Incorporating a half-twist, it had the advantage over conventional belts of a longer life because it could expose all of its surface area to wear and tear.Möbius strip belts are no longer manufactured because untwisted modern belts can be made more durable by constructing them from several layers of different materials.. In 1970, Intralox, a Louisiana based company, registered the first patent for all plastic, modular belting. In 1963-64, First Indian Small Scale Industrial Unit with Japanese Plant for Rubber Belts for Conveyor / Elevator / Transmission was installed near National Capital Territory of Delhi and its MrBelts Conveyor Belting has been widely used in Steel, Cement, Fertilizer, Thermal Power, Sponge Iron Plants and Coal/Mineral establishments, Port Trusts and similar material handling applications of Industry for the last over 4 decades
2.2 Types of Conveyor System
2.2.1 Wheel Conveyor System
A wheel conveyor system's setup consists of skate wheels that are mounted on an axle placed in a row. Depending on the weight of the material being transported, adjustment of both the wheel spacing and the slope for load movement is provided. Being simpler in construction, the system is flexible, scalable and more economical with light-duty applications as compared to a roller conveyor system.
2.2.2 Roller Conveyor System
A roller conveyor system has two variants, but both utilize a minimum of three rollers that provide support to the smallest load all the time. Then there are tapered rollers that orient the load around a curved path. The gravity-type system is alternative to the wheel conveyor system that is used for heavy-duty applications. It utilizes a slope for load movement to facilitate the accumulation process. The powered variant utilizes a belt or chain drive for force-sensitive power transmission useful in merging and/or sorting applications.
2.2.3 Chain Conveyor System
A chain conveyor system has one or more endless chains that directly carry the load. These chains are placed in a parallel chain manner that can be used in transporting pallets. One variant is the vertical chain conveyor that is used for transferring loads continuously in a vertical direction at high speeds.
2.2.4 Slat Conveyor System
A slat conveyor system uses slats placed at discrete positions, and these slats are connected to a chain. Through drives that control orientation and positioning of the load, the transported unit is able to retain its position while being conveyed. The system is used in applications transporting heavy loads that might otherwise damage the belt as in bottling and canning plants.
2.2.5 Vibrating Conveyor System
In vibrating conveyor systems, the main component is an elongated load-carrying structure called a trough, bed or tube, based on the application it is used for. A vibrating mechanism produces small amplitude vibrations at a high frequency. This conveys the individual product units and bulk materials. Due to its unique operational manner, it can be used to transport almost all kinds of granular as well as free-flowing materials.
2.2.6 Pneumatic Conveyor System
A pneumatic conveyor system uses pipes or ducts known as transportation lines. These ducts carry material mixture along with an air stream. The load gets transported to various locations through pipe lines propelled by the high velocity air streams.
2.3 Components and Breakdowns
The belt conveyor system (BCS) consists of (fig. 3):
â€¢ drive unit (electric motor, coupling multistage gearbox),
â€¢ pulleys (drive pulley and other),
â€¢ belts (textile or with steel cords) with their joints,
â€¢ other (belt cleaning systems, control system, etc.)
Fig 2.3.1 Belt conveyor transmission system components
In this section we will consider the type of faults that may appear in belt conveyor systems with reference to conveyor component s.
The drive unit consist of electric motor, damping coupling, two or three stage gear-box and coupling that connect output shaft with pulley (fig. 8). A crucial object in this subsystem is gearbox. According to Matuszewski  in a considered lignite open cast mine even 14% of gearboxes may be replaced each year due to unexpected failures. These failures are related to the geared wheel wear or damages (broken tooth) and bearings (mainly over limit backlash due to environmental impact, also typical failures like outer/inner race, rolling element).
The mining pulley consist of two bearings, shaft, shell and coating (special material in order to improve belt-pulley contact). The most frequent failures for pulleys are: bearings and shells. For gearboxes number of failures related to geared wheels is 50%. Other critical failure is the damage of input shafts (probably because of overloading) . It may be surprising that bearing faults are not so frequent in gearboxes.
The failure analysis of idlers and belts are a bit different issue [7, 8, 11]. Idlers are used for supporting belts with transported materials. In some sense, idlers are similar to pulleys and consist of bearings and shells. One may expect similar types of failures. The support system for belt consists of three idlers. Because of different load for each idler usually side idlers are more subjected to damage. It needs to be added that in CM context of idlers change of condition is not the only one. Worn bearings in idlers will significantly increase external load for drive units so power consumption will increase. Damaged idlers and pulleys may be the reason of damage for belts.
