Linear Manipulator control Flashcards
What is the purpose of a control system in manipulators?
Needed to compute the actuator torque commands for the desired position trajectory. (dynamics)
What is the con of open loop control?
It is not realistic due to disturbances
How is feedback used in a closed-loop system
feedback from the joint sensors is fed into the control system
-then used to find servo error
-MIMO (multi-input, multi-output)
Give the servo error in terms of desired angle and angular velocity
øe = ød - ø (error = desired - actual)
ø_dote = ø_dotdesired - ø_dot
What is the condition for a second order linear system being stable
zeta *w > 0
w^2 > 0
For a second order system, how do we model the PD controller?
f = equation of second order system
f = -kp(x) - kv(xdot)
b’ = b+kv
k’ = k +kp
How do we change the behaviour of a control system?
Changing the controller gains
How does control law partitioning work?
In addition to the controller(servo) a model-based portion is included in the system.
f = af’ + ß
a and ß are chosen so the mass appears to be 1
-
ß = bxdot + kx
a = m
xdot2 = f’
When we have a PID controller, how is the servo portion modelled?
f’ = xd_dot2 +kvxe_dot + kpxe + ki ∫xe dt
What does the integral part of the controller do?
Reduces steady state error to 0
Define effective inertia
The combined inertia from the motor and inertial laods
For high geared joints (where n»_space;1), what assumption do we make?
To ensure the link is never underdamped, we use the maximum values of inertia
Effective inertia is a constant Imax + n^2 Imotor
What is an assumption made about gearings, shafts, bearings and links and why?
These parts are not flexible. This is good if:
-the system is sufficiently stiff
-the natural frequency of the resonances are high
what is key about choosing the natural frequency
The natural frequency is chosen based on the lowest structure resonance
wn < 1/2 Wres
When we have a disturbance, how is that written in terms of error with a PD controller
xe_dot2 + kvxe_dot +kpxe = 1/m fdist
