Introduction to Automatic Control Systems

Basic Information Instructor Contact Information Degang Chen, 2134 Coover Hall djchen@iastate.edu; 294-6277 Office Hour: MWF 12:00 – 2:00 pm Or any other time convenient to you Please include "EE475" in the subject line in all email communications to avoid auto-deleting or junk-filtering TA Jon Watson, 3201 Coover Hall Office Hour: 1:00-2:00 pm, TR, ALC Village B, #6 E-mail: jonrwat@gmail.com; Voice phone: 515-520-9569

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Catalog Description E E 475. Automatic Control Systems. (3-0) Cr. 3. F.Prereq: 324. Stability and performance analysis of automatic control systems. The state space, root locus, and frequency response methods for control systems design. PID control and lead-lag compensation. Computer tools for control system analysis and design. Nonmajor graduate credit.

Prerequisite by topics Knowledge and proficiency in Matlab Concept and solution of linear ordinary differential equations Laplace transform and its applications Poles, zeros, transfer functions, frequency response, Bode plots Vectors and matrices Complex numbers

OBJECTIVES On completion of EE 475, the student will be able to do the following either by hand or with the help of computation tools such as Matlab: Define the basic terminologies used in controls systems Explain advantages and drawbacks of open-loop and closed loop control systems Obtain models of simple dynamic systems in ordinary differential equation, transfer function, state space, or block diagram form Obtain overall transfer function of a system using either block diagram algebra, or signal flow graphs, or Matlab tools. Compute and present in graphical form the output response of control systems to typical test input signals Explain the relationship between system output response and transfer function characteristics or pole/zero locations Determine the stability of a closed-loop control systems using the Routh-Hurwitz criteria Analyze the closed loop stability and performance of control systems based on open-loop transfer functions using the Root Locus technique Design PID or lead-lag compensator to improve the closed loop system stability and performance using the Root Locus technique Analyze the closed loop stability and performance of control systems based on open-loop transfer functions using the frequency response techniques Design PID or lead-lag compensator to improve the closed loop system stability and performance using the frequency response techniques

Topics Covered Review of signal systems concepts and techniques as applied to control system Block diagrams and signal flow graphs Modeling of control systems using ode, block diagrams, and transfer functions Modeling and analysis of control systems using state space methods Analysis of dynamic response of control systems, including transient response, steady state response, and tracking performance. Closed-loop stability analysis using the Routh-Hurwitz criteria Stability and performance analysis using the Root Locus techniques Control system design using the Root Locus techniques Stability and performance analysis using the frequency response techniques Control system design using the frequency response techniques If there is time, Control system design using the state space techniques

Textbook Automatic Control Systems, Golnaraghi and Kuo, ninth edition, Wiley, 2009 Price: $114.84 & this item ships for FREE with Super Saver Shipping. 20 new from $86.04 7 used from $101.57

Other References Feedback Control of Dynamic Systems (6th Edition) by Gene Franklin, J.D. Powell, and Abbas Emami-Naeini (Hardcover - Oct 11, 2009) Buy new: $150.00 $120.00  Modern Control Engineering (5th Edition) by Katsuhiko Ogata (Paperback - Aug 30, 2009) Buy new: $150.00 $135.00 

Other References Modern Control Systems (11th Edition) (Pie) by Richard C. Dorf and Robert H. Bishop (Hardcover - Aug 10, 2007) Buy new: $159.00 $115.32 65 Used & new from $104.97 Control Systems Engineering, Just Ask! Package by Norman S. Nise (Hardcover - Jun 21, 2004) Buy new: $140.60 28 Used & new from $7.00

Other References Modern Control Theory (3rd Edition) by William L. Brogan (Paperback - Oct 11, 1990) Buy new: $150.00 $133.34 22 Used & new from $120.41 Feedback Control Systems (4th Edition) by Charles L. Phillips and Royce D. Harbor (Hardcover - Aug 19, 1999) Buy new: $159.00 $121.62 35 Used & new from $99.97

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Control System Terminology Input - Excitation applied to a control system from an external source. Output - The response obtained from a system Feedback - The output of a system that is returned to modify the input. Error - The difference between the reference input and the output. Discuss Slide

Negative Feedback Control System + + + CONTROLLED DEVICE CONTROLLER - 1. All weapons system must have some form of control system. Normally a negative feedback control system. 2. Input: Stimulus or excitation to a control system from an external source usually in order to produce a specific response from the system. Example: signal sent from a radar dish to the weapons control computer. 3. Output: The response from the system such as a gun turning toward target. 4. Feedback: That portion the output of a system that is returned to modify the input and thus serve as a performance monitor. Example: The gun needs to tell the weapons computer where it is pointing so that the computer can compare that to where it should be pointing. 5. Error: The difference between the input stimulus and the output response. Specifically the difference between the input and feedback. Discuss the + and - signs on the Comparater and the error is reference signal minus the feedback signal. FEEDBACK ELEMENT

Types of Control Systems Open-Loop Simple control system which performs its function with-out concerns for initial conditions or external inputs. Must be closely monitored. Closed-Loop (feedback) Uses the output of the process to modify the process to produce the desired result. Continually adjusts the process. 1. Introduction: a. Most equipment have some form of a controller to make it function. b. Most have something more than just an on/off switch as a controller. c. Two major types of controllers in use: 2. Open-Loop. a. Performs its action without regard to the output or any external input. Example: The controller on a washing machine. a. It will run the washer through the cycle without regard for the cleanliness of the clothes in the machine, if there is soap in the machine, temperature of the water, how much clothes are in the machine, etc. 3. Closed-Loop (Feedback) a. Senses the output of the controller or process. b. Uses this output to change the process to meet the desired result. c. Controller can determine how accurate the output is or if it producing the desired result. d. Control action depends on the output of the system. Example: Aircraft auto Pilot set to keep plane at altitude.