Depends on application, belts used in conveyor systems may be divided into two groups: textile belts and steel cords belts. In underground mines usually the textile belts are used. In lignite mines both types may be applied. Expected problems for belts are related to belt (tear, puncture, cut of belt and abrasion of bottom/top covers) and its joints (connected using glue, vulcanized or mechanical joint) [10, 11]. Because of dimension and weight of a belt it needs to be transported in rolls, pieces up to 100-400 m long, depends on a belt type. In order to replace damaged a gearbox or pulley heavy machinery is required. In some cases due to environmental impact (for example rain) it takes a few times longer time.
If one consider the impact of damaged idlers it is another story. The idlers are quite small in comparison to pulleys; however, number of idlers is huge. Damaged idlers may cause failure of belt (the cut of a belt) or even may start fire (belt slipping on damaged idler may increase temperature up to 400°C, 450°C is the limit for so called "difficult-to-burn" belt) and as it was mentioned energy consumption is arising dramatically.
Any of mentioned failure generates cost of breakdown of machines working in series. It as to be mentioned that a conveyor system, that with random material to be transferred the smoothness and stability of the conveyor belt transmisssion system should be guaranteed to extend all the components lifetime.
2.4 Significance of Research
The belt conveyor is one of key components for most of manufacturing systems. Intelligent control of the conveyor leads to the feasibility of a Flexible Manufacturing System (FMS). For most of the assembly lines in manufacturing systems, different processing works applied to products mainly come from workers who is sitting along the conveyor. The products are conveyed by the belt conveyor from one working area to the next. If the average number of products entering one working area is greater than the average number leaving that area, the manufacturing process stagnates. It means that conveying speed is too fast so that more products are conveyed to workers in that working area than the quantity they can handle. Therefore, the conveying speed of belt conveyor needs to be adaptively changed based on the stagnation condition at each working area. On the other hand, if the defective rate of products monitored at outlet of conveyor is too large even though no stagnation has occurred at each working area, the conveyor still needs to be adaptively slowed down so that workers have more time to give their processing works with more cares In the long run, maximum number of manufactured products conveyed to the outlet of conveyor is hoped to be achieved if the speed of belt conveyor can be intelligently controlled Since the conveyor is driven by a servo motor, adaptive control algorithm can be designed to control the motor speed based on stagnation conditions at working areas or the defective rate monitored at the conveyor outlet.
In addition, belt conveyor is one of main electromechanical systems in heavy industry, especially in the coal transport system, its safe operation plays an important role in the whole coal output systems.Safety is an important aspect in our life, and coal mine still is a high-risk industry in the world. As one of main components in the coal transport system, the safe operation of belt conveyor plays an important role in the whole coal output systems. As the belt conveyors get longer, quicker and bulkier, it is often occurred that the belt rupture, coal vibration, belt slip on the drive pulley, uncontrolled running of the belt conveyor, belt fire and other safety accidents, which bring huge economical losses and threat miner life. In order to insure the miner safety and the normal production, it is significant to carry on safety investigation of the belt conveyor. Higher productivity and reliability are common goals for conveyor systems in mining operations. Key objectives include optimized mass flows, reduced energy costs and a well-coordinated workflow between the conveying and transport processes.And the key to this problem is to make sure that the transmission system should be operating at a smooth and steady speed. In a word, the steady speed of the conveyor belt transmission system is vitally important.[wiki]
3.0 MOTORS FOR CONVEYOR
3.1 General Motors
An electric motor is an electromechanical device that converts electrical energy into mechanical energy.Electric motors are found in applications as diverse as industrial fans, blowers and pumps, machine tools, household appliances, power tools, and disk drives. Electric motors may be classified by the source of electric power, by their internal construction, by their application, or by the type of motion they give.
3.1 Conveyor Motor Types
For a conveyor transmission system, the drive unit develops with time. And the motors still using in this era come to the 4 main types: brushed DC motor; brushed DC motor; . The working mechanism of the 4 kinds are discussed as well as their merits and drawbacks.
3.2.1 Brushed DC motors
A brushed DC motor has a set of rotating windings wound on an armature mounted on a rotating shaft. The shaft also carries the commutatora long-lasting rotary electrical switch that periodically reverses the flow of current in the rotor windings as the shaft rotates. The magnets field produced by the armature interacts with a stationary magnetic field produced by either permanent magnets or another winding a field coil, as part of the motor frame. The force between the two magnetic fields tends to rotate the motor shaft.
