Control Systems - Module 1 PDF

Republic of the Philippines Bulacan State University City of Malolos, Bulacan College of Engineering Department of Electrical Engineering Prepared By: Eleazer C. Nabong, REE, MEng, MSc Faculty – College of Engineering...

Republic of the Philippines Bulacan State University City of Malolos, Bulacan College of Engineering Department of Electrical Engineering Prepared By: Eleazer C. Nabong, REE, MEng, MSc Faculty – College of Engineering  Unit 1 – INTRODUCTION to CONTROL SYSTEMS ANALYSIS Title of the Lesson  Definition of Terms  Historical Development  Advantage/Disadvantage of Control Systems  Types of Control Systems  Basic Elements of a Closed-loop System Duration: 3 hours Introduction Humans have created control systems as technical innovations to enhance the quality and comfort of their lives. Human engineered control systems are part of automation, which is a feature of our modern life. They are applied in several aspects of our daily life – in heating and air conditioning to control our living environment and in many of our household and office appliances (i.e., rice cookers, automatic washing machines, printers, xerox machines, etc.). They significantly relieve us from the burden of operation of complex systems and processes and enable us to achieve control with desired precision. Control systems enable accurate positioning and control of machine tools in metal cutting operations (like CNC) and automated manufacturing processes. The system automatically guides and control space vehicles, aircraft, large sea going vessels, and high-speed ground transportation systems. Modern automation of a plant involves components such as sensors, instruments, computers, and application of techniques of data processing and control. The principles and techniques of automatic control may be applied in a wide variety of systems to enhance the quality of their performance. Control systems are not human inventions; they have naturally evolved in the earth’s living system. The action of automatic control regulates the conditions necessary for life in almost all living things. They possess sensing and controlling systems and counter disturbances. An automatic human temperature control system, for example, makes it possible to maintain the temperature of the human body constant at the right value despite varying ambient conditions. The human body is a very sophisticated biochemical processing plant in which the consumed food is processed, and glands automatically release the required quantities of chemical substances as and when necessary, in the process. The stability of the human body and its ability to move as desired is due to some very effective motion control systems. A bird in flight, a fish swimming in water or an animal on the run- all are under the influence of some very efficient control systems that have evolved in them. Control systems is an interdisciplinary field covering many areas of engineering and sciences. Control systems exist in many systems of engineering, sciences, and in the human body. Some types of control systems affect most aspects of our day-to-day activities. A control system is a means by which any quantity or process of interest in a machine, or in a process flow is maintained or altered to achieve a desired response. Understanding a system and knowing its properties is prerequisite to the creation of a controlled system. Before attempting to control a system, it is essential to know how it generally behaves and responds to external stimuli. Such an understanding is possible with the help of a model. The process of developing a model is known as modeling. Objectives After studying this unit, the student should be able to:  Define a control system and describe some applications.  Describe historical developments leading to modern day control theory.  Describe the basic features and configurations of control systems.  Describe control systems analysis and design objectives.  Describe the benefit from studying control systems. Page 2 of 20 Pre-test 1. What is the basic objective of a control system? 2. Name the two general classifications of control systems. 3. Give some examples of open-loop systems. 4. Give some examples of closed-loop systems. Lesson Content: TERMINOLOGIES The control system is a system of getting output by regulating, commanding, and directing the input known as a control system. In our human body, our brain controls our body parts to do specific work. So, in this case, the brain becomes the control system of our body. A control system consists of subsystems and processes (or plant) assembled for the purpose of obtaining a desired output with desired performance, given a specified input. Basic Components of Feedback/Closed-loop Control Systems 1. Plant: The portion of a system that is to be controlled or regulated is called a plant or process. It is a unit where actual processing is performed and if we observe in the above figure, the input of the plant is the controlled signal generated by a controller. A plant performs necessary actions on a controlled system and produces the desired output. 