Maglev Controller Design


 Edwin Rodgers
 1 years ago
 Views:
Transcription
1 Maglev Controller Design By: Joseph Elliott Nathan Maher Nathan Mullins For: Dr. Paul Ro MAE 435 Principles of Automatic Controls Due: May 1, 2009
2 NJN Control Technologies 5906 Wolf Dale Ct. Suite 1 Raleigh, NC April 30, 2009 Dr. Paul Ro Chief Engineer Magnetech Inc. 42 Broughton Dr. Raleigh, NC Dear Dr. Ro: After reviewing the proposal and design guidelines for the control system on Magnetech s new maglev train, we have come up with a suitable solution. We explored many different possible controller designs, including critically damped gain, PID, and dual polezero controllers. In our opinion, a controller of the following form is the most suitable given the design guidelines: 4 s s s 2 + 6s This controller provides the best control action possible for the design criteria. The time response of this controller has a quick settling time of ~1 second and a steadystate error of zero due to the introduction of a pure integrator. There is no overshoot with this controller design. The controller also uses less coil current than the maximum stated in the design guideline. The frequency response of this controller is also superior. It has a closedloop bandwidth from input to output of over 6.5 Hz, above the recommended 2 Hz. The Bode plot from disturbance to output shows that the controller should attenuate all disturbances, with a minimum attenuation of 10dB. This controller also has been shown to be stable for all gains, based on root locus analysis and gain margin. The gain margin is infinite for this system. The phase margin is 90 degrees, above the 30 degree recommended for a system like this. When testing this controller in a closedloop scenario with a step input and a sinusoidal disturbance of amplitude 1.0 (at the least attenuated frequency in the bandwidth), the response received was within 25% of the desired steady state output at all times. Testing with a step input and step disturbance of amplitude 1.0 gave a response within 20%. The coil current also did not exceed the maximum in either scenario. Please review the attached proposal for more detail involving this controller and other options that were considered but are not recommended. Sincerely, Nathan Maher Senior Staff Engineer Enclosure Joseph Elliott Senior Staff Engineer Nathan Mullins Senior Staff Engineer
3 Table of Contents 1. Introduction OpenLoop Response Critically Damped Proportional Control PID Controllers Custom Controller Design Final Evaluation References Appendix...20
4 Introduction As a contractor for Magenetch, Inc., we were introduced to the problem occurring with the control system on the new maglev train design. The problem was introduced as a need to control the air gap between the train and track. As experts in the field of controls, the associates at NJN Control Technologies considered multiple designs to devise the best controller for the job. This report details the issues posed by the maglev system and the corrections made by various controllers. Open Loop Response The original maglev train system for the air gap can be seen in Figure 1 below. Desired Air Gap R(s) Coil Current Air Gap C(s) Figure 1: Maglev Train System Amplitude This system transfer function is the mathematical approximation of how the maglev train system reacts to a given input. This transfer function is in the LaPlace Domain, and is inherent to the train s physical design (regardless of disturbance). Using a software package, Matlab, it is possible to graph the response of this system to a step input. Below is a graph of time response of the maglev train system with no control action. Time (s) Figure 2: Open Loop Time Response The step input applied to the system was a step input with amplitude of 1.0, beginning at a time of 1.0 second. As you can see from the figure, the response has several negative aspects. First, the steadystate error of the openloop response is very large. A perfect system would have the steadystate value of amplitude 1.0, while this system has the steadystate value of around 0.4. There also exists a large amount of oscillation in the response. Clearly control action is needed to correct the system s response. 4
5 Critically Damped Proportional Controller For all of the controllers attempted in this report, the same basic system block diagram is utilized. The following is the block diagram of the closed loop system. The controller is represented by Gc(s). Figure 3: Block Diagram of Maglev System with Controller in Place The first option for a controller is a pure proportional control. The proportional control acts like a spring. This proportional controller was selected so that the system will then be critically damped. A critically damped system will not have oscillation in the response. Judging by the rootlocus of the system, the resulting gain at critical damping was The root locus graph is shown below. Figure 4: Root Locus of Maglev System The Simulink block diagram used for this controller is shown below. In this case, K= See the Appendix for calculations. 5
6 Figure 5: Simulink Block Diagram for System with Proportional Gain Although this controller eliminated the oscillation, it did not eliminate steadystate error, and thus was unfit for a final solution. The time response graph showing this is below. Note that the final value is around 0.3, much different than the 1.0 step input. Figure 6: Time Response for System with Proportional Gain However, the coil current at this point was used as a reference point to define the maximum coil current. Since higher proportional gains can be used to control this system at large cost (due to the large amount of coil current involved), the problem proposed by Magnetech Inc. stated that the maximum coil current could be four times the critically damped coil current. This set the value of maximum coil current at 4*1.23=
