By Charles M. Bergren

This paintings seems below the hood of all robot initiatives, stimulating lecturers, scholars, and hobbyists to benefit extra in regards to the gamut of parts linked to keep watch over structures and robotics. It bargains a different presentation in supplying either idea and philosophy in a technical but enjoyable manner.

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The center horizontal line represents the final value of 1. 5 seconds, 4 seconds, 6 seconds. This is because each of those second-order systems was designed to have the same frequency. These curves show the effect of changing the damping. In Figure 2-17, marked Varying Frequency Only, we can see that all the curves have about the same overshoot and undershoot. 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.

This can be seen in the behavior of the individual functions in the solution. The exponential function e(-d ϫ v ϫ t) dies off over time as t goes to infinity. The larger the damping, the faster it does so. 5 ϫ t ϩ . 2 oscillates and provides the ringing. Designing the Control System Well, we’ve come through the math gauntlet and come up with a closed solution of how the model system behaves. Now, how do we make this useable? Remember our goals; we are going to answer the following: ■ ■ ■ ■ How the design of the control system determines how the robot will react How to characterize the robot’s performance and which design parameters to alter How to alter the robot’s design parameters How to get optimum performance from the robot Let’s tackle the first goal.

If you want to take this horizontal system and extrapolate it to a vertical system, just extend the spring to counteract the force of gravity’s acceleration on the mass. For our computations, the horizontal model takes this term out of the math since gravity does not stretch the spring (see Figure 2-14). The ground reference is, in this case, the earth. It’s not supposed to move under you (those of you in California take note). In reality, as you walk one way, the earth rotates the opposite way.

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