If you want to design multi-loop PIDs then I would consider using the relative gain array (RGA) to determine which manipulated variables should be paired with which controlled variables. You can then tune the controllers individually; just keep in mind that the controllers should not be very aggressive as your tuning ignores the interactions amongst the variables that exists.

If you find that the interactions are significant then using some multivariable approach, e.g., model predictive control, may give significantly better results.

Hi,

That depends on the nonlinear coupling effects. If the gear ratios are quite high (typically greater than 10), then you can consider each arm as a second order that is perturbated by dry friction, gravity and couplings. The value of the inertia should be taken as the maximum inertia value seen by the actuator. Otherwise, as stated by Hahn, you better to use the "computed torque" control which is, of course, more involved. Beware of the saturation of control.

You can refer to the book of Khalil and Dombre and our paper "A new closed-loop output error method for parameter identification of robot dynamics" although we dealt with a PD controller.

Best

As Alexandre Janot write, if the robot is considered as a perturbation for the motors, I suggest to get the inertia of the robot M(q) from the kinetic energy T expressed in matrix quadratic form T = 0.5 transpose(dq/dt)*M(q)*dq/dt, and then the diagonal elements of T are used to tune the PID (see the book of Spong and Vidyasagar, Robot Dynamics and Control). Since the inertia is a function of the configuration of the robot you can actualize its value on-line or take the suggestion of Alexandre (maximum value). Another control technique is feedforward control in which the compensation can be gotten off-line or computed torque in which the Dynamic Model of the controller is computed on-line. 

Dear Rene,

Thank you for your suggestions. Sounds good to use feedforward control which works fine with "classical" industrial robots.

Best, Alex

Sir, You could do multi loop tuning as possible. For a SISO system, follow the rules for tuning a cascade system as follows:

1) First tune the inner loop by eliminating the outer loop. With this try doing it for outer loop. Please refer literature for tuning cascade controller