7 PID Controllers One of the easiest ways to correct a system response is to add a Proportional, Derivative, Integral controller, or PID. This is an easy way to correct the system because it is easy to visualize what each portion of the controller does. Adding integral control action will correct the steadystate error of the system, but can contribute to too much oscillation. The derivative action will damp out the system response, but can create some error. For this system, several different PID controllers were examined. Each controller provided different responses and different advantages and disadvantages. Three different figures are used to display the effectiveness of these controllers. First of all, the time response will show the action of the controller with respect to time. This is important in determining steadystate error, oscillation, overshoot, settling and rise times. The following figure shows the time response of the maglev system with four different PID controllers. Figure 7: Time Response for System with PID Control The RC Bode plot is a graph of the system from input to output, with respect to frequency. Figure 8 shows how the system will react to different frequency inputs. The important thing to note on this plot is when the graph drops below 3dB. The frequency at this point is called the bandwidth of the system and is a cutoff point for a system having good command following. Beyond that point, the system will not follow the input. 7
8 Figure 8: RC Bode Plots for System with PID Control The Bode plot from DC, or from disturbance to output shows how well the system will reject a disturbance. Ideally, the magnitude plot from DC should be below zero for all frequencies. Figure 9: DC Bode Plots for System with PID Control 8
9 The open loop Bode plot is important for determining the system stability. Gain and phase margin can be gleaned, and the higher the value of each, the stabler the system. Gain margin must be >0, and phase margin must be >30 to satisfy most design criteria. Figure 10: Open Loop Bode Plots for System with PID Control Figure 11: Root Locus for System with PID Control 9
10 Root locus plots visualize the position of the poles and zeroes of both the train system and the controller. Information that can be gathered from these plots includes damping ratio, overshoot, and speed of the response with respect to gain. These figures will aid in the discussion of the four PID controllers explored during this stage of the investigation. The simulink diagram for the PID controllers is shown below: Figure 12: Simulink Block Diagram for System with PID Control PID 1 For the first PID controller, the gains were randomly selected as Proportional=2, Integral=2, Derivative=2. These gains did not work at all for this system, as they produced an unstable response and also required an infinite amount of coil current. The derivative gain in this case was too large and was causing the response to become unrealistic. From Figure 7, one can see that the time response was unacceptable because it had large oscillation and very long settling time. The steadystate error, while better than the proportional only case, was not very good. Judging from the Bode diagram from RC (Figure 8), this controller would also have very low bandwidth, and poor command following. It drops rapidly below 3dB, and the phase graph is also very inconsistent. The disturbance rejection of this system is okay because the magnitude of the DC Bode plot is below zero for all frequencies. PID 2 The second PID controller eliminated the derivative gain that was causing the issues (making it PI only). The second controller had Proportional=3 and Integral=6. For this controller, the main issue was the time response. The settling time was very long (5 sec). Also, the RC Bode plot showed some fluctuation in the magnitude plot. Because of these issues, it was decided to increase the proportional gain and integral gain in order to speed up the system settling time and eliminate the fluctuations in the RC Bode plot. PID 3 The third PI controller used Proportional=4.92 (the maximum) and Integral=50. This controller improved on the previous design with a low settling time and very high bandwidth. A concern arose with this PID: it had a ~3.4% overshoot, and the maximum allowed is 1.5% according to the design guideline indicating that ξ (damping ratio) must be greater than
11 PID 4 Our final PI controller is a variation of PID 3, lowering the Integral gain slightly to 30. This reduces the % overshoot to an acceptable level. The proportional gain was also reduced to meet the maximum coil current specification. The time response of this controller displays its fast rise time and settling time (~1.25 s) to a steady state error of zero. The RC Bode plot indicates this controller provides good command following well beyond the stated bandwidth of 2 Hz, out to ~7 Hz. The DC Bode plot exhibits good disturbance attenuation; a minimum attenuation of 10 db is achieved. Looking at the open loop Bode plot, the phase margin is determined to be ~90, well above the 30 minimum required for stability. This plot has an infinite gain margin, which is invalid in determining stability. PID Conclusion Through experimentation, it was determined that the maximum coil current tracks with the proportional gain in a PI controller. To reduce coil current, the proportional gain can be reduced, but this will sacrifice performance throughout the system. Increasing integral gain reduces settling time but can lead to increased oscillation. Custom Controller Design In this section, we took our knowledge of the system s response to PID control and applied it to a more customizable control solution in which two poles and two zeroes can be used in the controller. As in the section above, graphs of each system characteristic are made which include data from each controller. Figure 13: Time Responses for System with Custom Control 11
12 Figure 14: RC Bode Plots for System with Custom Control Figure 15: Open Loop Bode Plots for System with Custom Control 12
13 Figure 16: DC Bode Plots for System with Custom Control Figure 17: Root Locus of System with Custom Control 13
14 Controller 1 Controller 1 is defined by the transfer function below: 4.34 s s + 11 Equation 1 This controller was designed to direct the root locus (Figure 17) to the real axis quickly by adding a zero on the real axis. This function has good damping at low gain values. Due to this function s lack of a pure integrator, the time response (Figure 13) for this system revealed a large steady state error, rendering this function useless. It also has a bandwidth of zero as shown in Figure 14. Controller 2 Controller 2 was then made with integral action to mitigate steady state error. Equation 2 4 s s s Looking at the time response of the system, it does not rise close enough to unity right away, leading to a long settling time of 2.75s. The RC Bode plot (Figure 14) magnitude comes close to the 3 db limit at ~0.5 Hz, and the phase plot shows some oscillation of about 10 degrees. We sought to improve the RC Bode response and the settling time. The disturbance rejection was acceptable as evidenced by Figure 16. Controller 3 This controller improves on controller 2 while maintaining a similar root locus pattern. This method improves the time response and RC Bode somewhat, but not enough. The response of this system was not fast enough. Equation s s 2 + 8s Controller 4 We decided to move the zeroes off of the real axis for controller 4, and saw increased time response performance and a flatter RC Bode plot. By moving the zeroes of the controller closer to the poles of the system, the response sped up. Equation 4 4 s s s 2 + 5s Controller 5 This is our final controller. The performance of this controller is the best we have to offer given the coil current restriction. The transfer function of this controller is given below: Equation 5 4 s s s 2 + 6s 14
