Since torque feedback is the inner loop, it normally suffers a smaller delay than that in the outer-impedance loop. Next, we will study the effect of time delays given this gain design criterion. Note that, for simplicity, the gain design above ignores time delay, which does affect system stability. , although system dynamics in our case are restricted to specific patterns such as the critically damped one we design. This advantage avoids the commonly adopted complicated yet heuristic controller tuning procedures, like the ones in Refs.
The resulting benefit is that selecting a natural frequency uniformly determines all the gains of torque and impedance controllers. In our earlier method, the simplification comes from the selection of ω 1, ω 2, ζ 1, ζ 2 parameters in Eq. ( 14) maintains the properties of the fourth-order system. Note that, representing a fourth-order system by two multiplied second-order systems in Eq. These four equations with coupled gains can be solved by Matlab’s fsolve() function. (16) I j b m + I m b j + I j β B τ k I m I j = 4 ω n, k ( I j ( 1 + β K τ ) + I m + β B τ ( b j + B q ) ) + b j b m I m I j = 6 ω n 2, k ( b j + B q ) ( 1 + β K τ ) + k ( b m + β B τ K q ) I m I j = 4 ω n 3, ( 1 + β K τ ) k K q I m I j = ω n 4.
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