Wyniki wyszukiwania - BazTech

1

Regular design equations for the discrete reduced-order Kalman filter

Hippe P.

Archives of Control Sciences

|

2012

|

Vol. 22, no. 2

161-174

EN

In the presence of white Gaussian noises at the input and the output of a system Kalman filters provide a minimum-variance state estimate. When part of the measurements can be regarded as noise-free, the order of the filter is reduced. The filter design can be carried out both in the time domain and in the frequency domain. In the case of full-order filters all measurements are corrupted by noise and therefore the design equations are regular. In the presence of noise-free measurements, however, they are not regular so that standard software cannot readily be applied in a time-domain design. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation causes no problems. However, the known proof of optimality of the factorization result requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for the reduced-order discrete-time Kalman filter in the time and in the frequency domains so that standard software is applicable. They also allow to formulate the conditions for the stability of the filter and to prove the optimality of the existing solutions.

2

Regular design equations for the continuous reduced-order Kalman filter

Hippe P.

Archives of Control Sciences

|

2011

|

Vol. 21, no. 4

349-361

EN

Reduced-order Kalman filters yield an optimal state estimate for linear dynamical systems, where parts of the output are not corrupted by noise. The design of such filters can either be carried out in the time domain or in the frequency domain. Different from the full-order case where all measurements are noisy, the design equations of the reduced-order filter are not regular. This is due to the rank deficient measurement covariance matrix and it can cause problems when using standard software for the solution of the Riccati equations in the time domain. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation does not cause problems. However, the known proof of optimality of the factorization result also requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for reduced-order Kalman filters in the time and in the frequency domains for linear continuous-time systems. They allow to use standard software for the design of the filter, to formulate the conditions for the stability of the filter and they also prove that the existing frequency domain solutions obtained by spectral factorization of a non-regular polynomial matrix equation are indeed optimal.

3

Windup prevention for MIMO systems in the frequency domain

Hippe P., Deutscher J.

Archives of Control Sciences

|

2009

|

Vol. 19, no. 4

355-369

EN

Input saturation can have an undesired influence on the transients of the closed loop system and it can even lead to an unstable behavior. Controller windup is caused by badly damped or unstable modes in the compensator and controller windup is due to fast dynamics of the closed loop system. In a two-step approach one can first prevent controller windup by the so-called observer technique and if, in addition, there exists the danger of plant windup one adds an additional dynamic element to prevent it. There also exists a one-step approach that prevents controller and plant windup at the same time. This paper shows how both approaches to windup prevention can be designed directly in the frequency domain without recourse to time domain arguments. A simple example demonstrates the windup effects and their prevention.

4

Windup prevention in the presence of ampiltude and rate saturation

Hippe P.

Archives of Control Sciences

|

2006

|

Vol. 16, no. 3

315-326

EN

The purpose of this contribution is to show, that by inserting an appropriate nonlinear dynamic model at the output of the compensator, basically all known techniques for windup prevention developed for amplitude restrictions are also applicable in the presence of actuators with joint amplitude and rate saturation.