Rolling Radar Concept

Preliminary Design Report

Senior Design Team 05426

Brian McManus

Aaron Halterman

Caleb Herry

Gabe Ferencz

Gabe Chan

Department of Mechanical Engineering

Kate Gleason College of Engineering

Rochester Institute of Technology

76 Lomb Memorial Drive

Rochester, NY 14623-5604

Executive Summary

This report summarizes the progress made by the Rolling Radar Concept Senior Design Team. The goal of this project is to assess the feasibility of Lockheed Martin’s Rolling Radar Concept. This radar concept consists of a large, self-supporting array that rolls along a circular electrified rail. This array is attached to an axle that is supported by a smaller wheel at the other end of the axle. The array is propelled by a gravitational drive that rotates along an inner magnetic track that creates a moment enabling the array to overcome its inertia. The gravitational drive is magnetized and rotates by the electromagnetic force provided by the inner electromagnetic track.

The main focus of our project concerns the feasibility and reliability of the current design. This feasibility will be determined based on our analysis. Our project does not fit the typical mold of most senior design projects in that we are not building the conceptconstructing a prototype. Our emphasis for Senior Design 1 was primarily on the analysis of the control system, the weight of the gravity drive, and the magnetism of the EM track to control the gravity drive. Our concept development work therefore mostly entails the selection of an accurate controller to model the system, research to optimize the EM track system, and a practical selection of parametric graphs for gravity drive weight and other parameters in Microsoft Excel.

Much analysis was done for Senior Design 1 concerning the kinematics of the control system and the analysis for weight of the gravity drive. At this point neither the size nor the weight of the array is known; parametric studies need to be completed to evaluate the effect different parameters have on the capabilities of the radar. Optimizing these parameters was a main goal of Senior Design 1.

The purpose of this document is to provide the current research, analysis, and feasibility assessments, as well as plans for Senior Design 2. The research completed is provided in the Concept Development section. Various controllers, for example, are evaluated in this section for the control system to portray the method of selection for this aspect. The Feasibility section outlines which concept was chosen that will best suit the radar. This section also discusses the feasibility assessments that have been completed to date. Once our parametrics allow us to optimize parameters, specific performance specifications will be provided along along with an overall feasibility assessment of the aspects our analysis does not allow us to assess at this point in time. The analysis will be discussed in depth in the Analysis and Synthesis of Design section. Plans for further work in Senior Design 2 will be provided in the Future Work section.

