A Caltech Library Service

Optimal controller design methods for linear systems with uncertain parameters--development, evaluation, and comparison


Vinkler, Aharon P. (1979) Optimal controller design methods for linear systems with uncertain parameters--development, evaluation, and comparison. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9fwb-er39.


In many physical systems, an accurate knowledge of certain parameters is very difficult or very expensive to obtain. The designer of a remotely piloted vehicle flight control system, for example, frequently has available little data regarding aerodynamic coefficients, due to a lack of wind tunnel tests. Commonly used controller design methods, based on nominal values of plant parameters, often fail to achieve a satisfactory design in the face of parameter uncertainty.

In this work two methods have been developed for the design of linear, constant gain feedback controllers for systems with uncertain parameters:

1) The multistep guaranteed cost control method is based on the concept of minimizing an upper bound of a cost functional in the face of parameter uncertainty. An algorithm has been developed to analyze the effect of parameter uncertainties on closed-loop system stability. An extension of this algorithm results in a technique for choosing constant feedback gains which guarantee a stable closed-loop system that possesses some of the desirable features of optimally designed control systems.

2) The minimum discrete expected cost method is based on the concept of minimizing the expected value of a cost functional over a finite number of points in the range of parameter uncertainty. The design process makes use of statistical information about the uncertain parameters and incorporates in its cost functional whatever effects accompany a large departure in the plant parameters from their nominal values.

An extensive comparison of these two methods, together with the guaranteed cost control method, the minimax method, and the uncertainty weighting method, has been done in the context of the design of a fifth-order lateral autopilot for an RPV with uncertain aerodynamic coefficients. All five methods were evaluated on the bases of performance and design effort required. Both new methods were found to avoid some of the drawbacks associated with other techniques. The two newly developed methods are easy to implement and offer the designer tools for use in real control system design.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Stewart, Homer Joseph
Thesis Committee:
  • Unknown, Unknown
Defense Date:2 April 1979
Record Number:CaltechETD:etd-10312006-104019
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4340
Deposited By: Imported from ETD-db
Deposited On:15 Nov 2006
Last Modified:19 Apr 2021 22:28

Thesis Files

PDF (Vinkler_ap_1979.pdf) - Final Version
See Usage Policy.


Repository Staff Only: item control page