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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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**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. • 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)**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)**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**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.**Actuator Dynamics**• Referring to Figure 6.5, we set , the equation of motion of this system is then**Actuator Dynamics**• In Laplace domain:**Set-Point Tracking**• PD Controller**Set-Point Tracking**• PD Controller • The resulting closed-loop system is**Set-Point Tracking**• The tracking error: • For a step input and a constant disturbance: • The steady state error is**Example**• Consider the second-order system • The closed-loop characteristic polynomial is • Suppose . With**Set-Point Tracking**• PID Controller**Set-Point Tracking**• The closed-loop system is now the 3rd-order system • Routh-Hurwitz criterion: The system is stable if**Feedforward Control**Then, Clearly, in addition to the stability of the closed-loop system, the feedforwardtransfer function F(s) must itself stable.**State Space Design**• By choosing state variables • The system given by Eq.(6.39) and (6.40) becomes**State Feedback Control**Linear Quadratic Regulation Control Subject to**Linear Quadratic Regulation Control**Performance Index Subject to**Linear Quadratic Regulation Control**Optimal Control Riccati Equation

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