Analysis of the Basic Principle behind Process Engineering Control - Term Paper Example

Engineering Control Introduction The basic principle behind process control is a simple one: one or more characteristics of the process must be measured on a regular basis and compared with a desired value, and then the process must be adjusted as necessary based on the results of this measurement. In this way, the current state of the process becomes an input into the next state of the process, which in turn will influence future states; this connection between measurement of current state and actions taken to influence future states is known as feedback. The following diagram outlines the basic structure of a feedback loop: Output value (y) Set point (v) Comparator Process or plant controller Feedback-based control systems are found all over in the natural world. In order to survive, living creatures need to maintain a stable internal environment (known as homeostasis), and this is accomplished through a myriad of feedback loops. Some, like eating when we feel hungry, are obvious; but many others are unnoticed by critically important to maintaining life. For example, blood calcium levels are held steady by controlling the activity levels of cells that build up or break down bone tissue: when calcium levels are high, bone-building cells are stimulated to build more bone and thus remove calcium from the bloodstream, and vice versa. Coordinated movement is also accomplished through feedback; touching your own nose, for example, involves a complex interplay between the actions of the muscles moving your arm and hand, vision, and proprioception. The ability of the brain to manage such feedback loops, and even to create new ones, enables us to use tools, drive cars, and so on. Feedback may be “positive” or “negative”—that is, a change in the controlled system may lead to feedback that in turn causes further change in the same direction (positive feedback), or to feedback that acts against the detected change and influences the system to return to its previous state (negative feedback). As a general rule, negative feedback loops are required in order for systems to achieve relative stability; positive feedback loops, which tend to amplify changes that have already occurred, are inherently destabilizing. Much like organisms, mechanical systems such as manufacturing plants need control systems to maintain their stable operation. The current experiment is designed to demonstrate some of the features of a feedback-based engineering control system, including its properties, concepts, and terminology. A number of key terms and concepts are involved: Feedback Closed-loop control Proportional control Integral control Set-point tracking Steady-state error Stability Controller tuning Step response Theory A key to understanding and controlling any system is the transfer function—a description, in mathematical form, of how the system’s output reflects its input. Any system that accepts some form of input and creates some form of output that varies based on this input has—at least in theory—a transfer function, and most fields of engineering derive and use such functions as a primary tool for controlling processes. Once a system’s transfer function is known, its output can be predicted based on its input; and, significantly for process control, the necessary change in input(s) can be calculated in order to produce a desired output. Input, system output. In the above diagram, for example, a sine-wave input produces a sine-wave output with amplitude reduced by a factor of approximately 0.4 and no change in phase or frequency. The system’s transfer function could thus be written as “output = 0.6 * input”; and for a desired output level, the required input level would be equal to 1 / 0.6. Inputs to a control system are conventionally identified by the letter u, and output as the letter y; the time-dependent functions u(t) and y(t) have Laplace transforms U(s) and Y(s). The actual transfer function is typically designated as G(s) or H(s). The conventional transfer function is thus: Input, transfer function and output. More complex systems may have multiple transfer functions; for example, a system with a feedback loop has one transfer function for its main process, and a separate transfer function for its feedback; the system’s transfer equation combines both transfer functions. Processes are often represented as block diagrams, with each block representing one system with its own transfer function; the lines between blocks represent the signals that pass between them: Input, transfer functions and output for a feedback-control system. In the above example, the small circle represents the combination of the input U(s) with feedback; the minus-sign indicates that the feedback in this case is negative. In other cases, inputs may be summed: More than one transfer functions may be involved even without a feedback loop. Such transfer functions may operate in series, where the output of the first transfer function is the input to the second: Two transfer functions in series. Or they may operate in parallel, with each transfer function receiving the same input and the output of the two transfer functions combined: Two transfer functions in parallel. Systems that utilize feedback loops for control are known as closed-loop control systems; those that do not utilize feedback are known as open-loop control systems. A typical example of a computer-controlled closed-loop system (with an analog-to-digital converter to make the measured output intelligible to the computer) is illustrated below: A closed-loop control system. While biological feedback-based control systems operate on an essentially continuous basis, engineered control system generally involve discrete measurements taken at a fixed frequency. The drive signal (that is, the signal from the controller that causes change in the controlled system) is typically changed once each measurement cycle; in any case, it is not changed more