Many of the limitations of the classic commutator DC motor are due to the need for brushes to press against the commutator. This creates friction. Sparks are created by the brushes making and breaking circuits through the rotor coils as the brushes cross the insulating gaps between commutator sections. Depending on the commutator design, this may include the brushes shorting together adjacent sections - and hence coil ends - momentarily while crossing the gaps. Furthermore, the inductance of the rotor coils causes the voltage across each to rise when its circuit is opened, increasing the sparking of the brushes. This sparking limits the maximum speed of the machine, as too-rapid sparking will overheat, erode, or even melt the commutator. The current density per unit area of the brushes, in combination with their resistivity, limits the output of the motor. The making and breaking of electric contact also generates electrical noise; sparking generates RFI. Brushes eventually wear out and require replacement, and the commutator itself is subject to wear and maintenance (on larger motors) or replacement (on small motors). The commutator assembly on a large motor is a costly element, requiring precision assembly of many parts. On small motors, the commutator is usually permanently integrated into the rotor, so replacing it usually requires replacing the whole rotor. Therefore, DC motor brush design entails a trade-off between output power, speed, and efficiency/wear.
3.2.2 brushed DC motor
In this motor, the mechanical "rotating switch" or commutator/brush gear assembly is replaced by an external electronic switch synchronized to the rotor's position. Brushless motors are typically 85-90% efficient or more whereas DC motors with brush are typically 75-80% efficient.
Brushless DC motors are commonly used where precise speed control is necessary. They have several advantages over conventional motors:they are very efficient, running much cooler than the other equivalent motors; without a commutator to wear out, the life of a DC brushless motor can be significantly longer compared to a DC motor using brushes and a commutator; brushless motors have no chance of sparking, unlike brushed motors, making them better suited to environments with volatile chemicals and fuels. Also, sparking generates ozone which can accumulate in poorly ventilated buildings risking harm to occupants' health.
Modern DC brushless motors range in power from a fraction of a watt to many kilowatts. Larger brushless motors up to about 100 kW rating are used in electric vehicles. There are numerous applications using a Brush DC Motor that could instead utilize the Brushless DC Motor. However a few factors might prevent the changeover. The first factor is start-up cost. Although the Brushless DC Motor is lower-maintenance than the Brush DC Motor, initial cost is more expensive, due to its advantageous construction. Second is complexity. A controller is required in order to operate a Brushless DC Motor, and is usually more convoluted than most controllers. A Brushless DC Motor also requires additional system wiring, in order to power the electronic commutation circuitry.
3.2.3 asynchronous AC motor
An asynchronous AC motor is an induction motor where power is transferred to the rotor by electromagnetic induction, much like transformer action. . Polyphase induction motors are widely used in industry.The simple design of AC motor is simply a series of three windings in the exterior (stator) section with a simple rotating section (rotor). The changing field caused by the 50 or 60 Hertz AC line voltage causes the rotor to rotate around the axis of the ac motor. The AC motor has the advantage of being the lowest cost motor for applications which require more than about 1/2 hp (325 watts) of power. This is due to the simple design of ac motor. Meanwhile, the simple design of the AC motor results in extremely reliable, low maintenance operation. Unlike the DC motor, there are no brushes to replace for ac motors. If run in the appropriate environment for its enclosure, AC motor can expect to need new bearings after several years of operation. In fact if the application is well designed, an AC motor may not need new bearings for more than a decade.
Although the most common and simple industrial motor is the three phase AC induction motor, there are still disadvantages of ac motor.
Expensive speed control
The electronics required to handle an AC inverter drive are considerably more expensive than those required to handle a DC motor. However, if performance requirements can be met -- meaning that the required speed range is over 1/3rd of base speed -- AC inverters and AC motors are usually more cost-effective than DC motors and DC drives for applications larger than about 10 horsepower, because of cost savings in the AC motor.
Inability to operate at low speeds
Standard AC motors should not be operated at speeds less than about 1/3rd of base speed. This is due to thermal considerations. In fact a DC motor should be considered for these applications.
Poor positioning control
Positioning control is also expensive and crude. Even a vector drive is very crude when controlling a standard AC motor. Servo motors are more appropriate for these applications.
3.2.4 Synchronous Electric Motor
A synchronous electric motor is an AC motor distinguished by a rotor spinning with coils passing magnets at the same rate as the alternating current and resulting magnetic field which drives it. Another way of saying this is that it has zero slip under usual operating conditions. Contrast this with an induction motor, which must slip to produce torque.