15 A compilation of the critical system plots for Controller 5 is shown below: Figure 18: Controller 5 Diagram Compilation Controller 5 has a very good time response, with no overshoot. By moving the pole farther out on the real axis, the overshoot was decreased. The settling time is worse than controller 4, but the difference is very small. The closeness of the zeroes to the system poles allows for a response very close to the input. The RC Bode plot magnitude crosses the 3dB threshold at ~6.52 Hz well beyond the 2 Hz required for a maglev system. While there is a sharp peak in the disturbance rejection as shown in Figures 16 and 18, this peak does not go above 9 db, so an ample attenuation of the disturbance is achieved. The gain margin for this system is infinity, and the phase margin is ~90 degrees, as determined by the open loop Bode plot in Figure 15. The following figure shows the block diagram in Simulink for this controller. 15
16 Figure 19: Simulink Block Diagram for System with LeadLag Control Evaluation of Final Controller When designing this controller, it was possible to get a very good response from the system while still staying in the allowable control current range to keep the cost of the system down. In this section, the different goals listed in Part C of the design guidelines will be examined with respect to the chosen controllertrain system. First of all, the root locus of the system shows that it will never go unstable. This is important for a situation like a Maglev train where safety is of great concern and control of the gap between the train and track must be maintained. The time response of the system has a very fast rise time. The system is not very oscillatory and has no overshoot. The time response also shows that the system settles quickly, within about one second, and thanks to the addition of a pure integrator, there is no steady state error in our design. Judging by the RC Bode diagram for the system, we can see that this controller allows for a bandwidth of around 6.5 Hz. This means that the system will be capable of tracking a wide range of input frequencies very well. Taking a look at the DC Bode plot, we see that our controller has adequate disturbance rejection characteristics. The Bode plot for the system never amplifies the system disturbance and always maintains an attenuation of at least 9 db over all frequencies. The open loop Bode plot was also examined to determine gain and phase margins. The gain margin of this system with the chosen controller is infinite, (as displayed in the root locus). The phase margin of the system was determined to be about 90 degrees, well above the 30 degree design guideline for most systems. To demonstrate the effectiveness of our controller, different disturbances were input. We explored the effects of both step and sinusoidal disturbances on the time response. 16
17 Figure 20: System Response to Step Disturbance with Controller 5 Figure 20 shows the time response of our system to a step input of 1. This should simulate driving the train to twice its standard height. Due to our control action, the train remained within 20% of its nominal height. Figure 21: System Response to Sinusoidal Disturbance with Controller 5 17
18 In Figure 21, we see the effects of a sinusoidal disturbance of magnitude 1 at the frequency least attenuated by our controller. Controller 5 reduces the effect of this disturbance, maintaining a position within 25% of the nominal value. Having decided on our controller, there are some things that could have been improved. The damping ratio of our system is much smaller than suggested which, if increased, could eliminate the small amount of oscillation seen in our system. This would potentially slow the system down but with some more manipulation of the poles and zeros a controller could possibly have been developed that would be as fast as our system but with less oscillation. The DC Bode diagram shows that our system has good disturbance rejection, though this could have been improved given more time. We would also have liked to try a feed forward disturbance rejection setup to entirely, or nearly entirely, eliminate the influence of any disturbance on the train s height. The cost was a major limitation during the design of this controller. If the control current could have been raised, the controller would have responded better and been faster at damping out disturbances. Given the limitations, the controller does a very good job of controlling the system by keeping it stable and eliminating the effect of disturbances quickly. Another limitation of the system was the restriction on polezero cancellation. The design guidelines stated that the zeroes of the controller could not be placed within 2.0 rad/s of the poles of the system. In general, it was found that the closer the zeroes of the controller got to those poles, the better the response of the system became. The system response became faster and tracked the input better. By placing the poles as close as possible to the zeroes without breaking the restriction, we were able to produce the best response. Without this restriction, it would have been possible to produce a faster and more accurate response. 18
19 References Franklin, Gene F., J. David Powell, and Abbas EmamiNaeini. Feedback Control of Dynamic Systems. 5th ed. Upper Saddle River, NJ: Pearson Prentice Hall, Ro, Paul I. "Design Project for MAE 435." to the author Ro, Paul I. "Lecture notes for MAE 435." to the author
20 Appendix This appendix holds the calculations for the critically damped case. Based on Figure 3 in the body of the report, the system transfer function is: Equation 6 Adding a critically damped gain K, the closed loop system transfer function becomes: Equation 7 The closedloop characteristic equation is: Equation 8 The standard second order equation has the form: Equation 9 Where ωn is the natural frequency, and ζ is the damping ratio. Thus, we can equate: Equation 10 In a critically damped case, the damping ratio ζ=1. Knowing this, it is possible to solve for gain K thusly: Equation 11 Since there cannot be negative gain, the correct critically damped gain is K= The limit on coil current is 4*K=