frequently since there would be no new information available to determine a new drive-signal setting. Each time a new measurement is taken, the control system determines any change needed in the control signal; this control signal, in turn, causes the controlled system to approach (or remain at) the desired state. There are several general types of control system available. The simplest is the on-off controller—a system (for example, a standard thermostat) that turns something on or off depending on a measured value. On-off controllers are cheap and effective (and, as a result, in very wide use), but because they lack the ability to make precise changes in the controlled system, they tend to create oscillations within limits rather than genuine stability. (Anyone who has sat in a room changing from slightly-too-warm to slightly-too-cold and back again is familiar with this disadvantage of on-off control systems.) Proportional controllers are more complex than on-off controllers, but offer more precise, smoother operation. Instead of just turning something on or off, a proportional controller varies the drive signal in proportion to the current error—the difference between the measured value and the desired result. For example, the driver of a car will make a large change (flooring the gas pedal or the brake) when a large change in velocity must be made quickly, but will make much smaller corrections to maintain cruising speed on a level, straight road. The relationship between the size of the current error and the size of the resulting correction is described as the controller’s gain, expressed mathematically as Kp. A proportional control system is shown in the diagram below: An integral controller is similar to a proportional controller, but instead of responding proportionally to each new current error, the integral controller responds to the integral of the error (that is, the total error over a period of time); the integral controller has a transfer function expressed as Ki/s rather than the proportional controller’s simple gain function Kp. Integral controllers avoid one typical weakness of proportional controllers: the latter are typically subject to “droop”, meaning that since the proportional controller responds only weakly to a minor deviation from the desired state, in some situations a proportional controller will leave a system in a relatively steady state that is close to the desired state, but never quite reaches the desired state. Integral controllers avoid this because they react more strongly to small deviations that persist over time; but on the other hand, integral controllers are also more subject to “overshoot” than proportional controllers. One of the most common control systems for industrial operations is known as “PID”—Proportional-Integral-Derivative. This type of controller examines input measurements in three ways: the proportional element compares the most recent measurement to the desired value and determines the current error; the integral element calculates its error based on the sum of a set of recent measurements; and the derivative element measures the trend of recent measurements, providing a damping effect (and thus reducing overshoot) when the measured value is changing rapidly. The results of all three of these elements are weighted according to individually-configured gains and combined to determine the output function, which will impact the state of the system and thus bring the measured parameter back into its desired range. (Another way of explaining the three elements of PID control is that they represent responses to the controlled system’s present, past, and predicted future, respectively.) The proportional element is usually dominant in a PID controller, with the integral and derivative elements present as correctives. It is common for one (or sometimes even two) of the elements in a PID controller to be left out or disabled (by setting the relevant gain Kp, Ki, or Kd equal to zero); in particular, the derivative element is often left out, resulting in a PI (Proportional-Integral) controller. The derivative element, while often useful since it responds to predicted errors that have not yet occurred, is also very sensitive to measurement errors since it involves a degree of extrapolation; this means that for some systems the derivative element can lead to lower, rather than improved, stability. Both simple proportional controllers and more complex PID controllers are superior to on-off controllers in that they do not suffer from the latter’s constant over-control-and-correct behavior. Which variation (generally PID, PI, P, or I) is optimal for controlling a particular process depends on the nature of that process, and of the measurements available to the control apparatus. Although PID control systems are relatively simple in theory and structure, there are many variations in how they are used. PID control parameters require a good deal of “tweaking” for optimal operation, and many engineers and plant operators in fact never properly “tune” their PID controllers for optimal performance. System Response Parameters While PID controllers can be tuned by trial and error, this process can be very time-consuming. Instead, several parameters that characterize the response (that is, the transfer function) of the system to be controlled can be measured while the system is in an “open loop” state—that is, without a feedback-based controller in operation. These parameters, in turn, can be entered into an algorithm (of which many exist) that determines a set of optimal or near-optimal gains to be used in configuring a PID controller. There are three principal parameters measured for this purpose: the system’s pure time delay (also known as “dead time”)—the interval between a controller’s change in signal (opening a valve, turning on a heater, or whatever else the controller will control) and the first observed change in the measured value that represents a response to this signal change; the system’s time