-- Introduction to Adaptive Control

posted Mar 16, 2011, 7:35 AM by Javad Taghia   [ updated Apr 24, 2011, 12:33 AM ]
Adaptive Control is one approach which is taken for controlling systems when we are not able to use conventional P.I.D Controllers. The problem is a kind of complexity in our plant. For example there are some unexpected disturbances in our plant or the change in plant's parameters in some systems; specially systems which are changing during the time. For example if the wearing is considerable in a system or the dynamic of the system varies during time because of change in mass or other properties of the plant. So, the assumption of Linear time invariant system is not always acceptable. We have to adapt the controller to overcome the problems and perform control in range of tolerance. There are different applications for adaptive control from aviation to robotics.

There are different methods for design such controllers.
  • High gain robust controller.
  • Self-oscillating adaptive systems.
  • Variable structure adaptive controller
  • Gain scheduling
  • Auto-tuning
  • Model-reference adaptive controller
  • Self-tuning regulators
There are two important categories for adaptive controllers which are more common. The first one is MRAC (Model-reference adaptive controller) and the other one is Self-tuning regulators. 
Each one has advantages. The most important advantage of MRAC controllers is less on-line computational effort comparing to Self-tuning regulators.
In self-tuning regulators we are able to use system identification in order to update the transfer function of our plant on-line. this is an advantage because we are able to cope with unexpected situations and also we are able to perform more robust control. Calculation cost is considerable because the parameters are under monitor continuously. 

In the following picture you can see a MRAC in general form. 

As it is clear, we have one Model we calculate the ym  is the output from the model. We compare this output with the real plant output. by use of some methods such as MIT rule or other approaches we try to calculate new parameters for  regulator. So, we are able to tolerate changes in the plant by adjustment mechanism. 

On the other hand we have self-tuning controller (STR). 
As you can see in STR, we have the outer loop which is monitor the change in the plant to change design characteristics for regulator parameters. If we ignore the estimation block the STR controller is not adoptable to plant changes. Minimum variance controllers by using system identification method recursive least square (RLS) are common approach as an adoptable minimum variance controller, a good candidate fro STR. 

-Pictures are from lecture notes Dr. Olena Kuzmicheva Bremen university Germany.