2. Feedback: It is a controlled action in which the output is sampled, and a proportional signal is given to the input for automatic correction of any changes in the desired output. The output is given as feedback to the input for correction i.e., information about the output is given to input for correcting the changes in output due to disturbances. The feedback signal is fed to the error detector. Negative feedback is preferred as it results in better stability and accuracy. The other disturbance signals are rejected. 3. Error detector: The function of the error detector is to compare the reference input with the feedback signal. It produces an error signal which is a difference of two inputs which are a reference signal and a feedback signal. The error signal is fed to the controller for necessary Page 3 of 20  controlled action. This error signal is used to correct the output if there is a deviation from the desired value. 4. Controller: the element of a system within itself or external to the system which controls the plant is called a controller. The error signal will be a weak signal and so it must be amplified and then modified for better control action. In most of the systems, the controller itself amplifies the error signal and integrates or differentiates to generate a control signal. An amplifier is used to amplify the error signals and the controller modifies the error signal. Other Terminologies 1. Disturbance or Noise Input. A disturbance or noise input is an undesired stimulus or input signal affecting the value of the controlled output. 2. Feed Forward (Control) Elements. The feed forward (control) elements are the components of the forward path that generate the control signal applied to the plant or process. The feed forward (control) elements include controller(s), compensator(s), or equalization elements, and amplifiers. 3. Feedback Elements. The feedback elements establish the fundamental relationship between the controlled output and the primary feedback signal. They include sensors of the controlled output, compensators, and controller elements. 4. Feedback Path. The feedback path is the transmission path from the controlled output back to the summing point. 5. Forward Path. The forward path is the transmission path from the summing point to the controlled output. 6. Input Transducer. Input transducer converts the form of input to that used by the controller. 7. Loop. A loop is a path that originates and terminates on the same node, and along which no other node is encountered more than once. 8. Loop Gain. The loop gain is the path gain of a loop. 9. Negative Feedback. Negative feedback implies that the summing point is a subtractor. 10.Path. A path is any collection of a continuous succession of branches traversed in the same direction. 11.Path Gain. The product of the branch gains encountered in traversing a path is called the path gain. 12.Positive Feedback. Positive feedback implies that the summing point is an adder. 13.Primary Feedback Signal. The primary feedback signal is a function of the controlled output summed algebraically with the reference input to establish the actuating or error signal. An open-loop system has no primary feedback signal. 14.Reference Input. The reference input is an external signal applied to the control system generally at the first summing input, to command a specified action of the process or plant. It typically represents an ideal or desired process or plant output response. Page 4 of 20 15.Summing Point. As shown in the figure above, a summing point is a small circle called with the appropriate plus or minus sign associated with the arrows entering the circle. The output is the algebraic sum of the inputs. There is no limit on the number of inputs entering a summing point. 16.Takeoff Point. A takeoff point allows the same signal or variable as input to more than one block or summing point, thus permitting the signal to proceed unaltered along several different paths to several destinations as shown. 17.Time Response. The time response of a system, subsystem, or element is the output as a function of time, generally following the application of a prescribed input under specified operating conditions. 18.Transducer. A transducer is a device that converts one energy form into another. Advantages of Control Systems Control systems are built for four primary reasons: 1. Power Amplification For example, a radar antenna, positioned by the low-power rotation of a knob at the input, requires a large amount of power for its output rotation. A control system can produce the needed power amplification, or power gain. 2. Remote Control Robots designed by control system principles can compensate for human disabilities. Control systems are also useful in remote or dangerous locations. For example, a remote-controlled robot arm can be used to pick up material in a radioactive environment. 3. Convenience of input form Control systems can also be used to provide convenience by changing the form of the input. For example, in temperature control system, the input is a position on a thermostat. The output is heat. Thus, a convenient position input yields a desired thermal output. 