constant, a measure of how fast the observed value changes once the pure time delay interval has passed; and the system’s gain, a measure of the direction and size of change in the observed value caused by a given change in the controller’s output signal. The experiment Description of apparatus In order to investigate the properties and performance of a PID controller, a simple system was used consisting of a blower to draw air from the environment, propel it past a heating grid, and then along a tube with several thermometers along it. The objective was to tune the controller to reach and maintain a particular temperature in the air flowing through the tube. In addition to the basic hardware, a computer was configured to receive temperature measurements and send a control signal to the heating grid, with a software package acting as the PID controller. This program had tunable gains for its proportional, integral, and derivative control elements. Test procedure The experiment consisted of four sections; the first three involved manual tuning of the PID controller (with the derivative element disabled in all three cases), while the fourth case used observations of open-loop system response and a special computer program to create a set of tuning parameters for the PID controller. 1. For the first set of runs, Ki and Kd were set to zero to create a pure proportional controller; the controller’s set point was set at 25 degrees, and the heat sensor furthest from the heating grid was connected to the controller. For each run, a different proportional gain Kp was used and the results plotted. The proportional gain at which the system began to behave in an unstable manner was noted, as was the gain which gave the best response. 2. For the second set of runs, Kp was set to zero and Ki was varied in order to test a pure integral controller. The set point and measurement location were the same as for the previous set of runs. Again, the results of each run were graphed, and a note was made of the optimal setting for Ki and the gain at which instability began. 3. For the third set of runs, Kd was left at zero but Kp and Ki were varied; various combinations of Kp and Ki were graphed until an apparently optimal pair of settings had been found. As before, the onset of instability was noted. 4. For the fourth portion of the experiment, a different software package was used to test the apparatus in “open loop” mode and determine its transfer-function parameters by measuring its step response. The transfer function was calculated using the formula: Where K is the system’s D.C. gain, Td is its pure time delay, and Tp is the system’s time constant, as measured by the open-loop run. Each student calculated K, Td, and Tp separately; then the average value for each of these parameters was entered into a simulation program which used them to calculate optimal Kp, Ki, and Kd paramaters for the PID controller. Finally, the experiment was run as in Sections 1-3 above, using these optimal parameters, and the results were graphed. Results The results of the various experimental runs are presented as graphs on the following pages. The calculation of D.C. gain, pure time delay, and time constant were performed using the following formulae: Gain Time Constant Pure Time Delay The three members of the team calculated the following values for K, Tp, and Td: K Tp Td Member 1 1.33 0.91 0.38 Member 2 1.23 0.88 0.44 Member 3 1.28 0.73 0.37 Average 1.28 0.84 0.397 Accuracy of results The main source of inaccuracy in this experiment was the characteristics of the system being controlled—basically the response of the heating grid to the control signal and the precision of the heat sensor. The computerized controller itself was not a significant source of inaccuracy. It was observed that repeated runs with the same controller settings produced graphs that were not completely identical, but were similar enough to indicate that the system in fact behaved in a very predictable manner. Of course, in a real-world industrial environment, more elaborate control and measurement equipment would be used to reduce the system’s errors, and thus result in more efficient operation of the controlled system. Conclusion The various trial-and-error runs allowed us to observe the behavior of the system with various proportion and integral gains, with the PID controller operating in pure-proportional, pure-integral, and proportional-integral modes. We observed the following: The proportional controller gave relatively stable results with a large error when Kp was set low; as Kp was increased, the system reached its set point faster, but experienced overshoot and became increasingly unstable. The integral controller showed a relatively slow response for all values of Ki, but at higher values of Ki the integral controller caused unstable system behavior. It was apparent that trial and error could be used to derive optimal or near-optimal PID controller settings; but in a real-world application, this would be very time-consuming and (given the likelihood of significant overshoot with an untuned or badly-tuned controller) could easily result in damage to expensive system components. The alternative approach, measuring open-loop system performance and thus deriving optimal PID controller parameters, is clearly much faster and much more economical than the trial-and-error method; but it became clear that precise and accurate measurements are necessary to ensure that the parameters derived are really optimal. The limitations of our measurements in this experiment resulted in less than fully successful controller optimization. References This report was based on the following references: “Flight control E2.2” class notes. The lab handout. The following Internet sites: 1. http://www2.mne.psu.edu/me86/Chapter3/Chapt3.pdf 2. www-control.eng.cam.ac.uk/ extras 3. www.cdc.gov/niosh/asphalt.html - 50k 4. www.standards.its.dot.gov/Documents/TCIP1407.pdf 5. http://www.miamidade.gov/emprel/pay_plan/job_008390.htm Read More