Designing Compensators 4 Introduction 4-2 The SIsO Design Tool Opening the SISO Design Tool 3 Importing Models into the SISO Design Tool 4-5 Feedback Structure 4-6 Bode Diagram Design 4-8 Example: DC Motor 4-8 Adjusting the Compensator gain Right-Click Menus 4-9 djusting the Bandwidth 4-9 Adding an Integra 4-12 Adding a Lead Network 4-14 Moving Compensator Poles and Zeros Changing Units on a Plot 4-19 Adding a Notch Filter 4-20 Root Locus Design 4-24 Example: Electrohydraulic Servomechanism 4-25 Changing the Compensator Gain Adding Poles and Zeros to the Compensator 4-31 Editing Compensator Pole and Zero Locations Exporting the Compensator and Models 439 Storing and Retrieving Intermediate Designs 4-40 Functions For Compensator Design Root Locus design 4-42 ceme 4-42 Linear-Quadratic-Gaussian (LQG) Design......... 4-46 Example: LQG Design 4-51 Example: LQG Design for Set Point Tracking 4-55iii 4 Designing Compensators Introduction .......................................... 4-2 The SISO Design Tool ................................. 4-3 Opening the SISO Design Tool . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 Importing Models into the SISO Design Tool . . . . . . . . . . . . . . . 4-5 Feedback Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6 Loop Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7 Bode Diagram Design ................................. 4-8 Example: DC Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Adjusting the Compensator Gain . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Right-Click Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9 Adjusting the Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9 Adding an Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12 Adding a Lead Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14 Moving Compensator Poles and Zeros . . . . . . . . . . . . . . . . . . . 4-17 Changing Units on a Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19 Adding a Notch Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20 Root Locus Design ................................... 4-24 Example: Electrohydraulic Servomechanism . . . . . . . . . . . . . . 4-25 Changing the Compensator Gain . . . . . . . . . . . . . . . . . . . . . . . 4-30 Adding Poles and Zeros to the Compensator . . . . . . . . . . . . . . 4-31 Editing Compensator Pole and Zero Locations . . . . . . . . . . . . 4-36 Exporting the Compensator and Models . . . . . . . . . . . . . . . . . 4-39 Storing and Retrieving Intermediate Designs . . . . . . . . . . . . . 4-40 Functions For Compensator Design ................... 4-42 Root Locus Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42 Pole Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42 Linear-Quadratic-Gaussian (LQG) Design . . . . . . . . . . . . . . . . 4-46 Example: LQG Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-51 Example: LQG Design for Set Point Tracking . . . . . . . . . . . . . 4-55