Control (1)(Take class notes)Topics to be covered• General response for a voltage-controlled DC motor with proportional control of position• Steady-state error• Overshoot – velocity feedback for damping• Integrator for reducing steady-state error• First consider a linear proportional control for DC motor controlling robot joint• Motor transfer function:• Motor input: = / +- = -Motor transfer function• From the above, one has• From the above one can obtain• Use the U12M4T motor, one has = -= = //= . . Characteristic equation• From the above transfer function, one can obtain the characteristic equation using the denominator.• The characteristic equation is used to solve the root of a second order system• The root can determine the speed of response and damping• There are three cases for the roots:- Case 1 when ξ >1 called over damped - Case 2 when ξ =1 called critical damped- Case 3 when ξ1 called underdamped- How does the system respond to a unit-step input? 60 5.7=605.702ξ 0ξξ1 ξξ1ξ For the U12M4T motor 5.7= / /2/• Note- Kband B both increase the damping- Kb is equivalent to a negative feedback- Increasing K1decreasing damping- K1 can be used to control the system proportional controlPerformance• Steady-state error- Assume unit step input: * No stead-state error for a unit step input- Consider a load of robot linkFor steady-state:• Problems with proportional control:- Overshoot increases with increasing gain- Steady-state error decreases with increasing gainΔ= 1 →∞ → //=1 = Increasing K1decreasing position
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