Advantages of a Closed-Loop Feedback System Increased Accuracy Increased ability to reproduce output with varied input. Reduced Sensitivity to Disturbance By self correcting it minimizes effects of system changes. Smoothing and Filtering System induced noise and distortion are reduced. Increased Bandwidth Produces sat. response to increased range of input changes. 1. Increased Accuracy a. Ability to faithfully reproduce the output. 2. Reduced Sensitivity to Disturbances a. Ability of the system to produce the same output repeatedly in spite of variations and fluctuations within the control system (worn gears, sticky components etc.) b. Changes within the system are reduced and the effects of the changes can be minimized. 3. Smoothing and filtering. Undesirable effects of noise and distortion within the system are reduced. 4. Increased Bandwidth. Can operate satisfactorily over a wide range of frequencies or variations in the input.

Major Types of Feedback Used Position Feedback Used when the output is a linear distance or angular measurement. Rate & Acceleration Feedback Feeds back rate of motion or rate of change of motion (acceleration) Motion smoothing Uses a electrical/mechanical device call an accelerometer 1. Discuss slide. 2. A you can see from the example of the gun turret, these types of feedback provide additional information that is used to improve the response time of the system. - The light on when the proper position was reached. But... - The additional information modifies the system response and improve the response time. 3. This additional information when add to the feedback loop is call DAMPING.

Fire Control Problem Present Future Position Ship’s Bearing Heading Present Range Future Range Range Change Bearing Change Go over diagram to show the geometry of the problem. Show a. Development of Bearing Change b. Development of Range Error Goal is to determine the target’s course and speed so we can predict where the target will be at the time it takes the weapon to reach the target. We are trying to solve a solution with respect to time: ie. We want to adjust the aim point such that the target and the weapon arrive at the same point at the same time. We then convert the Bearing change to a time reference by calling it a bearing rate. ie. how much the bearing changes with time. We do the same thing with range. Getting this solution is just a little better than a trial and error process. It is a multiple step process when one solution is tried and the errors fed back to improve the next solution trial. This is called an iteration process.

Fire Control Problem Input Target data Own ship data Computations Relative motion procedure Exterior ballistics procedure

Fire Control Problem Solutions Weapons time of flight Bearing rate Line of Sight(LOS): The line between the target and the firing platform Speed across LOS Future target position Launch angles Launch azimuth Launch elevation Weapon positioning orders The above determines weapon trajectory: The line the weapon must travel on to intercept the target.

The Iterative Process to the Fire Control Solution Step 1 Step 2 The iterative process starts with an initial guess of the solution. The aiming point is put into the computer and the position of the target is computed at the time the weapon reaches the aim point. The error is fed back to refine the aim point. For example: Step 1 a. The aim point is where the target is at the time of fire. At impact the target will move down its track. Step 2 a. The bearing error is used to change the bearing of the aim point. b. Note: If only used bearing error, the weapon would always fall short so the range error is also used The iterative process continues until the the weapon and the target’s solution intersect at the flight time of the weapon. As a review: What Information does the computer need to solve this problem? 1. Target position 2. Target data over a period of time to determine target course speed and range. 3. Weapons speed to compute time of flight Step 3 Last Step

A 3-Dimensional Problem Line of Sight Present Range Target Elevation 1. In the previous examples we were concerned with two dimensions. The actual problem could be 3-dimensional. 2. The problem is essentially the same but have different names. Gun Elevation Horizontal Reference Plane

Solving the Fire Control Problem Continuously Measure Present Target Position Stabilize Measured Quantities Compute Relative Target Velocity Ballistic Calculations Relative Motion Time of Flight Future Target Position Prediction Procedure Unstabilized Launch Angles Environmental Inputs Launch Angles (Stabilized) Weapons Positioning orders 1. Continuously measure target Position. 2. Stabilize Measured Quantities a. Remove the effects of own ship roll pitch and yaw b. Standardize points of reference (difference between location of sensors and weapons. 3. Compute Relative Velocity of the Target 4. Prediction Procedures a. Does the trial and error flight calculation to weapon and target interception at the flight time of the weapon. b The output is the launch angles as if the launch platform is stabilized. (i.e. not rock, roll, pitch and yaw) 5. Motion of the launch platform is added to the launch angle to give the weapons position order. 6. Sequence is repeated.

Idle-speed control system.

Figure 1-5 (p. 5) Solar collector field.

Conceptual method of efficient water extraction using solar power.

Important components of the sun-tracking control system.

Antenna azimuth position control system: a. system concept; b. detailed layout; c. schematic; d. functional block diagram

a. Video laser disc player; b a. Video laser disc player; b. objective lens reading pits on a laser disc; c. optical path for playback showing tracking mirror rotated by a control system to keep the laser beam positioned on the pits. (a) (b) (c) © Pioneer Electronics, Inc.

Computer hard disk drive, showing disks and read/write head Courtesy of Quantum Corp.

Response of a position control system showing effect of high and low controller gain on the output response High gain; fast but oscillating Control goal; fast reaction, lower overshoot, less settling time

The control system design process

Aircraft attitude defined

Winder © J. Ayers, 1988.

Control of a nuclear reactor

Grinder system © 1997, ASME.

High-speed proportional solenoid valve © 1996, ASME.

High-speed rail system showing pantograph and catenary © 1997, ASME.