These motors can be made to operate at leading power factor and thereby improve the pf of an industrial plant from one that is normally lagging to one that is close to unity. And the key feature of a synchronous AC motor is it operates at a constant speed, irrespective of load, from no-load to full load. As well, electromagnetic power varies linearly with the applied voltage. These motors can be constructed with wider air gapes than induction motors making them mechanically better.What's more, efficiency of operation is usually high, especially in the low speed and unity power factor ranges.
However, the disadvantages are also quite obvious. These motors cannot be used for variable speed jobs as there is no possibility of speed adjustment. And it requires external source for supplying dc excitation, cannot be started under load, the starting torque being zero, may fall out of synchronism and stop when over-loaded and so on. In addition, for some applications these motors are not desirable as for driving shafts in small work-shops having no power available for starting and in cases where frequent starting or strong starting torque is required.
3.3 AC Motor for Conveyor
Through the comparisons above, transmission system with AC motors are simple to make and can be reliable.And for the low cost, AC motors are overwhelmingly preferred for fixed speed applications in our industrial applications and for commercial and domestic applications where AC line power can be easily attached. In fact over 90% of all motors are AC induction motors. AC induction motors are found in air conditioners, washers, dryers, industrial machinery, fans, blowers, vacuum cleaners, and many, many other applications.
Using an AC drive for conveyor control allows the speed to be adjusted to changing needs. A partly loaded conveyor with a higher speed than necessary wastes energy and causes unnecessary wear. In controlling conveyors, AC drives also improve process control by enabling the collection of measurement and supervision information. The soft start of the conveyor with AC drives reduces the stress on gearboxes when the conveyor is started.
This paper mainly deals with the AC asynchronous motors, because for industry like coal mine, the asynchronous ones are the mainstream with many successful applications.In the design of the induction motor, operational characteristics can be determined through a series of calculations. Performing these calculations can help the engineer provide a motor that is best suited to a particular application.
3.3.1 SYNCHRONOUS SPEED
The speed with which the stator magnetic field rotates, which will determine the speed of the rotor, is called the Synchronous Speed (SS). The SS is a function of the frequency
of the power source and the number of poles (pole pairs) in the motor. The relationship
to calculate the SS of an induction motor is:
SS = Synchronous Speed (RPM)
f = frequency (cycles / second) = 60
P = number of poles (pole pairs)
3.3.2 MOTOR SLIP
The rotor in an induction motor can not turn at the synchronous speed. In order to induce an EMF in the rotor, the rotor must move slower than the SS. If the rotor were to somehow turn at SS, the EMF could not be induced in the rotor and therefore the rotor would stop. However, if the rotor stopped or even if it slowed significantly, an EMF would once again be induced in the rotor bars and it would begin rotating at a speed less than the SS.
The relationship between the rotor speed and the SS is called the Slip. Typically, the Slip is expressed as a percentage of the SS. The equation for the motor Slip is:
%S = Percent Slip
SS = Synchronous Speed (RPM)
RS = Rotor Speed (RPM)
3.3.3 EQUIVALENT CIRCUIT
To analyze the operating and performance characteristics of an induction motor, an
Equivalent Circuit can be drawn. We will consider a 3-phase, Y connected machine, the
Equivalent Circuit for the stator is as shown below:
Fig 3.3.1 Equivalent Circuit
V1 = Stator Terminal Voltage
I1 = Stator Current
R1 = Stator Effective Resistance
X1 = Stator Leakage Reactance
Z1 = Stator Impedance (R1 + jX1)
IX = Exciting Current (this is comprised of the core loss component = Ig, and a magnetizing current = Ib)
E2 = Counter EMF (generated by the air gap flux)
3.4 Speed Control of AC Asynchronous Motor
With respect to the use of AC asynchronous motor, when used with a load that has a torque curve that increases with speed, the motor will operate at the speed where the torque developed by the motor is equal to the load torque. Reducing the load will cause the motor to speed up, and increasing the load will cause the motor to slow down until the load and motor torque are equal. Operated in this manner, the slip losses are dissipated in the secondary resistors and can be very significant. So the speed control of an AC asynchronous motor in the industry world is quite important.
From Equ.1 we can get the speed torque characteristic of the machine as Fig. 3.3.2. The curve is rather steep and goes from zero torque at synchronous speed to the stall torque at a value of %S. Normally Slip may be such that stall torque is about three times that of the rated operating torque of the machine, and hence may be about 0.3 or less. This means that in the entire loading range of the machine, the speed change is quite small. The machine speed is quite stiff with respect to load changes. The entire speed variation is only in the range SS to (1âˆ’%S)SS, SS being dependent on supply frequency and number of poles.
