CDS 110b: Two Degree of Freedom Control Design

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CDS 110b Schedule Project Course Text

In this set of lectures we describe the problem of trajectory generation and tracking. We use differential flatness to generate feasible trajectories for the system, which are then tracked by a local (gain-scheduled) controller.

Course Materials

References and Further Reading

Frequently Asked Questions

What's an example of a system that isn't differentially flat?

While many systems are differentially flat, there are many systems that aren't. One example is given by the following set of differential equations


\aligned \dot x_1 &= u_1 \\ \dot x_2 &= u_2 \\ \dot x_3 &= x_1 u_2 - x_2 u_1 \\ \dot x_4 &= x_3 u_1 \\ \dot x_5 &= x_3 u_2. \endaligned


Showing that this system isn't differentially flat is complicated and relies on mathematical tools that are beyond those that we present in the class. If you are interested in learning more, take a look at a survey article on differential flatness by Martin, Murray and Rouchon.