Sergei Avanessov

Fixed-order stabilising controller design by a mixed randomised/deterministic method

A novel mixed randomised/deterministic method for fixed-order controller design is proposed for discrete-time single-input single-output plants. It is based on the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are then projected onto the affine set of closed-loop characteristic polynomials and the stable line segments in the controller parameter space are determined. A novel approach is proposed for global and local optimisation over reflection segment bunches on the basis of the weighted sum of absolute values of reflection coefficients.

Stability domain approximation for the robust PID controller parameters by reflection segments approach

An innovative method for robust stabilizing PI, PD controller design and its stabilizing area approximation is presented for discrete-time SISO plants. It starts from the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are projected onto affine set of closed-loop characteristic polynomials which is defined by the controller parameters and the stable line segments in the controller parameter space are then determined. The segments of two systems with different parameters are used to generate a rectangular and polygonal approximations of the stabilizing area of robust controller parameters that stabilize both systems.

Reflection segments based robust PID controller solution for benchmark problem

A number of methods has been published in the recent years in order to demonstrate a stable and satisfactory solution for the benchmark test problem of a flexible transmission system. This paper presents a new approach for PID stabilization for the benchmark problem via generation of stable segments in the controller coefficient space and their subsequent optimization methods in order to find the best suited robust solution.

Robust fixed order controller design by a mixed randomized/deterministic method

A novel mixed randomized/deterministic method to robust fixed-order controller design is proposed for discrete-time SISO plants. It is based on the random generation of Schur stable polynomials using reflection coefficients and reflection polytopes of polynomials. Stable reflection segments are projected onto affine set of closed-loop characteristic polynomials and the stabilizing polytopes in the controller parameter space are determined.

Reflection segments based stability domain approximation of the robust PID controller parameters

An innovative method for robust stabilizing PI,PD controller design and its stabilizing area approximation is presented for discrete-time SISO plants. It starts from the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are projected onto affine set of closed-loop characteristic polynomials which is defined by the controller parameters and the stable line segments in the controller parameter space are then determined. The segments of two systems with different parameters are used to generate a rectangular and polygonal approximations of the stabilizing area of robust controller parameters that stabilize both systems.

Fixed order stabilizing controller design via random reflection segments

A novel randomized approach to fixed-order controller design is proposed for discrete-time SISO plants. It is based on the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are projected onto affine set of closed-loop characteristic polynomials which is defined by the controller parameters and the stable line segments in the controller parameter space are then determined. A novel approach is proposed for global and local optimization over reflection segment bunches on the basis of the weighted sum of absolute values of reflection coefficients.

Fixed order stabilizing controller design via reflection segments of polynomials

A novel randomized approach to fixed-order controller design is proposed for discrete-time SISO plants. It is based on the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are projected onto affine set of closed-loop characteristic polynomials which is defined by the controller parameters and the stable line segments in the controller parameter space are then determined.

Stability domain of fixed order controllers via reflection segments of polynomials

A novel randomized approach to fixed-order controller design is proposed for discrete-time SISO plants. It is based on the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are projected onto affine set of closed-loop characteristic polynomials which is defined by the controller parameters and the stable line segments in the controller parameter space are then determined. The stability domain of a fixed order controller is defined as a set of stabilizing line segments generated by the set of stable reflection segments of the closed-loop system.

Four types of stable polytopes via reflection coefficients of polynomials

Abstract The geometry of stable discrete polynomials using their coefficients and reflection coefficients is investigated. Four different methods of generating stable polytopes by the use of reflection coefficients of polynomials are defined. The volumes of stable polytopes are calculated.

Stable polytope of reflection vector sets

The geometry of stable discrete polynomials using their coefficients and reflection coefficients is investigated. Stable polytopes of different reflection vector sets are defined and the volume of these stable polytopes is calculated.