|M.Sc Student||Zimmerman Yaron|
|Subject||An Innovative Method for Optimization Based, High Order|
|Department||Department of Civil and Environmental Engineering||Supervisor||Professor Emeritus Per-Olof Gutman|
|Full Thesis text|
A new automatic method for tuning the parameters of high order linear controllers is presented. The auto-tuning is achieved by solving an unconstrained minimization problem that is related to the shaping of the open loop frequency function. The definition of the cost function in this work is based on the formulation of the closed loop requirements by the QFT methodology. A new term is defined, called ’Nichols Distance’, which is a signed measure of the distance from a Horowitz-Sidi bound to the corresponding compensated nominal open loop frequency response value where the sign indicates on which side of the Horowitz-Sidi bound the frequency response value lies. The cost function is a sum of exponential functions where the arguments are weighted Nichols Distances. Since the Horowitz-Sidi bounds do not constitute hard constraints, an unconstrained optimization problem is obtained. The well-known Nelder-Mead search algorithm is used to illustrate the minimization of the cost function through which the controller parameters are found. Theoretical aspects of the convexity of the cost function, and the choice of initial controller parameters are discussed.
The method makes it possible to design high order controllers and hence gives the control engineer an easy-to-use and efficient tool for finding a robust design with potentially better performance. The effort demanded from the designer is similar to that required to tune a low order controller, such as a PI or PID, with other methods. The capabilities of the new method are demonstrated on three examples.