An Introduction to System Modeling and Control

14State Variables

14.1 Statespace Form

Consider the mass–spring–damper system in Figure 14.1.

Figure 14.1. (a) Spring–mass–damper system. (b) Damper cross section.

If then the spring is neither compressed nor stretched, which is to say the spring is relaxed. The force on the mass due to the spring is

Note that if the spring is pulling to the left while if the spring is pushing to the right. The damper (dashpot) is illustrated in more detail on Figure 14.1b. The force of the damper on is proportional to its velocity and is given by

Note that if then the mass along with the ...