MODELING AND CONTROL STRATEGIES FOR MULTIPROCESS ARC WELDING POWER SOURCES by JONATHON C. KELM Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Thesis Adviser: Prof. Kenneth A. Loparo Department of Electrical Engineering & Computer Science CASE WESTERN RESERVE UNIVERSITY January, 2020 Modeling and Control Strategies for Multiprocess Arc Welding Power Sources Case Western Reserve University Case School of Graduate Studies We hereby approve the thesis1 of JONATHON C. KELM for the degree of Doctor of Philosophy Prof. Kenneth Loparo 11/15/2019 Committee Chair, Adviser Date Department of Electrical Engineering & Computer Science Prof. Vira Changkong 11/15/2019 Committee Member Date Department of Electrical Engineering & Computer Science Prof. Robert Gao 11/15/2019 Committee Member Date Department of Mechanical & Aerospace Engineering Prof. Wei Lin 11/15/2019 Committee Member Date Department of Electrical Engineering & Computer Science 1We certify that written approval has been obtained for any proprietary material contained therein. Dedicated to my parents, who taught me everything that really matters. Table of Contents List of Tables vii List of Figures viii List of Initialisms xiv List of Symbols xviii Acknowledgements xxii Abstract xxiii Chapter 1. Introduction1 Background and Motivation1 Literature Review 14 Goals of this Work 25 Contributions of this Work 26 Thesis Organization 26 Chapter 2. Modeling 28 Welding Cables, Workpiece, and Welding Fixture 28 Electrode and Contact Tip 33 The Welding Arc 35 Summary of Load Impedances 37 Piecewise Linear Model 38 Sources of Uncertainty 47 Chapter 3. Review of the Existing System 51 iv Overview of the Existing Control System 51 Waveform Generator Reference Tracking 54 Chapter 4. Proposed Control Strategy 60 Overview of Sliding Mode Control 61 Simplified Model 62 Current Tracking 63 Voltage Tracking 87 Power Tracking 93 Regulation Mode Switching 93 Output Limiting 93 Advantages of SMC for Welding Power Sources 97 Drawbacks of Sliding Mode Control 97 Chapter 5. Hardware Implementation 99 Abortive Efforts 99 Hybrid Analog/Digital Solution 101 Examples 111 Chapter 6. Results 115 Experimental Setup 115 Current Step Command 116 Current Exponential Command 124 Chapter 7. Summary, Conclusions, and Future Work 127 Summary and Conclusions 127 Recommendations for Further Work 128 v Appendix A. Simulation 130 General Structure 130 Integration Method 135 Simulation Configuration 138 Load Change Simulation 140 Simulation Parameters 141 Complete References 142 vi List of Tables 1.1 Timeline of welding power source technology 16 2.1 Ranges of Model Parameters 50 4.1 Current error dynamics for various reference signals 80 4.2 Voltage error dynamics for various reference signals 89 A.1 Simulation parameters 141 vii List of Figures 1.1 Illustration of arc welding terminology3 1.2 \Chopper" style welding power source structure6 1.3 \Inverter" style welding power source structure7 1.4 Shielded Metal Arc Welding (SMAW) setup8 1.5 Flux-Cored Arc Welding (FCAW) setup8 1.6 Gas Metal Arc Welding(GMAW) setup9 1.7 Gas Tungsten Arc Welding(GTAW) setup 10 2.1 Circuit diagram showing sources of impedance in the welding circuit 29 2.2 Welding cable cross-section showing electrical and geometrical properties 30 2.3 Circuit diagram for welding cable transmission line model 30 2.4 AWG 0000 welding cable resistance versus cable length 31 2.5 AWG 0000 welding cable inductance versus cable length 32 2.6 AWG 0000 welding cable capacitance versus cable length 33 2.7 AWG 0000 welding cable resonant frequency versus cable length 34 2.8 Wire electrode fed through contact tube as in Gas Metal Arc Welding (GMAW) and FCAW 35 2.9 V-I characteristics for GMAW arcs of various lengths 37 2.10 Circuit diagram of power section and load 40 viii 2.11 Circuit diagram of power section and load when switch is closed 40 2.12 Circuit diagram of power section and load when switch is open 41 2.13 Relationship between switch position u and choke current iL(t) 43 2.14 Current filtering effect of the welding circuit impedance 44 2.15 Inductance vs. current for the output inductor of a typical welding power source 47 3.1 Block diagram of the existing control system 53 3.2 Example of a simplified FSM for a GMAW welding program 54 3.3 Example of a constant reference signal 55 3.4 Example of a ramp reference signal 57 3.5 Example of an exponential reference signal 57 3.6 Example of a parabolic reference signal 58 3.7 Output regulation modes in a representative sample of welding programs 59 4.1 Circuit diagram of simplified power source and load 63 4.2 Sample current error trajectories for u = 0 for a constant reference 65 4.3 Sample current error trajectories for u = 1 for a constant