Fig 3.3.2 Relationship between torque and speed of induction motor
The coming discussion shows that the several speed control methods for induction machine, when operating from mains is essentially a constant speed machine. Many industrial drives, typically for conveyor in a belt transmission system, have typically constant speed requirements and hence the induction machine is ideally suited for these. However,the induction machine, especially the squirrel cage type, is quite rugged and has a simple construction. Therefore it is good candidate for variable speed applications if it can be achieved.
3.4.1 Applied voltage control
One may note that if the applied voltage is reduced, the voltage across the magnetizing branch also comes down. This in turn means that the magnetizing current and hence flux level are reduced. Reduction in the flux level in the machine impairs torque production. If, however, the machine is running under lightly loaded conditions, then operating under rated flux levels is not required. Under such conditions, reduction in magnetizing current improves the power factor of operation. Some amount of energy saving may also be achieved.Voltage control may be achieved by adding series resistors (a lossy, inefficient proposition),or a series inductor/autotransformer (a bulky solution) ora more modern solution using semiconductor devices. A typical solid state circuit used for this purpose is the AC voltage controller or AC chopper. Another use of voltage control is in the so-called 'soft-start' of the machine.
3.4.2 Rotor resistance control
Clearly, the rotator speed is dependent on the rotor resistance. Further, the maximum value is independent of the rotor resistance. The slip at maximum torque is dependent on the rotor resistance. Therefore, we may expect that if the rotor resistance is changed, the maximum torque point shifts to higher slip values, while retaining a constant torque.
Note that while the maximum torque and synchronous speed remain constant, the slip at which maximum torque occurs increases with increase in rotor resistance, and so does the starting torque. whether the load is of constant torque type or fan-type, it is evident that the speed control range is more with this method. Further, rotor resistance control could also be used as a means of generating high starting torque.For all its advantages, the scheme has two serious drawbacks. Firstly, in order to vary the rotor resistance, it is necessary to connect external variable resistors (winding resistance itself cannot be changed). This, therefore necessitates a slip-ring machine, since only in that case rotor terminals are available outside. For cage rotor machines, there are no rotor terminals. Secondly, the method is not very efficient since the additional resistance and operation at high slips entails dissipation.The resistors connected to the slip-ring brushes should have good power dissipation capability.
3.4.3 Cascade control
The power drawn from the rotor terminals could be spent more usefully. Apart from using the heat generated in meaning full ways, the slip ring output could be connected to another induction machine. The stator of the second machine would carry slip frequency currents of the first machine which would generate some useful mechanical power. A still better option would be to mechanically couple the shafts of the two machines together. This sort of a connection is called cascade connection and it gives some measure of speed control as shown below. Let the frequency of supply given to the first machine be f1, its number poles be p1, and its slip of operation be s1. Let f2, p2ands2be the corresponding quantities for the second machine. The frequency of currents flowing in the rotor of the first machine and hence in the stator of the second machine is s1f1. Therefore f2 =s1f1. Since the machines are coupled at the shaft, the speed of the rotor is common for both. Hence, if n is the speed of the rotor in radians,
Note that while giving the rotor output of the first machine to the stator of the second, the resultant stator mm f of the second machine may set up an air-gap flux which rotates in the same direction as that of the rotor, or opposes it. this results in values for speed as
The latter expression is for the case where the second machine is connected in opposite phase sequence to the first. The cascade connected system can therefore run at two possible speeds.
3.4.4 Pole changing schemes
Sometimes induction machines have a special stator winding capable of being externally connected to form two different number of pole numbers. Since the synchronous speed of the induction machine is given by Equ.X where p is the number of pole pairs, this would correspond to changing the synchronous speed. With the slip now corresponding to the new synchronous speed, the operating speed is changed. This method of speed control is a stepped variation and generally restricted to two steps. If the changes in stator winding connections are made so that the air gap flux remains constant, then at any winding connection, the same maximum torque is achievable. Such winding arrangements are therefore referred to as constant-torque connections. If however such connection changes result in air gap flux changes that are inversely proportional to the synchronous speeds, then such connections are called constant-horsepower type.
