Small-Scale Robotic Arm Senior Capstone Project Ben Boyle and Kitera Hayes Project Advisor: Dr. Gary Dempsey April 29, 2004

Outline zObjectives zEquipment List zSystem Specifications zFunctional Description zBlock Diagram zSystem Parameters zSystem Identification zImplementation of Controllers zFlexible Rotary Joint zSystem Limitations zConclusion zCompleted Tasks zQuestions

Objectives zDetermination of Plant Model zFast System Response zWide Command Range (± 90 degrees) zHigh Stability Margin (GM, PM) zUser-friendly Software Interface zLow Resonant Frequency Mode with New Arm

Equipment List z200 MHz Pentium-based computer zQuanser System yRobotic Arm with Flexible Rotary Joint yPower Amplifier zSoftware yMATLAB (SIMULINK) yBorland C

Lab Workstation

Robotic Arm

System Specifications zCommand: ± 90 set points, ± 40 deg/sec velocity zPercent Overshoot = 0 % zSteady-State Error = ± 2 degrees zPhase Margin  70 degrees

Functional Description Positioning Figure 1 - Input/Output Description Command Input Small Scale Robotic Arm Control

Functional Description zSoftware Interface zPositioning Modes of Operation

Block Diagram System (Plant) Software Figure 2 - Block Diagram of Robotic Arm

System Parameters zSystem (Plant) yAmplifier   5 3 [A] yPosition Sensor    180  of travel yDC motor  5 [V] yExternal Gears  5:1 velocity reduction yInternal Gears  14.1:1 velocity reduction yAntialiasing Filter  first-order low-pass with 163 [rad/sec] zSoftware y200 [MHz] PC yA/D converter  12 bit plus sign,  5 [V] yD/A converter  12 bit,  5 [V]

System Identification zClosed-loop Results zOpen-loop Results zPlant Model Equation zPlant Model Verification

System Identification zClosed-loop Results y Gain k =  Best Fit x Close to 0% overshoot y Step input of ±20° y DC Gain x Gp(0) = 27°/[V]

System Identification k=0.025 D/A Gp R=20  E=12  Controller voltage= C=8  Controller Voltage = (12°)(.025) = [V] DC Gain [Gp(0)] = 8°/0.295 [V] = 27°/[V] Figure 3 – DC Gain Calculation of System

System Identification Figure 4 - Gain k = 0.025, Step input of ±20°, Closed-loop (Experimental Results)

System Identification zOpen-loop Results yVerify DC gain of plant yCalculate accurate time delay yHelp to determine plant model

System Identification Figure 5 - k = 1.0, Step input voltage of 0.74 [V], Open-loop (Experimental Results)

System Identification Input Voltage = 20°/(27°/[V]) = 0.74 [V] (Open-loop) Command Degree Calculation: (K)(Command Voltage)(DC Gain) = Command Degrees Theoretical Command Degrees  20° Experimental Command Degrees  17° Percent Error = 17.6%

System Identification zPlant Gp = k[a/(s+a) 2 ] zc(t) = k[1-e -at - at(e -at )] k = 1.0 and t = 2.86 seconds, c = ° zDouble a = Pole Identification using Laplace Transform

System Identification Typical Open-loop Poles Figure 6 – Second Order System (Poles = -0.76) Actual Open-loop Double Pole -0.76

System Identification zPlant Model Equation: 27e s (s/ ) 2 (OPEN-LOOP)

System Identification 20.48º Figure 7 - SIMULINK Scope Output for Open-loop System = 20.48º Plant Model Verification

System Identification 8.38º Figure 8 - SIMULINK Scope Output for Closed-loop System = 8.38º Plant Model Verification

P Controller Figure 9 - Theoretical P Controller OutputFigure 10 - P Controller System Output

PI Controller Figure 12 - PI Controller System OutputFigure 11 - Theoretical PI Controller Output

PID Controller Figure 13 - Theoretical PID Controller OutputFigure 14 - PID Controller System Output

Feed-Forward/PI Controller Figure 15 - Feed-Forward/PI Controller Block Diagram

Feed-Forward/PI Controller Figure 16 - Theoretical FF/PI Controller OutputFigure 17 - FF/PI Controller System Output

Controller Comparison P ControllerFF/PI Controller Figure 19 - FF/PI Controller System OutputFigure 18 - P Controller System Output

Flexible Rotary Joint

Figure 20 - P Controller System OutputFigure 21 - P Controller Flex Joint System Output

System Limitations zD/A Converter  ± 5 [V] zStatic Friction y Just matches the applied force to try and prevent motion y Modeling  Time delay e -std (linear) zKinetic Friction y Moving friction with respect to speeds zInertia y J = (mass)(radius 2 ) zGravity

System Limitations (a) With Friction(b) Without Friction Figure 22(a-b) – Friction Characteristics for Pendulum System -B/2J PENDULUM

System Limitations Figure 23 - Closed-loop Time Delay and % Overshoot Calculations for Varying Gain k Td avg = 56.2 [ms] Time Delay

Conclusion zPI Controller is slow zPID Controller does not work zSolution is FF/PI Controller

Completed Tasks zPlant Model and Validation zProportional, PI, and PID Controllers zFF Controller with PI yUser-friendly Software Interface zFuture Work yPlant Model for Flexible Rotary Joint yGripper Motor with Varying Loads yNotch Filter Incorporation

Questions?