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Robot Manipulator Control

Robot Manipulator Control. Juhng-Perng SU Ph.D. Professor Electrical Engineering National Dong- Hwa University. Chapter 6 Independent Joint Control. Manipulator Control Determine the time history of joint inputs required to cause the end effector to execute a command motion .

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Robot Manipulator Control

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  1. Robot Manipulator Control Juhng-Perng SU Ph.D. Professor Electrical Engineering National Dong-Hwa University

  2. Chapter 6 Independent Joint Control Manipulator Control Determine the time history of joint inputs required to cause the end effector to execute a command motion. • Joint Inputs • Voltage Inputs to the Motors • Joint Forces and Torques • command motion • A sequence of end-effector positions and orientations (P-to-P) • A continuous path (Path Tracking)

  3. Control Strategies • Hardware/Software Trade-off • Early aircraft were relatively easy to fly by possessed limited performance capabilities (Aerospace Industry) • Mechanical Design (Hardware) • Robot actuated by Permanent magnet DC motors with gear reduction (Linear Control) • Direct-drive robot using high-torque motors with no gear reduction (Nonlinear Control)

  4. Simplest Type of ControlIndependent Joint Control • Each Link is controlled as a single-input/single-output system. Coupling due to the motion of other links are treated as disturbances. Tracking and Disturbance Rejection

  5. Actuator Dynamics

  6. Actuator Dynamics • DC-motors can be classified according to the way in which the magnetic field is produced and the armature is designed. Here we discuss only the so-called permanent magnet motors whose stator consists of a permanent magnet. In this case we can take the flux, to be a constant. • The torque on the rotor is then controlled by controlling the armature current.

  7. Actuator Dynamics

  8. Actuator Dynamics

  9. Actuator Dynamics

  10. Actuator Dynamics

  11. Actuator Dynamics

  12. Actuator Dynamics • Referring to Figure 6.5, we set , the equation of motion of this system is then

  13. Actuator Dynamics • In Laplace domain:

  14. Actuator Dynamics

  15. Actuator Dynamics (Reduced Order)

  16. Actuator Dynamics (Reduced Order)

  17. Actuator Dynamics (Reduced Order)

  18. Set-Point Tracking • PD Controller

  19. Set-Point Tracking • PD Controller • The resulting closed-loop system is

  20. Set-Point Tracking • The tracking error: • For a step input and a constant disturbance: • The steady state error is

  21. Example • Consider the second-order system • The closed-loop characteristic polynomial is • Suppose . With

  22. Example (d=0)

  23. Example (d=40)

  24. Set-Point Tracking • PID Controller

  25. Set-Point Tracking • The closed-loop system is now the 3rd-order system • Routh-Hurwitz criterion: The system is stable if

  26. Set-Point Tracking

  27. Feedforward Control

  28. Feedforward Control Then, Clearly, in addition to the stability of the closed-loop system, the feedforwardtransfer function F(s) must itself stable.

  29. Feedforward Control

  30. Feedforward Control (Tracking)

  31. Feedforward Control (Disturbance)

  32. Feedforward Control (Disturbance)

  33. Robot Manipulator

  34. Robot Manipulator

  35. State Space Design • By choosing state variables • The system given by Eq.(6.39) and (6.40) becomes

  36. State Space Design

  37. State Space Design

  38. State Feedback Control

  39. State Feedback Control

  40. State Feedback Control Linear Quadratic Regulation Control Subject to

  41. Linear Quadratic Regulation Control Performance Index Subject to

  42. Linear Quadratic Regulation Control Optimal Control Riccati Equation

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