4. Compensation for disturbances Typically, we control such variables as temperature in thermal systems, position and velocity in mechanical systems, and voltage, current, or frequency in electrical systems. The system must be able to yield the correct output even with a disturbance. For example, consider an antenna system that points in a commanded direction. If wind forces the antenna from its commanded position, or if noise enters internally, the system must be able to detect the disturbance and correct the antenna’s position. Obviously, the system’s input will not change to make the correction. Consequently, the system itself must measure the amount that the disturbance has re- positioned the antenna and then return the antenna to the position commanded by the input. Page 5 of 20  Selected History Leading to the Development of Control System LIQUID LEVEL CONTROL 325 BC - Water Clock or Clepsydra invented by Ktesibios (see Figure). It is operated by water trickling into a measuring container at a constant rate. The level of water in the measuring container could be used to tell time. The water clock was developed to solve the problem of the first timekeeping device known as the sundial. The problem with the sundial was it was only functional when the sun was out. This was an obvious issue and sparked inventors to find a new way to solve the timekeeping problem. STEAM PRESSURE AND TEMPERATURE CONTROL 1681 - Dennis Papin invented the safety valve for regulating steam pressure. If the upward pressure from the boiler exceeded the weight, steam was released, and the pressure decreased. If it did not exceed the weight, the valve did not open, and the pressure inside the boiler increased. Thus, the weight on the valve top sets the internal pressure of the boiler. Also in the seventeenth century, Cornellis Drebbel in Holland invented a purely mechanical temperature control system for hatching eggs. The device used a vial of alcohol and mercury with a floater inserted in it. The floater was connected to a damper that controlled a flame. A portion of a vial was inserted into the incubator to sense the heat generated by the fire. As the heat increased, the alcohol and mercury expanded, raising the floater, closing the damper, and reducing the flame. Lower temperature caused the float to descend, opening the damper and increasing the flame. SPEED CONTROL 1745 - Windmill speed control was invented by Edmund Lee. Increasing winds pitched the blades farther back, so that less area was available. As wind decreased, more blade area was available. William Cubitt improved on the idea in 1809 by dividing the windmill sail into movable louvers. Figure b – Flyball Governor Page 6 of 20 1769 – James Watt’s steam engine and governor developed. The Watt steam engine is often used to mark the beginning of the Industrial Revolution in Great Britain. During the Industrial Revolution, great strides were made in the development of mechanization, a technology preceding automation (see figure b). STABILITY, STABILIZATION AND STEERING 1868 - J. C. Maxwell developed a theoretical framework for Watt’s governors by means of a differential equation analysis relating to performance of the overall system, thereby explaining in mathematical terms the reasons for oscillations within the system. It was gradually found that Maxwell’s governor equations were more widely applicable and could be used to describe phenomena in other systems. 1874 – Edward John Routh, using a suggestion from William Kingdon Clifford that was ignored earlier by Maxwell, was able to extend the stability criterion to fifth-order systems. 1877 - the topic for the Adams Prize was “The Criterion of Dynamical Stability.” In response, Routh submitted a paper entitled A Treatise on the Stability of a Given State of Motion and won the prize. This paper contains what is now known as the Routh-Hurwitz criterion for stability. TWENTIETH CENTURY DEVELOPMENTS 1927 - Harry Nyquist, a physicist who had studied noise extensively, turned his attention to the problem of stability in repeater amplifiers. He successfully tackled the problem by making use of standard function theory, thereby stressing the importance of the phase, as well as the gain, characteristics of the amplifier. Early 1930s - H. W. Bode and H. Nyquist at Bell Telephone Laboratories developed the analysis of feedback amplifiers. These contributions evolved into sinusoidal frequency analysis and design techniques currently used for feedback control systems. 1952 - Numerical control (precision technology) developed at Massachusetts Institute of Technology for control of machine-tool axes was developed. 1954 - George Devol develops “programmed article transfer,” considered to be the first industrial robot design. 1960 - Digital control became widespread due to computers, which were particularly relevant in the process control industries in which many variables must be measured and controlled, with a computer completing the feedback loop. 1961 - First Unimate robot was installed for tending die-casting machines. 