Controller Design in Frequency Domain
ECSE 4440 Control System Engineering Fall 2001 Project 3 Controller Design in Frequency Domain TA 1. Abstract 2. Introduction 3. Controller design in Frequency domain 4. Experiment 5. Colclusion 1. Abstract
More informationECE 3510 Final given: Spring 11
ECE 50 Final given: Spring This part of the exam is Closed book, Closed notes, No Calculator.. ( pts) For each of the timedomain signals shown, draw the poles of the signal's Laplace transform on the
More informationEE 402 RECITATION #13 REPORT
MIDDLE EAST TECHNICAL UNIVERSITY EE 402 RECITATION #13 REPORT LEADLAG COMPENSATOR DESIGN F. Kağan İPEK Utku KIRAN Ç. Berkan Şahin 5/16/2013 Contents INTRODUCTION... 3 MODELLING... 3 OBTAINING PTF of OPEN
More informationPositive Feedback and Oscillators
Physics 3330 Experiment #6 Fall 1999 Positive Feedback and Oscillators Purpose In this experiment we will study how spontaneous oscillations may be caused by positive feedback. You will construct an active
More informationΣ _. Feedback Amplifiers: One and Two Pole cases. Negative Feedback:
Feedback Amplifiers: One and Two Pole cases Negative Feedback: Σ _ a f There must be 180 o phase shift somewhere in the loop. This is often provided by an inverting amplifier or by use of a differential
More informationFirst Order System. Transfer function: Response to a unit step input is: Partial Fraction Expansion leads to: Inverse Laplace transform leads to:
First Order System Transfer function: Response to a unit step input is: Partial Fraction Expansion leads to: Inverse Laplace transform leads to: First Order System At t = T, the output is: T represents
More informationDesign of a TL431Based Controller for a Flyback Converter
Design of a TL431Based Controller for a Flyback Converter Dr. John Schönberger Plexim GmbH Technoparkstrasse 1 8005 Zürich 1 Introduction The TL431 is a reference voltage source that is commonly used
More informationNoise Canceling Headphones Shizhang Wu Supervisor: Ed Richter, Arye Nehorai, Walter Chen
Noise Canceling Headphones Shizhang Wu Supervisor: Ed Richter, Arye Nehorai, Walter Chen Department of Electrical and Systems Engineering Washington University in St. Louis Fall 2008 Abstract In this undergraduate
More informationMATLAB Control System Toolbox Root Locus Design GUI
MATLAB Control System Toolbox Root Locus Design GUI MATLAB Control System Toolbox contains two Root Locus design GUI, sisotool and rltool. These are two interactive design tools for the analysis and design
More informationLaboratory 4: Feedback and Compensation
Laboratory 4: Feedback and Compensation To be performed during Week 9 (Oct. 2024) and Week 10 (Oct. 2731) Due Week 11 (Nov. 37) 1 PreLab This PreLab should be completed before attending your regular
More informationUnderstanding Poles and Zeros
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.14 Analysis and Design of Feedback Control Systems Understanding Poles and Zeros 1 System Poles and Zeros The transfer function
More informationDCMS DC MOTOR SYSTEM User Manual
DCMS DC MOTOR SYSTEM User Manual release 1.3 March 3, 2011 Disclaimer The developers of the DC Motor System (hardware and software) have used their best efforts in the development. The developers make
More informationThe Calculation of G rms
The Calculation of G rms QualMark Corp. Neill Doertenbach The metric of G rms is typically used to specify and compare the energy in repetitive shock vibration systems. However, the method of arriving
More informationRoot Locus. E(s) K. R(s) C(s) 1 s(s+a) Consider the closed loop transfer function:
Consider the closed loop transfer function: Root Locus R(s) +  E(s) K 1 s(s+a) C(s) How do the poles of the closedloop system change as a function of the gain K? The closedloop transfer function is:
More informationUnderstanding Power Impedance Supply for Optimum Decoupling
Introduction Noise in power supplies is not only caused by the power supply itself, but also the load s interaction with the power supply (i.e. dynamic loads, switching, etc.). To lower load induced noise,
More informationMatlab and Simulink. Matlab and Simulink for Control
Matlab and Simulink for Control Automatica I (Laboratorio) 1/78 Matlab and Simulink CACSD 2/78 Matlab and Simulink for Control Matlab introduction Simulink introduction Control Issues Recall Matlab design
More informationTesting a power supply for line and load transients
Testing a power supply for line and load transients Powersupply specifications for line and load transients describe the response of a power supply to abrupt changes in line voltage and load current.
More informationFrequency response of a general purpose singlesided OpAmp amplifier
Frequency response of a general purpose singlesided OpAmp amplifier One configuration for a general purpose amplifier using an operational amplifier is the following. The circuit is characterized by:
More informationChapter 9: Controller design
Chapter 9. Controller Design 9.1. Introduction 9.2. Effect of negative feedback on the network transfer functions 9.2.1. Feedback reduces the transfer function from disturbances to the output 9.2.2. Feedback
More informationR f. V i. ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response
ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response Objective: Design a practical differentiator circuit using common OP AMP circuits. Test the frequency response
More informationTEACHING AUTOMATIC CONTROL IN NONSPECIALIST ENGINEERING SCHOOLS
TEACHING AUTOMATIC CONTROL IN NONSPECIALIST ENGINEERING SCHOOLS J.A.Somolinos 1, R. Morales 2, T.Leo 1, D.Díaz 1 and M.C. Rodríguez 1 1 E.T.S. Ingenieros Navales. Universidad Politécnica de Madrid. Arco
More informationChapter 12: The Operational Amplifier
Chapter 12: The Operational Amplifier 12.1: Introduction to Operational Amplifier (OpAmp) Operational amplifiers (opamps) are very high gain dc coupled amplifiers with differential inputs; they are used
More informationFrequency Response of Filters
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 2 Frequency Response of Filters 1 Introduction Objectives To
More informationEAC215 Homework 4. Page 1 of 6
EAC215 Homework 4 Name: 1. An integrated circuit (IC) opamp has (a) two inputs and two outputs (b) one input and one output (c) two inputs and one output 2. Which of the following characteristics does
More informationVCO K 0 /S K 0 is tho slope of the oscillator frequency to voltage characteristic in rads per sec. per volt.