3.4.5 Stator frequency control
The expression for the synchronous speed indicates that by changing the stator frequency also it can be changed. This can be achieved by using power electronic circuits called inverters which convert dc to ac of desired frequency. Depending on the type of control scheme of the inverter, the ac generated may be variable-frequency-fixed-amplitude or variable-frequency-variable-amplitude type. Power electronic control achieves smooth variation of voltage and frequency of the ac output. This when fed to the machine is capable of running at a controlled speed. However, consider the equation for the induced emf in the induction machine.
where N is the number of the turns per phase,Ï†m is the peak flux in the air gap and f is the frequency. Note that in order to reduce the speed, frequency has to be reduced. If the frequency is reduced while the voltage is kept constant, thereby requiring the amplitude of induced emf to remain the same, flux has to increase. This is not advisable since the machine likely to enter deep saturation. If this is to be avoided, then flux level must be maintained constant which implies that voltage must be reduced along with frequency. The ratio is held constant in order to maintain the flux level for maximum torque capability.Actually, it is the voltage across the magnetizing branch of the exact equivalent circuit that must be maintained constant, for it is that which determines the induced emf. Under conditions where the stator voltage drop is negligible compared the applied voltage, Equ.X is valid. In this mode of operation, the voltage across the magnetizing inductance in the 'exact'equivalent circuit reduces in amplitude with reduction in frequency and so does the inductive reactance. This implies that the current through the inductance and the flux in the machine remains constant.
3.5 AC MOTOR DRIVE
Manufacturing lines typically involve a variety of variable speed motor drives which serve to power conveyor belts, robot arms, overhead cranes, steel process lines, paper mills, and plastic and fiber processing lines to name only a few. Prior to the 1950s all such applications required the use of a DC motor drive since AC motors were not capable of smoothly varying speed since they inherently operated synchronously or nearly synchronously with the frequency of electrical input. To a large extent, these applications are now ser-viced by what can be called general-purpose AC drives. In general, such AC drives often feature a cost advantage over their DC counterparts and, in addition, offer lower maintenance, smaller motor size, and improved reliability. However, the control flexibility available with these drives is limited and their application is, in the main, restricted to fan, pump, and compressor types of applications where the speed need be regulated only roughly and where transient response and low-speed performance are not critical.
AC motor drives can be broadly categorized into two types, thyristor based and transistor based drives. Thyristors posses the capability of self turn-on by means of an associated gate signal but must rely upon circuit conditions to turn off whereas transistor devices are capable of both turn-on and turn-off. Because of their turn-off limitations, thyristor based drives must utilize an alternating EMF to provide switching of the devices (commutation) which requires reactive volt-amperes from the EMF source to accomplish.
4.0 PID ALGORITHM FOR PROCESS CONTROL
Over past 50 years, 'process control' has developed into a vital part of the engineering curriculum. Textbooks cover various aspects of industrial process control. It is hopeless to discuss all subjects of process control in this paper. However, a brief description of the scope of process control will be given and the specific role of this paper will become clear.
Although the new and effective theories and design methodologies being continually developed in the process control field, Proportional-Integral-Derivative (PID) controllers are still by far the most widely adopted con-trollers in industry owing to the advantageous cost/benefit ratio they are able to provide. In fact, although they are relatively simple to use, they are able to provide a satisfactory performance in many process control tasks. Indeed,their long history and the know-how that has been devised over the years has consolidated their usage as a standard feedback controller. However, the availability of high-performance microprocessors and software tools and the increasing demand of higher product quality at reduced costs still stimulates researchers to devise new methodologies for the improvement of performance and/or for an easier use of them. This is proven by the large number of publications on this topic (especially in recent years) and by the increasing number of products available on the market.
4.1 Process Control
For continuous manufacturing, on-demand production with on-aim quality is the goal of process operation. Many factors contribute to non-smooth process operation, and controller tuning is just one of them. Starting from the most fundamental level, process variations may come from the infrastructure of a control system in which the signal transmission, control panel arrange-ment, distributed control system (DCS) selection, and DCS configuration may be the source of the problem. If the infrastructure is not the source of variation, then one may go up to the instrumentation level, which includes the control valve sizing, sensor selection, and transmitter span determination. It is clear that a wrongly sized control valve or an incorrectly determined transmitter span cannot provide adequate resolution in the manipulated variable or the controlled variable. It then comes to the controller tuning level in which inadequate controller settings may lead to oscillation in process variables, and improved controller settings is the focus of this paper. If a controller retuning still cannot fix the problem, then we go to the controller structure level, in which one can try different types of controller. The actions in this level include: remove or add the derivative action, take out or add the integral action, use the gain scheduling, and add the dead time compensation.
Surveys indicate that the process control performance is, indeed, not as good as we think, and the situation remains pretty much the same a decade later. The reality leads us to reconsider the priorities in process control research. First, an improved process and control configuration redesign (e.g. selection and pairing of input and output variables) can improve control performance. As mentioned ear-lier, simultaneous design and control should be taken seriously to alleviate the problem of a small operating window and the requirement for sophisticated control configuration. Second, control valves contribute significantly to the poor control performance. It is difficult, if not impossible, to replace or to restore all the control valves to the expected performance. In other words, in many cases, this is a fact we have to face (e.g. dead band, stick-slip, etc.). One thing we can do is to devise a diagnostic tool to identify potential problems in control valves. We have seen the beginning of research effort in this direction. Third, and probably the easiest way to improve control performance, is to find appropriate tuning constants for PID controllers.