1980 - The need for high-speed control devices has been a contributing factor and has made great use of hardware techniques, such as parallel processors, whereas at the same time ideas from the field of artificial intelligence have been employed to cope with increased complexity needs of automated systems. 1990 - Export-oriented manufacturing companies emphasize automation to increase their production and lower manufacturing costs. 1997 - First ever autonomous rover vehicle, known as Sojourner, explores the Martian surface. This is the birth of “independent machines”. Page 7 of 20 Basic Types of Control System 1. Natural – examples: biological control systems 2. Man-made – examples: robots, fully automated systems, or any system that is completely independent from human intervention. 3. Combination – examples: biologically operated man-made devices. Classifications of Control System A. Base on Configuration A.1 Open-Loop - A system that utilizes a device (controller or control actuator) to control the process without using feedback. Thus, the output has no effect upon the signal to the process. Sometimes called Feedforward Control System Advantages: Simplicity and Low Cost Disadvantage: usually inaccurate Satisfactory if:  Disturbances are not too great  Changes in the desired value are not too severe  Performance specifications are not too stringent A.2 Closed-Loop - a system whose input value is proportional to the difference of a measurement of the actual output and desired output. Also called Feedback Control System Advantages of Closed-loop control system: High accuracy – cause the output to accurately follow the desired output; corrective action occurs as soon as the controlled variable deviates from the command Quick Response – can give a closed-loop response speed much greater than that of the components from which they are constructed. Flexibility – is tolerant of variation (due to wear, aging, environmental effects, etc.) in hardware parameters of components in the forward path, but not those in the feedback path (e.g. sensors) Page 8 of 20  Reduces the effect of distortion – greatly reduce the effect of the controlled variable of all external disturbances in the forward path An open-loop control system is converted to a closed-loop control system by adding: Measurement of the controlled variable (Output) Comparison of the measured and desired values of the controlled variable. B. Based on the Controlled Variable B.1 Servomechanisms. Feedback control systems used to control position, velocity, and acceleration are very common in industry and military applications. They are known as servomechanisms. A servomechanism is a power-amplifying feedback control system in which the controlled variable is a mechanical position or a time derivative of position such as velocity or acceleration. An automatic aircraft landing system is an example of servomechanism. The aircraft follows a ramp to the desired touchdown point. Another example is the control system of an industrial robot in which the robot arm is forced to follow some desired path in space. B.2 Regulators. A regulator or regulating system is a feedback control system in which the reference input (set-point) or command is constant for long periods of time, generally for the entire time interval during which the system is operational. The objective of the idle-speed control system is known as a regulator system. Another example of a regulator control system is the human biological system that maintains the body temperature at approximately 98.6ºF in an environment that usually has a different temperature. C. Base on Analysis and Design Methods C.1 Linear System. A linear system is a system where input/ output relationships may be represented by a linear differential equation. The plant is linear if it can be accurately described using a set of linear differential equations. This attribute indicates that system parameters do not vary as a function of signal level. For linear systems, the equations that constitute the model are linear. Similarly, the plant is a lumped-parameter (rather than distributed parameter) system if it can be described using ordinary (rather than partial) differential equations. This condition is Page 9 of 20  generally accomplished if the physical size of the system is very small in comparison to the wavelength of the highest frequency of interest. C.2 Time-Variant System. A time-variant is a system if the parameters vary as a function of time. Thus, a time-variant system is a system described by a differential equation with variable coefficients. A linear time variant system is described by linear differential equations with variable coefficients. Its derivatives appear as linear combinations, but a coefficient or coefficients of terms may involve the independent variable. A rocket-burning fuel system is an example of time-variant system since the rocket mass varies during the flight as the fuel is burned. C.3 Time-Invariant System. A