Robust controller design using Nyquist optimization

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Supervisor:
Dr. Kiss Bálint
Department of Control Engineering and Information Technology

Many developments have been made on robust controller design in recent years. Designing low-order, fixed-structure controller had significant importance among control engineers

since it can be used in various industrial environments and adapted, tuned easily when the

specifications change. In this thesis a novel approach for H∞ controller design for linear

parametrizable controllers is presented. In the conventional robust control methodology it

was proven that designing a controller with such high order as the plant is convex, but designing a fixed structure is generally NP-hard. Furthermore, high order controllers are difficult

to tune which hinders the applicability for industrial use. The aim of this thesis is to design low-order and fixed-structure (robust) controllers using a new controller design method.

Compared to the existing controller design methods, in this thesis a graphical alternative is

proposed by using the generalized Nyquist criterion.

The methodology is introduced as follows. First, a conventionally used control loop is transformed into a generalized structure by a linear lower fractional transformation. The tunable

parameter are extracted from the controller to a diagonal form and the remaining parts of the

controller are absorbed into the plant model. Stability and performance conditions are formulated by exploiting the generalized Nyquist criterion. In order to satisfy these conditions,

line constraints introduced in the Nyquist diagram. Due to the structure of the controller

and line constraints a multilinear feasibility problem is obtained. Using the aforementioned

technique, PD controllers are designed for an experimental DC motor setup. In order to design a fixed-structure robust controller, the above proposed synthesis is reformulated such as

to be able to find a model of the experimental setup. The previously mentioned method can

be adapted such that, a model matching algorithm is performed. Finally, using the obtained

model, a robust fixed-structure PD controller is designed.

A new controller design method in the frequency domain using the generalized Nyquist criterion was successfully applied to an experimental DC setup. V arious controllers were designed

for different control scenarios. The method proved to be directly applicable to frequency data

of the setup. Moreover, the controller design method was used for model matching. Finally,

the current controller design methodology was extended to include parametric uncertainties.

Furthermore, a robust fixed-structure controller was found and its operation was successfully

shown on the experimental DC motor setup.

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