4.2 PID Algorithm
The proportional-integral-derivative algorithm consists of three simple actions,i.e. P, I, and D actions.Applying a PID control law consists of applying properly the sum of three types of control actions: a proportional action, an integral action and a derivative one. These actions are described singularly hereafter.
4.2.1 Proportional Action
The proportional control action is proportional to the current control error,according to the expression
where Kp is the proportional gain. Its meaning is straightforward, since it implements the typical operation of increasing the control variable when the control error is large (with appropriate sign). The transfer function of a proportional controller can be derived trivially as
A proportional controller has the advantage of providing a small control variable when the control error is small and therefore to avoid excessive control efforts. The main drawback of using a pure proportional controller is that it produces a steady-state error. It is worth noting that this occurs even if the process presents an integrating dynamics(i.e. , its transfer function has a pole at the origin of the complex plane), in case a constant load disturbance occurs. This motivates the addition of a bias (or reset) term ub,namely,
The value of ub can be fixed at a constant level (usually at (umax+ umin)/2)or can be adjusted manually until the steady-state error is reduced to zero.It is worth noting that in commercial products the proportional gain is often replaced by the proportional band PB, that is the range of error that causes a full range change of the control variable, i.e. ,
4.2.2 Integral Action
The integral action is proportional to the integral of the control error, i.e. ,it is
where Ki is the integral gain. It appears that the integral action is related to the past values of the control error. The corresponding transfer function is:
The presence of a pole at the origin of the complex plane allows the reduction to zero of the steady-state error when a step reference signal is applied or a step load disturbance occurs. In other words, the integral action is able to set automatically the correct value of ub in (X.X) so that the steady-state error is zero. This fact is better explained in the resulting transfer function is
i.e., a PI controller results. For this reason the integral action is also often called automatic reset.Thus, the use of a proportional action in conjunction to an integral action, of a PI controller, solves the main problems of the oscillatory response and of the steady-state error associated to a pure proportional controller.It has to be stressed that when integral action is present, the so-called integrator windup phenomenon might occur in the presence of saturation of the control variable.
4.2.3 Derivative Action
While the proportional action is based on the current value of the control error and the integral action is based on the past values of the control error,the derivative action is based on the predicted future values of the control error. An ideal derivative control law can be expressed as:
where K dis the derivative gain. The corresponding controller transfer function is
In order to understand better the meaning of the derivative action, it is worth considering the first two terms of the Taylor series expansion of the control error at time Td ahead:
If a control law proportional to this expression is considered,
this naturally results in a PD controller. The control variable at time t is therefore based on the predicted value of the control error at time t + Td. For this reason the derivative action is also called anticipatory control,or rate action ,or pre-act .It appears that the derivative action has a great potentiality in improving the control performance as it can anticipate an incorrect trend of the control error and counteract for it. However, it has also some critical issues that makes it not very frequently adopted in practical cases. They will be discussed in the following sections.
4.2.4 Structures of PID Controllers
The combination of the proportional, integral, and derivative actions can be done in different ways. In the so-called ideal or non-interacting form, the PID controller is described by Equ.X, and the block diagram is shown in Fig.4.2.1:
Fig 4.2.1 PID algorithm diagram
and its transfer function can be parameterized as
where Kp is the proportional gain, Ti is the integral time constant, and Td is the derivative time constant. An alternative representation is the series or interacting form:
where the fact that a modification of the value of the derivative time constant Td affects also the integral action justifies the nomenclature adopted.It has to be noted that a PID controller in series form can be always represented in ideal form by applying the following formulas:
The reason for preferring the series form to the ideal form is that the series form was the first to be implemented in the last century with pneumatic technology. Then, many manufacturers chose to retain the know-how and to avoid changing the form of the PID controller. Further, it is sometimes claimed that a PID controller in series form is more easy to tune.
Another way to implement a PID controller is in parallel form,
In this case the three actions are completely separated. Actually, the parallel form is the most general of the different forms, as it allows to exactly switch off the integral action by fixing Ki = 0 (in the other cases the value of the integral time constant should tend to infinity). The conversion between the parameters of the parallel PID controller and those of the ideal one can be done trivially by means of the following formulas:
4.3 Controller Type Choose
For a given control task, it is obviously not necessary to adopt all the three actions. Thus, the choice of the controller type is an integral part of the over-all controller design, taking into account that the final aim is to obtain the best cost/benefit ratio and therefore the simplest controller capable to obtain a satisfactory performance should be preferred.In this context it is worth analyzing briefly some guidelines on how the con-troller type (P, PI, PD, PID) has to be selected.
