Abstract
To successfully control a large variety of systems, a close-loop control law is often used since it can easily accommodate for any errors present in the model of the system. In addition to containing the equations of motion, the model may also have to satisfy a set of inequality equations which are constraining the state variables. Unfortunately, most available methods do not provide a relatively easy or logical approach to incorporate these constraints into the control law. Fortunately, there exists two methods that provide a better approach to developing a feedback controller capable of constraining the state variables, and these two methods will be discussed in more detail. The first approach supplements a Lyapunov function with an artificial potential function to create regions of artificially high potential energy. By letting these regions coincide with the location of the state constraint boundaries, the system will inherently be repelled from the constraint limits. The other technique will define the controller as a cascade-saturation function, which is described as a nested series of saturation functions. By selecting this particular definition, global stability will be provided in addition to limiting the range of the state variables when Lyapunov analysis is performed. To help illustrate the capabilities of these methods, two typical physical systems are also provided, and these systems will both require a close-loop control law and satisfying a set of physical constraints. The first system involves alleviating the vibratory loads placed upon a satellite during launch by mounting it on a flexible support, and the other example is to incorporate angular constraints into a general attitude control law to allow a satellite to autonomously perform a given constrained rotational maneuver.
Bradford, Craig Allen (1996). Using feedback control to apply state variable inequality constraints. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -1996 -THESIS -B73.