reference 66 4.4 Desired current trajectory z2 = kiz1 for a constant reference 67 − 4.5 Current error trajectories with u = 0, u = 1, and sliding line σi = 0 68 4.6 Sliding mode existence for constant current, k < Rw + Ro + Ro 70 i Lw Lw L ix Rw Ro Ro 4.7 Sliding mode existence for constant current, ki + + 71 ≈ Lw Lw L 4.8 Sliding mode existence for constant current, k > Rw + Ro + Ro 72 i Lw Lw L 4.9 Relationship between switching function σ, control u, and hysteresis κ 74 4.10 Relationship between load resistance Rw and hysteresis κ for Fsw = 20 kHz 75 4.11 Relationship between load inductance Lw and hysteresis κ for Fsw = 20 kHz 76 4.12 Current step simulation, Fsw = 20 kHz 77 4.13 Current step simulation, Fsw = 80 kHz 78 4.14 Current standard deviation vs. switching frequency 79 4.15 Current exponential simulation 82 4.16 Current ramp simulation 84 4.17 Current parabola simulation 86 4.18 Voltage exponential simulation 91 4.19 Circuit diagram for the Open Circuit Voltage (OCV) case 92 4.20 Example operating region defined by current, voltage, and power limits 95 4.21 Example of output limiting, 20 V regulation at a 100 A minimum current 96 5.1 Original analog SMC control board 101 5.2 Hybrid analog/digital SMC PCB 103 x 5.3 Basic structure of the existing control hardware 104 5.4 Basic structure of the modified control hardware 104 5.5 Block diagram of the SMC hardware implementation 105 5.6 SMC algorithm flowchart 107 5.7 Band-limited derivative frequency responses for various values of τ 109 5.8 State diagram for CPLD gate drive logic 110 5.9 Oscilloscope trace showing hysteresis modulation signals 111 5.10 Oscilloscope trace showing detail of hysteresis modulation signals 112 5.11 Oscilloscope trace of 200 A current regulation at 20 kHz 112 5.12 Oscilloscope trace of 200 A current regulation at 10 kHz 113 5.13 Oscilloscope trace of current ramp regulation 113 5.14 Oscilloscope trace of current exponential regulation 114 6.1 Experimental load bank 116 6.2 84 µH coil of welding cable 116 6.3 255 µH coil of welding cable 117 6.4 LCR meter used for measuring cable inductance 117 6.5 Current step, 10 A to 100 A, with varying load resistance (existing controls) 119 6.6 Current step, 10 A to 100 A, with varying load resistance (SMC simulation) 119 xi 6.7 Current step, 10 A to 100 A, with varying load resistance (hardware implementation) 119 6.8 Current step, 20 A to 200 A, with varying load resistance (existing controls) 120 6.9 Current step, 20 A to 200 A, with varying load resistance (SMC simulation) 120 6.10 Current step, 30 A to 300 A, with varying load resistance (existing controls) 121 6.11 Current step, 30 A to 300 A, with varying load resistance (SMC simulation) 121 6.12 Current step, 10 A to 100 A, with varying load inductance (existing controls) 122 6.13 Current step, 10 A to 100 A, with varying load inductance (SMC simulation) 122 6.14 Current step, 20 A to 200 A, with varying load inductance (existing controls) 123 6.15 Current step, 20 A to 200 A, with varying load inductance (SMC simulation) 123 6.16 Current exponential, 20 A to 200 A, with varying load resistance (existing controls) 125 6.17 Current exponential, 20 A to 200 A, with varying load resistance (SMC simulation) 125 xii 6.18 Current exponential, 20 A to 200 A, with varying load inductance (existing controls) 126 6.19 Current exponential, 20 A to 200 A, with varying load inductance (SMC simulation) 126 A.1 Simulator \main loop" flowchart 132 A.2 Simulated load changes from R1 = 100 mΩ to R2 = 5 mΩ 140 xiii List of Initialisms AC Alternating Current. ADC Analog-to-Digital Converter. ADRC Active Disturbance Rejection Control. ANN Artificial Neural Network. AWG American Wire Gauge. AWPS Arc Welding Power Source. AWS American Welding Society. BLS Bureau of Labor Statistics. CAG Carbon Arc Gouging. CC Constant Current. CPLD Complex Programmable Logic Device. CTWD Contact Tip to Workpiece Distance. DAC Digital-to-Analog Converter. DC Direct Current. DCEN Direct Current Electrode Negative. DCEP Direct Current Electrode Positive. DCM Discontinuous Conduction Mode. DSP Digital Signal Processor. xiv EMC Electromagnetic Compatibility. emf Electromotive Force. EMI Electromagnetic Interference. EPDM Ethylene Propylene Diene Monomer. FCAW Flux-Cored Arc Welding. FLC Fuzzy Logic Control. FOC Fractional Order Control. FPGA Field Programmable Gate Array. FSM Finite State Machine. GMAW Gas Metal Arc Welding. GTAW Gas Tungsten Arc Welding. GTAW-P Pulsed Gas Tungsten Arc Welding. HM Hysteresis Modulation. I/O Input/Output. IEC International Electrotechnical Commission. IGBT Insulated Gate Bipolar Transistor. LAC Linear Average Control. LCR Inductance/Capacitance/Resistance. LTI Linear Time-Invariant.