Isn't There Enough Real Inertia Around?

The word inertia in everyday use suggests resistance to change and anunwillingness to act. This is hardly something we need in engineering practiceto solve the urgent problems we all face. Even in a motion-system context, theidea of adding inertia to a system, i.e. adding mechanical mass, is not usuallydesirable as it slows down system response. One familiar exception is adding aflywheel to an engine or machine to smooth out speed fluctuations. Two of themost important benefits of feedback control are command following anddisturbance rejection. Usually the focus of attention in a control system is oncommand following, but in many situations the ability of a system to rejectdisturbances, i.e., have high dynamic stiffness, is paramount.

For a motor-velocity feedback control system, increasing inertia Jreduces the high-frequency disturbance response, i.e., makes the systemdynamically stiffer at high frequencies. But the closed-loop command-followingis degraded. How do we add inertia without degrading command-followingperformance?

A common industry motion-control system has three cascaded feedback loops:motor current, velocity and position. Newton's 2^nd Law says torqueis proportional to angular acceleration, so if we can measure or estimateacceleration, we can scale the acceleration by inertia J to give units oftorque, and then by 1/K_T, the inverse of the motor torque constant,to give current. This is then multiplied by a gain K_AFB, andsubtracted from the current command to the current-control loop. K_AFBhas a similar effect to increasing inertia J; hence the alternate name electronic inertia. To ensure that thecommand-following performance remains the same, the velocity control gains mustbe scaled by the same factor (1 + K_AFB).

The velocity command response is unaffectedby the value of K_AFB because the loop gain increases in proportionto the inertia, producing no net effect. So why are we adding electronicinertia? The real benefit of acceleration feedback is that the disturbanceresponse is improved by acceleration feedback through the entire frequency range in proportion to the term (1 + K_AFB),as shown by the block diagram and transfer function and frequency-response plot.

This improvement cannot be realizedsignificantly above the bandwidth of the current loop, as the accelerationfeedback signal cannot improve the system at frequencies where the current loopcannot inject current. Of course, a robust acceleration feedback signal isrequired. This can be accomplished through differentiation of a position sensorsignal and filtering or through the use of an observer.

Formechatronics engineers, here is one situation where adding inertia is highlydesirable.

Inthis virtual world we live in, electronic inertia is almost expected. PeterSchmidt, Rockwell Automation, and Robert Lorenz, University of Wisconsin atMadison, have done foundational work in this area and their work should beconsulted for actual applications.

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