Position and Velocity versus Time The Cardinal Minima points occur at the peak overshoot points of step because the electromechanically  generated torque drops off with the cosine of the position of the overshoot. Obviously, to minimize the  impact and number of Minima occurrences, it is desirable to minimize the magnitude and number of overshoots, and the best method to do so is to increase damping. How to Compensate (How to Increase Damping)  If you find yourself at a conditionally marginal operating rate (or Cardinal-Minima) there are several  approaches that may be taken to address the issue. Fundamentally, the main issue with these conditionally marginal operating points is damping. While technically, damping is the loss of torque at  speed, an under-damped stepper motor that loses dynamic torque at resonant frequencies can regain  torque margin by increasing damping through drive methods or adding electromechanical damping in the actuator. Reference [3] details consequences, options and results of an under-damped system. Perhaps the two most common causes of under-damped resonant torque losses are drive method or too  excess inertia (Inertia Factor). Bipolar drives, whether two phase or three phase, are far superior to  unipolar or wave drive methods, in terms of adequately damped systems. As discussed, Inertia Factors greater than 5.0 can tend to have significant resonant torque losses at cardinal-operating frequencies. If  bipolar drive is already implemented, then internal electro-mechanical damping methods may be the best  solution to remedy under-damped systems. These methods, however, take away from copper volume for  motor torque generation, so the effective motor constant, or torque per square root watt, is reduced. Other methods, such as response shaping networks through sensor feedback and processing are effective, but increase the complexity and development of the drive electronics.  Slew Operation (Operating in the Pull-Out Region)  Thus far pull-in torque performance or the torque capacity to pull-in from rest has been discussed. Increased dynamic performance is achievable while operating in the pull-out or slew region. Increased torque capacity or velocity may be achieved by ramping (or slewing) up the step rate of the motor. This  will allow the actuator to operate in a performance region that may not be achievable from a dead stop. It  is important to not only ramp-up, but also ramp down step rate. It is not advisable to depend on counting  steps for positional information if operating in the slew region.   Calculating the linear performance in the slew region is similar to the pull-in analysis described above, but  Inertia Factor does not affect the Slew Rate Constant (K SR), as it affects Response Rate Constant (K RR).  The pull-out Torque is calculated by a linear approximation from the Slew Rate to the Torque at Low Pulse Rate. Cardinal Oscillatory effects as described above may impact slew operation, just as they effect  pull-in operation.   Comprehensive Torque Margin Analysis Torque Margin has been calculated, defined and interpreted by almost every imaginable method. Many  companies have their own methods to define and apply Torque Margin, but as described above and  addressed in [3], too much torque can result in under-damped performance. In addition to exaggerating  the cardinal minima, too much torque and severely under-damped systems may introduce fatigue and stressing of mechanical components. Additionally, too much torque equates to excess power, unnecessary heat loss and energy consumption. It is certainly prudent to assure torque requirements are  satisfied, but this does not mean the design engineer should simply increase torque at a mechanism to  ensure a robust system.  Components of Torque Know your torque contributors and their characteristics. In addition to bearing friction, gear frictions and  magnetic coulomb torques, acceleration torques must be accounted for at the step rate of the actuator.  381