Univ logo Selection of Input and Output Structure Afrouz Farshad Mehr Prof.Nicos Karcanias City University of London

Univ logo What is the problem? What we are taught in the university: We know the variables ‘w’, ‘z’, ‘v’ and ‘u’, design the controller “K”! Great !!!! I am ready to go for the job! What they want us to do in the job: Design a controller to achieve the required production rates and product quality! But:  We have thousands of variables.  We don’t know what the inputs(sensors)and outputs (actuators) are.  We would like to use as few sensors/actuators as possible.  We need to get the best control results by expending the least possible energy.  System should be stable  etc

Univ logo How to solve the problem? (2) (1) (3) (4)  First we look for the minimum input energy  Then We select the proper control inputs (actuators) which provides us with the minimum value of the minimum energy.  We use the duality to select the proper outputs (sensors) with the maximum output energy.

Univ logo  Select B such that (A,B) has the “best” energy based controllability properties  Select B such that (A,B) has the “best” properties for reduced norm state feedback design.  Use the duality for the selection output matrix “C”!  Select B, C such that (A,B,C) has the “best” properties for reduced complexity dynamic feedback and reduced gain design for the different types of dynamic feedback.  how selection of B, C may minimize the variations on a number of resulting overall system properties in the presence of uncertainty.

Univ logo Conclusion:  Input /output Structure Selection based on Energy  Feedback Gain and Input, Output Structure selection  Input, Output Selection for improved robustness/sensitivity of design

Univ logo Future works:  Multi-objective input/output selection  Searching algorithms for desirable Input-Output structure in discrete systems  Generalizing the results to nonlinear systems