1 Table of Contents

Executive Summary 2

1 Table of Contents 4

2 List of Figures 6

3 List of Equations 7

4 Recognize and Quantify the Need 8

5 Statement of Work 10

6 Concept Development 11

6.1 Control System 11

6.1.1 On/Off Control 12

6.1.2 Continuous Control 12

6.1.3. Proportional Control (P) 13

6.1.4 Proportional Integral Control (PI) 14

6.1.4 Proportional Integral Derivative Control (PID) 14

6.1.5 Tuning of Controller 15

6.3 Axle Position Sensing System 16

6.3.1 Optical Barcode Sensing System 16

6.3.2 Hall Effect Sensor System 18

6.3.3 Analyzing Position Sensing Systems 19

6.4 Carriage Position Sensing System 1920

6.5 Types of Magnets 20

6.5.1 Electromagnetic Track, Electromagnetic Carriage 21

6.5.2 Permanent Magnet Carriage, Electromagnetic Track 21

6.5.3 Electromagnetic Carriage, Permanent Magnet Track 22

6.5.4 Permanent Magnet Carriage, Permanent Magnet Track 23

6.5.5 Analyzing Magnet Configurations 24

6.6 Mathematical Model of Magnetic Track 26

7 Feasibility Assessment 26

7.1 Gravitational Drive Weight Analysis Feasibility 26

7.2 Axle Position Sensing Systems Feasibility 27

7.3 Types of Magnets 2728

8 Performance Objectives and Specifications 28

8.1 Design Objectives 29

8.1.1 Magnetic Propulsion System Design Objectives 29

9 Analysis and Synthesis of Design 30

9.1 System Model and Control 30

9.1.1 System Model Assuming Axle Twist is Negligible 30

9.1.2 System Model with Axle Twist 34

9.2 Array Size and Weight 38

9.2.1 Assumptions 39

9.2.2 Global Parameters 40

9.2.4 Parametric Analysis Method 41

9.3 Magnetic Propulsion System 4544

10 Future Plans 4645

10.1 Control System 4645

10.2 Reliability 4746

10.3 Parameterizing Gravitational Drive 4746

10.4 Derivation of a Mathematical Model of the System 4847

10.5 Electromagnet Power Requirements 4948

10.6 Control System 4948

10.7 Schedule 4948

11 References 5150

12 Appendix A - Schedule 5352

13 Appendix B - Excel 5453

2 List of Figures

Figure 1: Pugh's Method Comparison for Axle Position Sensing Systems 19

Figure 2: Pugh's Method Comparison for Electromagnets and Permanent Magnets 24

Figure 3: Specifications 29

Figure 4: FBD of Rolling Radar 31

Figure 5: Unity Feedback No Twist 32

Figure 6: Unity Feedback Position and Angular Velocity vs. Time 32

Figure 7: PID Controller with no Twist 33

Figure 8: Position and Angular Velocity vs. Time 33

Figure 9: FBD of rolling radar 34

Figure 10: Individual Components FBD 35

Figure 11: Unity Feedback with Axle Twist 36

Figure 12: Unity Feedback Position and Angular Velocity vs. Time 37

Figure 13: PID Control with Axle Twist 38

Figure 14: Position and Angular Velocity vs. Time 38

Figure 15: Parameter Plots 4443

Figure 16: Gravity Drive Mass with Start-up Time and Tilt Angle Variance 4544

3 List of Equations

Equation 1: Moment Equilibrium 31

Equation 2: Sum of Moments 31

Equation 3: Transfer Function 31

Equation 4: Main Array Moment Equation 35

Equation 5: Axle Moment Equation 35

Equation 6: Support Wheel Moment Equation 35

Equation 7: System Model Transfer Function with Twist 35

Equation 8: Shear Singularity Function 42

Equation 9: Moment Singularity Function 42

4  Recognize and Quantify the Need

The Rolling Radar Concept has many aspects that Lockheed Martin needs to assess. Due to time constraints and other factors, only a few of these aspects would fit the scope of our Senior Design project. As such, selection was chosen by the team based on time constraints and team skills. Another factor in the selection of aspects dealt with the inter-workings of the radar and the dependencies certain aspects have on one another. For example, it is necessary to analyze the weight of the radar in order to model an accurate control system, discussed in further detail below.

The weight of the gravitational drive is one of the main criteria for the feasibility of the design. If the gravity drive is determined to be too large, recommendations for alternate designs will need to be given to address the problem. The size of the radar array needs to be variable, as the final size will eventually be optimized by other parameters of the radar. Parametric graphs will therefore need to be generated.

A control system that uses the kinematics of motion of the radar needs to be addressed in order to analyze the stability and functionality of the radar. The weight of the gravity drive, discussed above, must be analyzed in order to have an accurate model of the radar. An accurate control system that is applicable to this design needs to be researched and developed.

The electromagnetic track (EM) is another important aspect of the radar that needs to be assessed. The EM track controls the gravity drive location, which ultimately controls the location and speed of the radar. The EM track also requires the weight of the gravity drive. The mechanics of this EM track as well as the selection of the magnets on the gravity drive and the EM track itself needs to be analyzed.

The current requirements are expressed in outline form below.

  1. Gravity Drive Size

1.1.  Determine Torque

1.1.1.  mg (mass of gravity drive)

1.1.2.  q (tilt angle)

1.1.3.  b (degree of gravity drive rotation)

1.1.4.  r (radius of array)

1.2.  Resisting forces on torque

1.2.1.  B (rolling resistance)

1.2.2.  Br (Kulumb resistance)

1.3.  Acceleration Capabilities

1.3.1.  m (see 1.1.1)

1.3.2.  q (see 1.1.2)

1.3.3.  b (see1.1.3)

1.3.4.  r (see 1.1.4)

1.3.5.  mtot (total inertia)

1.3.5.1.  ma (mass of array)

1.3.5.2.  msw (mass of support wheel)

1.3.5.3.  mr (mass of axle)

1.3.6.  t (time)

1.3.7.  w1 (rotation speed of array)

  1. Reliability

2.1.  Forces/Stresses

2.1.1.  Structural Support

2.1.1.1.  Ground Reaction Forces

2.1.1.2.  Component Analysis

2.1.1.2.1.  Main (Array) Wheel

2.1.1.2.1.1.  Material

2.1.1.2.1.2.  Internal Forces / Moments

2.1.1.2.1.3.  Fatigue life

2.1.1.2.2.  Support Axle

2.1.1.2.2.1.  Material

2.1.1.2.2.2.  Internal Forces / Moments / Torsions

2.1.1.2.2.3.  Fatigue life

2.1.1.2.3.  Support Wheel

2.1.1.2.3.1.  Material

2.1.1.2.3.2.  Internal Forces / Moments

2.1.1.2.3.3.  Fatigue life

  1. Control System

3.1.  Equations of Motion

3.1.1.  J1, J2

3.1.2.  B1, B2 (resistances)

3.1.3.  w1, w2 (rotation speeds, see1.3.7)