time-invariant system is a system described by a differential equation with constant coefficients. Thus, the plant is time invariant if the parameters do not change as a function of time. A linear time invariant system is described by linear differential equations with constant coefficients. A single degree of freedom spring mass viscous damper system is an example of a time-invariant system provided the characteristics of all the three components do not vary with time. C.4 Multivariable Feedback System. The block diagram represents a multivariable feedback system where the interrelationships of many controlled variables are considered. Feedback Systems Feedback is the property of a closed-loop system, which allows the output to be compared with the input to the system such that the appropriate control action may be formed as some function of the input and output. For more accurate and more adaptive control, a link or feedback must be provided from output to the input of an open-loop control system. So, the controlled signal should be fed back and compared with the reference input, and an actuating signal proportional to the difference of input and output must be sent through the system to correct the error. In general, feedback is said to exist in a system when a closed sequence of cause-and-effect relations exists between system variables. Important Features of Feedback (Closed-loop system) 1. Increased accuracy compared with open-loop system 2. Increased tendency toward oscillation or instability 3. Increased bandwidth (bandwidth of a system that ranges frequencies (input) over which the system will respond satisfactorily) 4. Reduced sensitivity (of the ratio of output to input) to variations in system parameters and other characteristics 5. Reduced effects of nonlinearities and distortion 6. Reduced effects of external disturbances or noise Page 10 of 20  The parameters G and H are constant gains. By simple algebraic manipulations, it can be shown that the input-output relation of the system is given by: The general effect of feedback is that it may increase or decrease the gain G. In practical control- systems, G and H are functions of frequency, so the magnitude of (1 + GH) is greater than 1 in one frequency range, but less than 1 in another. Thus, feedback affects the gain G of a non-feedback system by a factor (1 + GH). Basic Components of a Feedback or Closed-Loop System 1. Comparison element (Summing point) – It compares the required value of the variable being controlled with the measured value of what is being achieved and produces an error signal. This element together with control law element is collectively known as controller unit. 2. Control law or implementation element (controller) - It determines what action to take when an error signal is received. The control law used by the element may be just to supply a signal which switches on or off when there is an error, as in a room thermostat, or perhaps a signal which is proportional to the size of the error. With a proportional control law implementation, if the error is small a small control signal is produced and if the error is large a large control signal is produced. Other control laws include integral mode and derivative mode. 3. Correction element (actuator) - Often called the final control element, produces a change in the process which aims to correct or change the controlled condition. The term actuator is used for the element of a correction unit that provides the power to carry out the control action. 4. Process (plant)- The process or plant is the system in which there is a variable that is being controlled, e.g., it might be a room in a house with its temperature being controlled. 5. Measurement element (sensor) - This produces a signal related to the variable condition of the process that is being controlled. For example, it might be a temperature sensor with suitable signal processing. Control Systems Analysis and Design Objectives Control systems engineering consists of analysis and design of control systems configurations. Control systems are dynamic, in that they respond to an input by first undergoing transient response before attaining a steady-state response which corresponds to the input. There are three main objectives of control systems analysis and design. They are: 1. Producing the response to a transient disturbance which is acceptable 2. Minimizing the steady-state errors: Here, the concern is about the accuracy of the steady- state response 3. Achieving stability: Control systems must be designed to be stable. Their natural response should decay to zero values as time approaches infinity or oscillate. Page 11 of 20  System analysis means the investigation, under specified condition, of the performance of a system whose mathematical model is known. Analysis is investigation of the properties and performance of an existing control system. By synthesis we mean using an explicit procedure to find a system that will perform in a specified way. System design refers to the process of finding a system that accomplishes a given