Phase locked loop fundamentals The basic form of a phase locked loop (PLL) consists of a voltage controlled oscillator (VCO), a phase detector (PD), and a filter. In its more general form (Figure 1), the
More informationSystem Modeling and Control for Mechanical Engineers
Session 1655 System Modeling and Control for Mechanical Engineers Hugh Jack, Associate Professor Padnos School of Engineering Grand Valley State University Grand Rapids, MI email: jackh@gvsu.edu Abstract
More informationHITACHI INVERTER SJ/L100/300 SERIES PID CONTROL USERS GUIDE
HITACHI INVERTER SJ/L1/3 SERIES PID CONTROL USERS GUIDE After reading this manual, keep it for future reference Hitachi America, Ltd. HAL1PID CONTENTS 1. OVERVIEW 3 2. PID CONTROL ON SJ1/L1 INVERTERS 3
More informationDr. Yeffry Handoko Putra, S.T., M.T
Tuning Methods of PID Controller Dr. Yeffry Handoko Putra, S.T., M.T yeffry@unikom.ac.id 1 Session Outlines & Objectives Outlines Tuning methods of PID controller: ZieglerNichols Openloop CoonCohen
More informationUNIVERSITY OF NORTH CAROLINA AT CHARLOTTE. Department of Electrical and Computer Engineering
UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering Experiment No. 5  GainBandwidth Product and Slew Rate Overview: In this laboratory the student will explore
More informationElectronics for Analog Signal Processing  II Prof. K. Radhakrishna Rao Department of Electrical Engineering Indian Institute of Technology Madras
Electronics for Analog Signal Processing  II Prof. K. Radhakrishna Rao Department of Electrical Engineering Indian Institute of Technology Madras Lecture  18 Wideband (Video) Amplifiers In the last class,
More informationFILTER CIRCUITS. A filter is a circuit whose transfer function, that is the ratio of its output to its input, depends upon frequency.
FILTER CIRCUITS Introduction Circuits with a response that depends upon the frequency of the input voltage are known as filters. Filter circuits can be used to perform a number of important functions in
More informationDrivetech, Inc. Innovations in Motor Control, Drives, and Power Electronics
Drivetech, Inc. Innovations in Motor Control, Drives, and Power Electronics Dal Y. Ohm, Ph.D.  President 25492 Carrington Drive, South Riding, Virginia 20152 Ph: (703) 3272797 Fax: (703) 3272747 ohm@drivetechinc.com
More informationY(s) U(s) The continuous process transfer function is denoted by G: (Eq.4.40)
The Process PID control tuner provides the open and closed loop process system responses for a continuous process model (G) with a continuous PID controller (Gc). The Process model can be characterized
More informationFully Differential CMOS Amplifier
ECE 511 Analog Electronics Term Project Fully Differential CMOS Amplifier Saket Vora 6 December 2006 Dr. Kevin Gard NC State University 1 Introduction In this project, a fully differential CMOS operational
More informationLab #9: AC Steady State Analysis
Theory & Introduction Lab #9: AC Steady State Analysis Goals for Lab #9 The main goal for lab 9 is to make the students familar with AC steady state analysis, db scale and the NI ELVIS frequency analyzer.
More informationOPERATIONAL AMPLIFIERS. o/p
OPERATIONAL AMPLIFIERS 1. If the input to the circuit of figure is a sine wave the output will be i/p o/p a. A half wave rectified sine wave b. A fullwave rectified sine wave c. A triangular wave d. A
More informationPart I: Operational Amplifiers & Their Applications
Part I: Operational Amplifiers & Their Applications Contents Opamps fundamentals Opamp Circuits Inverting & Noninverting Amplifiers Summing & Difference Amplifiers Integrators & Differentiators Opamp
More informationDIRECT torque control (DTC) of induction motors has
76 IEEE POWER ELECTRONICS LETTERS, VOL. 3, NO. 2, JUNE 2005 Constant and High Switching Frequency Torque Controller DTC Drives C. L. Toh, N. R. N. Idris, Senior Member, IEEE, and A. H. M. Yatim, Senior
More informationCHAPTER 16 OSCILLATORS
CHAPTER 16 OSCILLATORS 161 THE OSCILLATOR  are electronic circuits that generate an output signal without the necessity of an input signal.  It produces a periodic waveform on its output with only the
More informationSystem Identification and State Feedback Controller Design of Magnetic Levitation System
International Journal of Engineering and Technical Research (IJETR) ISSN: 23210869, Volume2, Issue6, June 2014 System Identification and State Feedback Controller Design of Magnetic Levitation System
More informationThe front end of the receiver performs the frequency translation, channel selection and amplification of the signal.
