Linear Control of Manipulators Robot Control System Block
Linear Control of Manipulators
Robot Control System • Block diagram – Robot dynamics – Feedback (position servo error) (velocity servo error) ü Nonlinear & MIMO (multi-input multi-output) control system 2
Modeling of a Single Joint • Effective Inertia – Torque balance equation effective inertia effective damping 3
Modeling of a Single Joint (Example) 4
Independent Joint Control • Highly geared manipulators – Nonlinear system → Linear system – MIMO → N independent SISO Joint controller = DC motor controller 5
DC Motor Modeling • 6
DC Motor Modeling • DC motor system • Closed-loop control system 7
DC Motor Control • Closed-loop Control Θr E + - C(s) V Θ G(s) C(s): Controller Θ Θr t 8
DC Motor Control • PID Controller – Frequency Domain Θr + E + - + V G(s) Θ + 9
DC Motor Control • PID Controller – Time Domain Θr + E + - Error 크기에 비 례 + V G(s) Θ + Error 기울기에 비례 Error 면적에 비 례 10
DC Motor Control • P 제어기 – Increasing Kp (P Gain) Rise Time Overshoot Settling Time Steady State Error Decrease Increase Small change Decrease 2. 0 1. 0 0. 5 12
DC Motor Control • PD 제어기 – Increasing Kd (D gain) Rise Time Overshoot Settling Time Steady State Error Small change Decrease None 5 0 10 14
DC Motor Control • PID 제어기 – Increasing Ki (I gain) Rise Time Overshoot Settling Time Steady State Error Small change Increase Eliminate 16
PID Tuning • P, I, D Gain 의 관계 Rise Time Overshoot Settling Time Steady State Error Kp Decrease Increase Small change Decrease Kd Small change Decrease None Ki Small change Increase Eliminate 지능형 로봇 공학(사이텍미디어) 17
PID Tuning • Ziegler-Nichols Method – Plant 에 대한 step response (transient state) 로 부터 Kp, Kd, Ki 를 설정하는 실험적 방법 18
PID Tuning • Ziegler-Nichols Method-Case 1 – S-shaped step response 19
PID Tuning • Ziegler-Nichols Method-Case 2 20
Control of Second-Order System • damping ratio natural frequency 21
Control of Second-Order System • Control law • Closed-loop dynamics position-regulation system 22
Control-Law Partitioning • Controller Design – Model-based portion • System parameter related – Servo portion • Independent of system parameters Ø Can be used for nonlinear controller design 23
Control-Law Partitioning • Controller Design (example) 1) Model based portion Open-loop dynamics motion for a unit mass 2) Servo portion closed-loop dynamics critical damping condition 24
Control-Law Partitioning • Block Diagram • Example 25
Trajectory-Following Control • 26
Disturbance Rejection • Disturbance rejection – Maintain good performance in the presence of external disturbances or noise • Steady-state error 27
Disturbance Rejection • Addition of integral term PID controller • Steady-state error 28
- Slides: 28