task. Design is the selection and arrangement of the control system components to perform a prescribed task. The design of control systems is accomplished in two ways: design by analysis in which the characteristics of an existing or standard system configuration are modified, and design by synthesis, in which the form of the control system is obtained directly from its specifications. A system must be stable to produce the proper transient and steady-state response. Transient response is important because it affects the speed of the system and influences human patience and comfort, not to mention mechanical stress. Steady-state response determines the accuracy of the control system; it governs how closely the output matches the desired response. The design of a control system follows these steps: Step 1 Determine a physical system and specifications from requirements. Step 2 Draw a functional block diagram. Step 3 Represent the physical system as a schematic. Step 4 Use the schematic to obtain a mathematical model, such as a block diagram. Step 5 Reduce the block diagram. Step 6 Analyze and design the system to meet specified requirements and specifications that include stability, transient response, and steady-state performance. Example 1] Antenna azimuth position control system. Page 12 of 20 Example 2] A temperature control system operates by sensing the difference between the thermostat setting and the actual temperature and then opening a fuel valve, an amount proportional to this difference. Draw a functional close-loop block diagram identifying the input and output transducers, the controller, and the plant. Further, identify the input and output signals of all subsystems. Solution: Example 3] An aircraft’s attitude varies in roll, pitch, and yaw as defined in Figure. Draw a functional block diagram for a closed-loop system that stabilizes the roll as follows: The system measures the actual roll angle with a gyro and compares the actual roll angle with the desired roll angle. The ailerons respond to the roll-angle error by undergoing an angular deflection. The aircraft responds to this angular deflection, producing a roll angle rate. Identify the input and output transducers, the controller, and the plant. Further, identify the nature of each signal. Page 13 of 20  Solution: Example 4] During a medical operation an anesthesiologist controls the depth of unconsciousness by controlling the concentration of isoflurane in a vaporized mixture with oxygen and nitrous oxide. The depth of anesthesia is measured by the patient’s blood pressure. The anesthesiologist also regulates ventilation, fluid balance, and the administration of other drugs. To free the anesthesiologist to devote more time to the latter tasks, and in the interest of the patient’s safety, we wish to automate the depth of anesthesia by automating the control of isoflurane concentration. Draw a functional block diagram of the system showing pertinent signals and subsystems (Meier,1992). Solution: Example 5] The figure shown below is a schematic diagram of a liquid-level control system. Here the Here theautomatic automatic controller controllermaintains maintainsthe liquid level bylevel the liquid comparing the actual the by comparing levelactual with a desired levelaand level with correcting desired level any error by adjusting the opening of the pneumatic valve. Draw a closed-loop diagram of this control system and and correcting any error by adjusting the opening of the pneumatic valve. Draw a close-loop label diagram of this each element control of the controlsystem system.and label each element of the control system. Page 14 of 20 Equivalent Block Diagram Modern Applications of Control 1. Flight Control Systems Modern commercial and military aircraft are “fly by wire” Auto-landing Systems, unmanned aerial vehicles (UAVs) are already in place 2. Robotics High accuracy positioning for flexible manufacturing Remote environments: space, sea, noninvasive surgery, etc. 3. Chemical Process Regulation of flow rates, temperatures, concentrations, etc. 4. Communications and Networks Amplifiers and repeaters Congestion control of the Internet Power management for wireless communications 5. Automotive Engine control, transmission control, cruise control, climate control, etc. Emerging Application Areas 1. Material Processing Rapid thermal processing Control of vapor deposition for special purpose materials 2. Noise and Vibration Control Active mounts and speaker systems for noise and vibration reduction Variety of applications: cars, planes 3. Intelligent Vehicle Highway Systems Platooning of cars for high-speed, high-density travel on freeways 4. Smart Engine Compression systems: stall, surge, fluttering control for increased operability Combustion system: operation for leaner air/fuel ratios for low emissions Reflection/Learning Insights Control systems contribute to every aspect of modern society. In our homes we find them in everything from toasters to heating systems to DVD players. Control systems also have widespread applications in science and industry, from