Many receivers must be capable of handling a very wide range of signal powers at the input while still producing the correct output. This must be done in the presence of noise and interference which occasionally
More informationOperational Amplifiers  Configurations and Characteristics
Operational Amplifiers  Configurations and Characteristics What is an Op Amp An Op Amp is an integrated circuit that can be used to amplify both DC and AC signals. One of the most common Op Amps available
More informationThe output signal may be of the same form as the input signal, i.e. V in produces V out
What is an amplifier? Operational Amplifiers A device that takes an input (current, voltage, etc.) and produces a correlated output Input Signal Output Signal Usually the output is a multiple of the input
More informationENGR 210 Lab 11 Frequency Response of Passive RC Filters
ENGR 210 Lab 11 Response of Passive RC Filters The objective of this lab is to introduce you to the frequencydependent nature of the impedance of a capacitor and the impact of that frequency dependence
More informationlaboratory guide 2 DOF Inverted Pendulum Experiment for MATLAB /Simulink Users
laboratory guide 2 DOF Inverted Pendulum Experiment for MATLAB /Simulink Users Developed by: Jacob Apkarian, Ph.D., Quanser Hervé Lacheray, M.A.SC., Quanser Michel Lévis, M.A.SC., Quanser Quanser educational
More informationResponse to Harmonic Excitation Part 2: Damped Systems
Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost
More informationRLC Resonant Circuits
C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document
More informationOp Amp Bandwidth and Bandwidth Flatness. OPEN LOOP GAIN db. Figure 1: Frequency Response of Voltage Feedback Op Amps
TUTORIAL Op Amp Bandwidth and Bandwidth Flatness BANDWIDTH OF VOLTAGE FEEDBACK OP AMPS The openloop frequency response of a voltage feedback op amp is shown in Figure 1 below. There are two possibilities:
More informationSee Horenstein 4.3 and 4.4
EE 462: Laboratory # 4 DC Power Supply Circuits Using Diodes by Drs. A.V. Radun and K.D. Donohue (2/14/07) Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 Updated
More informationQNET Experiment #06: HVAC Proportional Integral (PI) Temperature Control Heating, Ventilation, and Air Conditioning Trainer (HVACT)
Quanser NIELVIS Trainer (QNET) Series: QNET Experiment #06: HVAC Proportional Integral (PI) Temperature Control Heating, Ventilation, and Air Conditioning Trainer (HVACT) Student Manual Table of Contents
More informationHarmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies
Soonwook Hong, Ph. D. Michael Zuercher Martinson Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies 1. Introduction PV inverters use semiconductor devices to transform the
More informationChapter 8. CurrentFeedback Op Amp Analysis. Excerpted from Op Amps for Everyone. Literature Number SLOA080. Literature Number: SLOD006A
Chapter 8 CurrentFeedback Op Amp Analysis Literature Number SLOA080 Excerpted from Op Amps for Everyone Literature Number: SLOD006A Chapter 8 CurrentFeedback Op Amp Analysis Ron Mancini 8.1 Introduction
More information054414 PROCESS CONTROL SYSTEM DESIGN. 054414 Process Control System Design. LECTURE 6: SIMO and MISO CONTROL
05444 Process Control System Design LECTURE 6: SIMO and MISO CONTROL Daniel R. Lewin Department of Chemical Engineering Technion, Haifa, Israel 6  Introduction This part of the course explores opportunities
More informationController Design using the Maple Professional Math Toolbox for LabVIEW
Controller Design using the Maple Professional Math Toolbox for LabVIEW This application demonstrates how you can use the Maple Professional Math Toolbox for LabVIEW to design and tune a ProportionalIntegralDerivative
More informationManufacturing Equipment Modeling
QUESTION 1 For a linear axis actuated by an electric motor complete the following: a. Derive a differential equation for the linear axis velocity assuming viscous friction acts on the DC motor shaft, leadscrew,
More informationParameter Definition with the reader. Since the scope of this article is practical in nature all theoretical derivations have been omitted, hoping to
Freescale Semiconductor Application Note Document Number: AN535 Rev. 1.0, 02/2006 PhaseLocked Loop Design Fundamentals by: Garth Nash Applications Engineering Abstract The fundamental design concepts
More informationA simple method to determine control valve performance and its impacts on control loop performance
A simple method to determine control valve performance and its impacts on control loop performance Keywords Michel Ruel p.eng., Top Control Inc. Process optimization, tuning, stiction, hysteresis, backlash,
More informationSecond Order Systems
Second Order Systems Second Order Equations Standard Form G () s = τ s K + ζτs + 1 K = Gain τ = Natural Period of Oscillation ζ = Damping Factor (zeta) Note: this has to be 1.0!!! Corresponding Differential
More informationEECE 460 : Control System Design
EECE 460 : Control System Design PID Controller Design and Tuning Guy A. Dumont UBC EECE January 2012 Guy A. Dumont (UBC EECE) EECE 460 PID Tuning January 2012 1 / 37 Contents 1 Introduction 2 Control
More informationTESTS OF 1 MHZ SIGNAL SOURCE FOR SPECTRUM ANALYZER CALIBRATION 7/8/08 Sam Wetterlin
TESTS OF 1 MHZ SIGNAL SOURCE FOR SPECTRUM ANALYZER CALIBRATION 7/8/08 Sam Wetterlin (Updated 7/19/08 to delete sine wave output) I constructed the 1 MHz square wave generator shown in the Appendix. This
More informationPrecision Diode Rectifiers
by Kenneth A. Kuhn March 21, 2013 Precision halfwave rectifiers An operational amplifier can be used to linearize a nonlinear function such as the transfer function of a semiconductor diode. The classic
More informationEDUMECH Mechatronic Instructional Systems. Ball on Beam System
EDUMECH Mechatronic Instructional Systems Ball on Beam System Product of Shandor Motion Systems Written by Robert Hirsch Ph.D. 9989 All Rights Reserved. 999 Shandor Motion Systems, Ball on Beam Instructional
More informationVFD 101 Lesson 4. Application Terminology for a VFD
VFD 101 Lesson 4 Application Terminology for a VFD This lesson covers the application terminology associated with a Variable Frequency Drive (VFD) and describes each term in detail. When applying a Variable
More informationAC 20123923: MEASUREMENT OF OPAMP PARAMETERS USING VEC TOR SIGNAL ANALYZERS IN UNDERGRADUATE LINEAR CIRCUITS LABORATORY
AC 2123923: MEASUREMENT OF OPAMP PARAMETERS USING VEC TOR SIGNAL ANALYZERS IN UNDERGRADUATE LINEAR CIRCUITS LABORATORY Dr. Tooran Emami, U.S. Coast Guard Academy Tooran Emami received her M.S. and Ph.D.
