Model reference adaptive control with a constrained linear reference model

For systems with limited control authority and a control design that does not prevent saturation from occurring, using a linear reference model can introduce problems, especially when the external command is not necessarily conditioned to respect the capabilities of the plant. An example of this is commanding a large step command that cannot really be achieved linearly by the plant due to limited control authority. Linear reference models will attempt to elicit a linear response in the plant when no such response is possible (peaking). Although providing a realistic command that can be tracked is the job of the planner or trajectory generator, it is desirable if unrealistic commands can be handled at the reference model by shaping its own response trajectory in a way that prevents premature saturation of control signals. This paper introduces reference models that are linear locally but limit their internal dynamics using saturation functions as a part of its dynamics.