3.1.4.  k (axle spring constant)

3.1.4.1.  Axle material

3.1.5.  Tk (torque)

3.2.  Simulink Diagrams

3.2.1.  Inputs

3.2.1.1.  Tk (see 3.1.5)

3.2.2.  Gc(s): Gc = Gcontroller * Gactuator

3.2.2.1.  Gcontroller

3.2.2.1.1.  PID Controller

3.2.2.1.1.1.  Integrator and differentiator blocks

3.2.2.1.2.  D(s): Disturbances

3.2.2.1.2.1.  Wind

3.2.2.1.2.1.1.  Dryden wind plots

3.2.2.2.  Gactuator

3.2.2.2.1.  Mechanics of motion (see 3.1)

3.2.2.3.  H(s): Bar Code Reader

  1. Electromagnetic Propulsion System

4.1.  Components of System

4.1.1.  Types of Magnets

4.1.1.1.  Electromagnets around array

4.1.1.2.  Drive Carriage Magnetism

4.1.2.  Orientation of Magnets

4.2.  Mathematical Model of System Orientation

4.2.1.  Orientation of drive carriage relative to platform

4.2.2.  Amount of force produced by different configurations

4.2.2.1.  Effect of configurations on speed of array

4.3.  Materials for Magnets

4.3.1.  Durability of Magnets

4.3.2.  Feasibility

5 Statement of Work

A statement of work is necessary to quantify the amount of work needed in the time given. A tentative work breakdown was generated in the first week of SD1. This breakdown is shown in Appendix A with the schedule.

6 Concept Development

6.1 Control System

One of the requirements of was to have a servo controller system designed and analyzed for the gravitational drive. Many servo controllers are being used in the industrial world. Most are designed to control the rotational motion of different motors. The system that we need to control is different in that we need to control the translation of a gravity drive along an arc to create a moment, which will then create the rotational motion. To choose a control system we first needed to analyze how different controllers work to meet the requirements of our system.

A system controller, in simple terms, is a device that measures an input, usually some type of error, and then tries to minimize the error by maintaining a desired value by adjusting an output device. Controllers change the value of the system variable by adjusting the control output. An industrial system controller typically uses a control output to drive a control valve or actuator to control a system variable like fluid flow, pressure, velocity, or position to a desired setpoint. Our application has proved to be atypical as will be discussed later. Most system controllers do not work directly with the system variable and setpoint, but rather work with an error signal, as mentioned earlier. This is calculated by determining the difference between the actual value and the required value, i.e. the setpoint. The error represents the deviation of the system variable from the setpoint. Being that the actual value is required to determine the error, some type of sensor or measurement device is usually. Generally there will be the need for some type of conversion gain to make sure that the sensor and the system variable are speaking the same language, so to speak.

When evaluating the error, positive error indicates that the system variable is above the setpoint, and a negative error indicates that it is below the setpoint. For example, the angular velocity is greater or less than the desired speed. Because the system variable information is fed back from the system being controlled, this type of controller is sometimes called an error feedback controller. The controller uses the value of the error to determine the control output necessary to maintain the system variable at the setpoint. If the error is negative for example the controller will tell the actuator to speed up or boost its effect.

6.1.1 On/Off Control

The simplest types of controllers are called ON/OFF controllers, because they simply turn an output device ON or OFF depending on the value of the error. To keep the output from cycling rapidly ON and OFF, most ON/OFF controllers incorporate a deadband. A deadband is a range that encloses the desired output value. The controller output remains in the current state until the error moves out of the deadband. Because of deadband, the system variable controlled by an ON/OFF controller is always cycling back and forth around the setpoint. This means that there is generally not a steady state value. ON/OFF control is often called "bang-bang" control because the control output is cycled between two extremes.

6.1.2  Continuous Control

Most industrial processes use continuous controllers, in which the control output is an analog value that is continuously adjusted. This has the obvious advantage of eliminating all of the ups and downs and steady state oscillations in the system variable that are experienced with ON/OFF control. Most continuous controllers used in industry today use proportional, integral, and derivative action, and are thus called PID (proportional-integral-derivative) controllers. Being that this type of controller is the most common it was our first choice to control the gravity drive. However in choosing controller we needed to first look at the individual costs and benefits the various types of control. Each of these controller actions is explained in detail in the following sections.

6.1.3. Proportional Control (P)

The simplest continuous controller uses proportional control. These controllers get their name from the fact that the control output is proportional to the error signal. This type of control is simply a gain on the error signal. A large error generates a large control output, and a small error generates a small control output. .