More informationOpAmp Simulation EE/CS 5720/6720. Read Chapter 5 in Johns & Martin before you begin this assignment.
OpAmp Simulation EE/CS 5720/6720 Read Chapter 5 in Johns & Martin before you begin this assignment. This assignment will take you through the simulation and basic characterization of a simple operational
More informationdspace DSP DS1104 based State Observer Design for Position Control of DC Servo Motor
dspace DSP DS1104 based State Observer Design for Position Control of DC Servo Motor Jaswandi Sawant, Divyesh Ginoya Department of Instrumentation and control, College of Engineering, Pune. ABSTRACT This
More informationAnalog Filter Design Demystified
FILTER CIRCUITS (ANALOG) VIDEO CIRCUITS Dec 03, 2002 Analog Filter Design Demystified This article shows the reader how to design analog filters. It starts by covering the fundamentals of filters, it then
More informationLoop Bandwidth and Clock Data Recovery (CDR) in Oscilloscope Measurements. Application Note 13046
Loop Bandwidth and Clock Data Recovery (CDR) in Oscilloscope Measurements Application Note 13046 Abstract Time domain measurements are only as accurate as the trigger signal used to acquire them. Often
More informationOperational Amplifiers
Operational Amplifiers Introduction The operational amplifier (opamp) is a voltage controlled voltage source with very high gain. It is a five terminal four port active element. The symbol of the opamp
More informationSection 5.0 : Horn Physics. By Martin J. King, 6/29/08 Copyright 2008 by Martin J. King. All Rights Reserved.
Section 5. : Horn Physics Section 5. : Horn Physics By Martin J. King, 6/29/8 Copyright 28 by Martin J. King. All Rights Reserved. Before discussing the design of a horn loaded loudspeaker system, it is
More informationDesigning Stable Compensation Networks for Single Phase Voltage Mode Buck Regulators
Designing Stable Compensation Networks for Single Phase Voltage Mode Buck Regulators Technical Brief December 3 TB47. Author: Doug Mattingly Assumptions This Technical Brief makes the following assumptions:.
More informationCurrent Loop Tuning Procedure. Servo Drive Current Loop Tuning Procedure (intended for Analog input PWM output servo drives) General Procedure AN015
Servo Drive Current Loop Tuning Procedure (intended for Analog input PWM output servo drives) The standard tuning values used in ADVANCED Motion Controls drives are conservative and work well in over 90%
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT 4 Understand singlephase alternating current (ac) theory Single phase AC
More informationLab 7: Operational Amplifiers Part I
Lab 7: Operational Amplifiers Part I Objectives The objective of this lab is to study operational amplifier (op amp) and its applications. We will be simulating and building some basic op amp circuits,
More informationController and Platform Design for a Three Degree of Freedom Ship Motion Simulator
33 Controller and Platform Design for a Three Degree of Freedom Ship Motion Simulator David B. Bateman, Igor A. Zamlinsky, and Bob Sturges Abstract With the use of towtank experiments, data may be generated
More informationMotor Control. Suppose we wish to use a microprocessor to control a motor  (or to control the load attached to the motor!) Power supply.
