Download presentation

Presentation is loading. Please wait.

Published byMohammed Ailey Modified over 2 years ago

1
I NTRODUCTION TO R OBOTICS CPSC - 460 Lecture 5B – Control

2
C ONTROL P ROBLEM Determine the time history of joint inputs required to cause the end-effector to execute a command motion. The joint inputs may be joint forces or torques.

3
C ONTROL P ROBLEM Given: A vector of desired position, velocity and acceleration. Required: A vector of joint actuator signals using the control law.

4
4 R OBOT M OTION C ONTROL (I) Joint level PID control each joint is a servo-mechanism adopted widely in industrial robot neglect dynamic behavior of whole arm degraded control performance especially in high speed performance depends on configuration

5
R OBOT M OTION C ONTROL (II) – C OMPUTED T ORQUE The dynamic model of the robot has the form: is the torque about z k,if joint k is revolute joint and is a force if joint k is prismatic joint Where: M(Θ) is n x n inertia matrix, is n x 1 vector of centrifugal terms G(Θ) is a n x 1 vector of gravity terms

6
PD CONTROL The control law takes the form Where:

7
PD CONTROL

8
M ODEL BASED CONTROL The control law takes the form: K p and K D are diagonal matrices.

9
C ONTROL P ROBLEM

10
S TABLE R ESPONSE

11
Evaluating the response steady-state error settling time rise time overshoot overshoot -- % of final value exceeded at first oscillation rise time -- time to span from 10% to 90% of the final value settling time -- time to reach within 2% of the final value ss error -- difference from the system’s desired value

12
P ROJECT The equations of motion: 22 11 (x, y) l2l2 l1l1

13
P ROJECT S IMULATION AND D YNAMIC C ONTROL OF A 2 DOF P LANAR R OBOT Problem statement: - The task is to take the end point of the RR robot from (0.5, 0.0, 0.0) to (0.5, 0.3, 0.0) in the in a period of 5 seconds. - Assume the robot is at rest at the starting point and should come to come to a complete stop at the final point. - The other required system parameters are: L 1 = L 2 = 0.4m, m 1 = 10kg, m 2 = 7kg, g = 9.82m/s2.

14
P ROJECT Planning 1. Perform inverse position kinematic analysis of the serial chain at initial and final positions to obtain ( 1i, 2i ) and ( 1f, 2f ). 2. Then, obtain fifth order polynomial functions for 1 and 2 as functions of time such that the velocity and acceleration of the joints is zero at the beginning and at the end. These fifth order polynomials can be differentiated twice to get the desired velocity and acceleration time histories for the joints.

15
P ROJECT Use a PD control law where K p and K v are 2x2 diagonal matrices, and s is the current(sensed) value of the joint angle as obtained from the simulation. Tune the control gains to obtain good performance

16
B LOCK DIAGRAM

17
2DOF R OBOT The forward kinematic equations: The inverse kinematic equations: The Jacobian matrix 22 11 (x, y) l2l2 l1l1

Similar presentations

OK

IVR 30/10/2009 Herrmann1 IVR: Control Theory Overview: PID control Steady-state error and the integral method Overshoot and ringing in system with time.

IVR 30/10/2009 Herrmann1 IVR: Control Theory Overview: PID control Steady-state error and the integral method Overshoot and ringing in system with time.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on high voltage engineering books Ppt on nuclear family vs joint family Ppt on how to use powerpoint 2013 Ppt on joint forest management in india Ppt on cross-sectional study designs Dentist appt on saturday Download ppt on acids bases and salts for class 10 Ppt on atm machine software Ppt on pricing policy of htc Ppt on statistics in maths what is the factor