steering ships and planes to guiding missiles. Control systems also exist naturally; our bodies contain numerous control systems. Even economic and psychological system representations have been proposed based on control system theory. Control systems are used where power gain, remote control, or Page 15 of 20  conversion of the form of the input is required. A control system has an input, a process, and an output. Control systems can be open loop or closed loop. Open-loop systems do not monitor or correct the output for disturbances; however, they are simpler and less expensive than closed-loop systems. Closed-loop systems monitor the output and compare it to the input. If an error is detected, the system corrects the output and hence corrects the effects of disturbances. Control systems analysis and design focuses on three primary objectives: 1. Producing the desired transient response 2. Reducing steady-state errors 3. Achieving stability A system must be stable to produce the proper transient and steady-state response. Transient response is important because it affects the speed of the system and influences human patience and comfort, not to mention mechanical stress. Steady-state response determines the accuracy of the control system; it governs how closely the output matches the desired response. The design of a control system follows these steps: Step 1 Determine a physical system and specifications from requirements. Step 2 Draw a functional block diagram. Step 3 Represent the physical system as a schematic. Step 4 Use the schematic to obtain a mathematical model, such as a block diagram. Step 5 Reduce the block diagram. Step 6 Analyze and design the system to meet specified requirements and specifications that include stability, transient response, and steady-state performance. Post-test 1. Name three applications for feedback control systems. 2. Name three reasons for using feedback control systems and at least one reason for not using them. 3. Give three examples of open-loop systems. 4. Functionally, how do closed-loop systems differ from open-loop systems? 5. State one condition under which the error signal of a feedback control system would not be the difference between the input and the output. 6. If the error signal is not the difference between input and output, by what general name can we describe the error signal? 7. Name two advantages of having a computer in the loop. 8. Name the three major design criteria for control systems. 9. Name the two parts of a system’s response. Assignment 1. In humans, hormone levels, alertness, and core body temperature are synchronized through a 24-hour circadian cycle. Daytime alertness is at its best when sleep/wake cycles are in sync with the circadian cycle. Thus, alertness can be easily affected with a distributed work schedule, such as the one to which astronauts are subjected. It has been shown that the human circadian cycle can be delayed or advanced through light stimulus. To ensure optimal alertness, a system is designed to track astronauts’ circadian cycles and increase the quality of sleep during missions. Core body temperature can be used as an indicator of the circadian cycle. A computer model with optimum circadian body temperature variations can be compared to an astronaut’s body temperatures. Whenever a difference is detected, the Page 16 of 20  astronaut is subjected to a light stimulus to advance or delay the astronaut’s circadian cycle (Mott, 2003). Draw a functional block diagram of the system. Indicate the input and output signals, intermediate signals, and main subsystems. Give discussion of the functional flow of your block diagram. 2. Control of HIV/AIDS. As of 2012, the number of people living worldwide with Human Immuno- deficiency Virus/Acquired Immune Deficiency Syndrome (HIV/ AIDS) was estimated at 35 million, with 2.3 million new infections per year and 1.6 million deaths due to the disease (UNAIDS, 2013). Currently there is no known cure for the disease, and HIV cannot be completely eliminated in an infected individual. Drug combinations can be used to maintain the virus numbers at low levels, which helps prevent AIDS from developing. A common treatment for HIV is the administration of two types of drugs: reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). The amount in which each of these drugs is administered is varied according to the amount of HIV viruses in the body (Craig, 2004). Draw a block diagram of a feedback system designed to control the amount of HIV viruses in an infected person. The plant input variables are the amount of RTIs and PIs dispensed. Show blocks representing the controller, the system under control, and the transducers. Label the corresponding variables at the input and output of every block. Give discussion of the functional flow of your block diagram. Suggested Readings/Content 1. https://youtu.be/HcLYoCmWOjI?list=PLBlnK6fEyqRhqzJT87LsdQKYZBC93ezDo – Introduction to Control Systems. 2. https://youtu.be/8m0VP5_feOY?list=PLBlnK6fEyqRhqzJT87LsdQKYZBC93ezDo – Close- loop control system. Answer Key Page 17 of 20