Motor Control Suppose we wish to use a microprocessor to control a motor  (or to control the load attached to the motor!) Operator Input CPU digital? D/A, PWM analog voltage Power supply Amplifier linear,
More informationActive Vibration Isolation of an Unbalanced Machine Spindle
UCRLCONF206108 Active Vibration Isolation of an Unbalanced Machine Spindle D. J. Hopkins, P. Geraghty August 18, 2004 American Society of Precision Engineering Annual Conference Orlando, FL, United States
More informationControl System Definition
Control System Definition A control system consist of subsytems and processes (or plants) assembled for the purpose of controlling the outputs of the process. For example, a furnace produces heat as a
More informationMoving Average Filters
CHAPTER 15 Moving Average Filters The moving average is the most common filter in DSP, mainly because it is the easiest digital filter to understand and use. In spite of its simplicity, the moving average
More informationOverdamped system response
Second order system response. Im(s) Underdamped Unstable Overdamped or Critically damped Undamped Re(s) Underdamped Overdamped system response System transfer function : Impulse response : Step response
More informationDirect and Reflected: Understanding the Truth with YS 3
Direct and Reflected: Understanding the Truth with YS 3 Speaker System Design Guide December 2008 2008 Yamaha Corporation 1 Introduction YS 3 is a speaker system design software application. It is
More informationε: Voltage output of Signal Generator (also called the Source voltage or Applied
Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and
More informationNotch Filter Design. August 29, 2005
Notch Filter Design William East Brian Lantz August 29, 2005 1 Introduction This report summarizes an investigation made into designing notch filters with the control system for seismic isolation of Advanced
More informationThe Effective Number of Bits (ENOB) of my R&S Digital Oscilloscope Technical Paper
The Effective Number of Bits (ENOB) of my R&S Digital Oscilloscope Technical Paper Products: R&S RTO1012 R&S RTO1014 R&S RTO1022 R&S RTO1024 This technical paper provides an introduction to the signal
More informationLock  in Amplifier and Applications
Lock  in Amplifier and Applications What is a Lock in Amplifier? In a nut shell, what a lockin amplifier does is measure the amplitude V o of a sinusoidal voltage, V in (t) = V o cos(ω o t) where ω o
More informationCIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis
CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis 3.1 Introduction The steadystate behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the
More informationECGAmplifier. MB Jass 2009 Daniel Paulus / Thomas Meier. Operation amplifier (opamp)
ECGAmplifier MB Jass 2009 Daniel Paulus / Thomas Meier Operation amplifier (opamp) Properties DCcoupled High gain electronic ec c voltage amplifier Inverting / noninverting input and single output
More informationHomework Assignment 03
Question 1 (2 points each unless noted otherwise) Homework Assignment 03 1. A 9V dc power supply generates 10 W in a resistor. What peaktopeak amplitude should an ac source have to generate the same
More informationPID Controller Tuning: A Short Tutorial
PID Controller Tuning: A Short Tutorial Jinghua Zhong Mechanical Engineering, Purdue University Spring, 2006 Outline This tutorial is in PDF format with navigational control. You may press SPACE or, or
More informationTHE EDUCATIONAL IMPACT OF A GANTRY CRANE PROJECT IN AN UNDERGRADUATE CONTROLS CLASS
Proceedings of IMECE: International Mechanical Engineering Congress and Exposition Nov. 722, 2002, New Orleans, LA. THE EDUCATIONAL IMPACT OF A GANTRY CRANE PROJECT IN AN UNDERGRADUATE CONTROLS CLASS
More informationCurrent and Temperature Ratings
Document 3611 Current and Temperature Ratings Introduction This application note describes: How to interpret Coilcraft inductor current and temperature ratings Our current ratings measurement method and
More informationA Simulink Modeling to Develop a Control System of Stirred Tank Heater with Multifarious Operating Conditions
A Simulink Modeling to Develop a Control System of Stirred Tank Heater with Multifarious Operating Conditions Abdur Raquib Ridwan Lecturer Islamic University of Technology, EEE Department Ishtiza Ibne
More informationTechnical Note #3. Error Amplifier Design and Applications. Introduction
Technical Note #3 Error Amplifier Design and Applications Introduction All regulating power supplies require some sort of closedloop control to force the output to match the desired value. Both digital
More informationApplication Note 2. Analog Audio Parametric Equalizer
Application Note 2 App Note Application Note 2 Highlights Pot and Switch Components Target Optimizer for Curve Parameters Potentiometer Analysis Noise Analysis LEQ, HEQ, BEQ Filters n Design Objective
More informationOperational Amplifiers: Part 2. Nonideal Behavior of Feedback Amplifiers DC Errors and LargeSignal Operation
Operational Amplifiers: Part 2 Nonideal Behavior of Feedback Amplifiers DC Errors and LargeSignal Operation by Tim J. Sobering Analog Design Engineer & Op Amp Addict Summary of Ideal Op Amp Assumptions
More informationMicrocontrollerbased experiments for a control systems course in electrical engineering technology
Microcontrollerbased experiments for a control systems course in electrical engineering technology Albert LozanoNieto Penn State University, WilkesBarre Campus, Lehman, PA, USA Email: AXL17@psu.edu
More informationROOT LOCUS TECHNIQUES
ROOT LOCUS TECHNIQUES In this lecture you will learn the following : The definition of a root locus How to sketch root locus How to use the root locus to find the poles of a closed loop system How to use
More informationAPPLICATION BULLETIN
APPLICATION BULLETIN Mailing Address: PO Box 11400, Tucson, AZ 85734 Street Address: 6730 S. Tucson Blvd., Tucson, AZ 85706 Tel: (520) 7461111 Telex: 0666491 FAX (520) 8891510 Product Info: (800) 5486132
More informationDesigning interface electronics for zirconium dioxide oxygen sensors of the XYA series
1 CIRCUIT DESIGN If not using one of First Sensors ZBXYA interface boards for sensor control and conditioning, this section describes the basic building blocks required to create an interface circuit Before
More informationCancellation of LoadRegulation in Low DropOut Regulators
Cancellation of LoadRegulation in Low DropOut Regulators Rajeev K. Dokania, Student Member, IEE and Gabriel A. RincόnMora, Senior Member, IEEE Georgia Tech Analog Consortium Georgia Institute of Technology
More information