As already mentioned, a P controller has the disadvantage, in general, of giving a non zero steady-state error. However, in control tasks where this is not of concern, such as for example in surge tank level control or in inner (secondary) loops of cascade control architectures, where the zero steady-state error is ensured by the integral action adopted in the outer (primary) controller, a P controller can be the best choice, as it is simple to design (indeed, if the process has alow-order dynamics the proportional gain can be set to a high value in order to provide a fast response and a low steady-state error). Further, if an integral component is present in the system to be controlled (such as in mechanical servo systems or in surge vessels where the manipulated variable is the difference between inflow and outflow) and no load disturbances are likely to occur,then there is no need of an integral action in the controller to provide a zero steady-state control error. In this case the control performance can be usually improved by adding a derivative action, i.e. , by adopting a PD controller. In fact, the derivative action provides a phase lead that allows to increase the bandwidth of the system and therefore to speed up the response to a set-point change. If the zero steady-state error is an essential control requirement, then the simplest choice is to use a PI controller. Actually, a PI controller is capable to provide an acceptable performance for the vast majority of the process control tasks (especially if the dominant process dynamics is of first order) and it is indeed the most adopted controller in the industrial context. This is also due to the problems associated with the derivative actions, namely the need of properly filtering the measurement noise and the difficulty in selecting an appropriate value of the derivative time constant.
In any case, the use of the derivative action, that is, of a PID controller, provides very often the potentiality of significantly improve the performance.For example, if the process has a second-order dominant dynamics, the zero introduced in the controller by the derivative action can be adopted to cancel the fastest pole of the process transfer function. However, it is also often claimed that if the process has a significant (apparent) dead time, then the derivative action should be disconnected. Actually, the usefulness of the derivative action has been the subject of some investigation. Recent contributions to the literature have shown that the performance improvement given by the use of the derivative action decreases as the ratio between the apparent dead time and the effective time constant increases but it can be very beneficial if this ratio is not too high.Finally, it is worth noting that for processes affected by a large dead time(with respect to the dominant time constant) the use of a dead-time compensator controller, such as a Smith predictor based scheme (Palmor, 1996) or the so-called PID-deadtime controller (where the time-delay compensation is added to the integral feedback loop of the PID controller in automatic reset configuration) (Shinskey, 1994), can be essential in obtaining a satisfactory control performance (Ingimundarson and H¨agglund, 2002).
4.4 PID Parameter Tuning
The selection of the PID parameters, i.e. , the tuning of the PID controllers,is obviously the crucial issue in the overall controller design. This operation should be performed in accordance to the control specifications. Usually, as already mentioned, they are related either to the set-point following or to the load disturbance rejection task, but in some cases both of them are of primary importance. The control effort is also generally of main concern as it is related to the final cost of the product and to the wear and life-span of the actuator.It should be therefore kept at a minimum level. Further the robustness issue has to be taken into account.
A major advantage of the PID controller is that its parameters have a clear physical meaning. Indeed, increasing the proportional gain leads to an increasing of the bandwidth of the system and therefore a faster but more oscillatory response should be expected. Conversely, increasing the integral time constant(decreasing the effect of the integral action) leads to a slower response but to a more stable system. Finally, increasing the derivative time constant gives a damping effect, although much care should be taken in avoiding to increase it too much as an opposite effect occurs in this case and an unstable system could eventually result.
The functionality of automatically identifying the process model and tuning the controller based on that model is called automatic tuning (or, simply,auto-tuning). In particular, an identification experiment is performed after an explicit request of the operator and the values of the PID parameters are updated at the end of it .
The design of an automatic tuning procedure involves many critical issues, such as the choice of the identification procedure (usually based on an open-loop step response or on a relay feedback experiment, of the apriori selected (parametric or nonparametric) process model and of the tuning rule. Advanced (more expensive)control units might provide a self-tuning functionality, where the identification procedure is continuously performed during routine process operation in order to track possible changes of the system dynamics and the PID parameters values are modified adaptively. In this case all the issues related to adaptive control have to be taken into account.
4.5 Advantages and Disadvantages of PID Control
From the information mentioned above, we can easily find the merits and drawbacks of a PID controller to sum up this chapter.
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