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By Charles M. Bergren

This paintings seems below the hood of all robot initiatives, stimulating academics, scholars, and hobbyists to benefit extra concerning the gamut of components linked to regulate structures and robotics. It bargains a different presentation in offering either thought and philosophy in a technical but wonderful approach.

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75, and so on. This is because each of those second-order systems was designed to have the same damping. These curves show the effect of changing the frequency. We will examine the characteristics of the curves on the graph and discuss which characteristics are of immediate interest. 5 0 0 2 4 6 8 10 Time t FIGURE 2-16 The second-order system responds differently as the damping is varied. 2 0 0 2 4 6 8 10 Time t FIGURE 2-17 The second-order system responds differently as the frequency is varied.

We can use the equations herein to control any of the aforementioned systems without further investigation. We leave it up to the reader to investigate the mathematics of calculus that hold that acceleration is the derivative of velocity, and velocity is the derivative of position. Suffice it to say that positive acceleration builds up speed, negative acceleration (braking or accelerating in reverse) decreases speed, positive speed accumulates distance (position), and negative speed (moving backwards) decreases distance (position).

We certainly know from the bridge example that it’s important. It’s also extremely complex in the mathematical theory and we need not go into it here, but we should look at several pieces of advice. First, we should identify just what instability is. Some control systems, if not designed right, can oscillate way too much, upset the mechanics, and ruin the operation of the robot. These oscillations can stem from various flaws in the design. ■ Resonant frequencies As we just mentioned, make sure the mechanics and other physical elements of the system, such as the frictional components and spring elements, do not have resonant frequencies.

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