Adam Owczarkowski

Stability analysis of simple anti-windup compensation in approximate pole-placement control of a second order oscillatory system with time delay

The main aim of this paper is to present analysis of anti-windup compensation impact on tracking performance for a second-order plant with time delay and continuous-time PID controller tuned by pole-placement. The paper uses a first-order non-Pade approximation of the delay in order to streamline the solution of the Diophantine equation. In the case of using Pade approximation, the solution could only be obtained approximately, because of greater number of variables than equations. The paper also studies influence of time delay approximation with first-order model to make approximate pole-placement possible. The performance of the system is compared on the basis of computing differences between integral of absolute and squared tracking errors for the system with and without compensation, as well as observing the excess of windup phenomenon taking place. The control system quality is described on the basis of two quality indices in the case of stable oscillatory second-order plant and square-wave reference signal.

Tracking control of an inertial wheel pendulum by LQR regulation

This article describes universal tracking control method. It is based on model linearization in every point of trajectory. Tested device is an inertial wheel pendulum (IWP). This is an underactuated nonlinear object - two degrees of freedom (angle from vertical and angle of rotation of electric motor) and one actuator (current). The linear quadratic regulator (LQR) and the model of the object are analytically considered. Many experiments are presented and confirm proper and stable operation of the system and some constraints.

Robust LQR and LQI control with actuator failure of a 2DOF unmanned bicycle robot stabilized by an inertial wheel

Abstract Essential ingredients for robust control are the ability to cope with different types of system behavior following modeling imperfections and the ability to assure a certain performance level. In this paper, we propose to use an actuator fault-tolerant control law to govern, during experiments, the stabilization of a bicycle robot with an inertial wheel in order to take into account unmodeled uncertainty introduced by using a linearized model in an LQR fashion. Our proposal is illustrated by signal plots and the values of performance indices obtained from a set of experiments.

Performance of Feedback Linearization Based Control of Bicycle Robot in Consideration of Model Inaccuracy

This paper considers the influence of model inaccuracy on control performance when feedback linearization is used. For this purpose we use plant of bicycle robot. The problem is analysed in two ways: by simulations with artificially changed parameters and by comparison of simulated data with the results obtained from the real object. The collected data show that, even if the model differs from the real object, control method provides good results. This indicates that feedback linearization, method strongly relying on model, can be successfully used for some real plants.

Robust LQR with actuator failure control strategies for 4DoF model of unmanned bicycle robot stabilised by inertial wheel

The paper presents analysis of two control strategies, i.e. LQR and LQI, in application to control of continuous-time nonlinear system on the basis of its linearised discrete-time model, taking robustness approach into account. The applied control laws assure robustness subject to actuator failure what has been used to obtain better control quality (in the sense of selected performance indexes) in comparison to control laws that take no uncertainty into account. The uncertainty resembles here actuator failure or mismodeling case, whenever applied control signal results in different behaviour of the closed-loop system than desired, as in actuator failure case alone.

Modelling of Electrohydraulic Drive with a Valve Controlled by Synchronous Motor

The article describes modelling of electrohydraulic servo drive. In the drive a new type of proportional valve with a synchronous motor controlled by dedicated power electronics is used. The model of the electrohydraulic servo drive prepared in Matlab-Simulink is described. The study included the examination of the basic characteristics such as step response.

Dispersed filters for power system state estimation

The article proposes an approach to power system state estimation allowing the division of the network into smaller parts and performing calculations for each part at the same time. The latter can be implemented in parallel, but the main aim has been to propose a method for dispersed calculations, i.e. calculations that may be performed on computing units located at various points of the whole power system. In the paper, there are 3 algorithms for which dispersed versions have been proposed: Extended Kalman Filter, Particle Filter and Extended Kalman Particle Filter. As a result of the simulations, it has been verified that the Dispersed Particle Filter works better than simple Particle Filter. In two other cases, distributed algorithms work worse, but for the Extended Kalman Filter degradation in the estimation quality is not significant.

Robust Actuator Fault-Tolerant LQR Control of Unmanned Bicycle Robot. A Feedback Linearization Approach

Robust control must be able to cope with various system behavior subject to mismodeling and able to assure some performance level. In the paper, we propose to use actuator fault-tolerant control law to stabilize a bicycle robot model with inertial wheel to take into account the unmodeled uncertainty introduced by using linearized model in a LQR fashion with feedback linearization. Our proposal is illustrated by signal plots and performance indexes’ values obtained from a set of experiments and is a natural extension of the results presented in the past.

A Comparison of Control Strategies for 4DoF Model of Unmanned Bicycle Robot Stabilised by Inertial Wheel

Three control strategies have been compared in the paper, comprising LQR, LQI and LMI-optimised LQR-like control in application to stabilisation of 4DoF model of unmanned bicycle robot with inertial wheel. The robot had been modeled by nonlinear state-space equations, and controller design has been based on its linearisation. As a result of numerical simulation based on Euler integration procedure, the characteristics of the proposed strategies have been found with respect to the introduced performance indices.

Particle filter in multidimensional systems

The article presents studies on the estimation quality of a particle filter applied to small multidimensional objects. For the purposes of the article, a new type of network has been proposed, in which each node is associated with one state variable. Based on performed simulations it has been found that particle filter implemented for small systems (1- or 2-dimensional) is a good choice. However, for larger objects Kalman filter may return better results (it depends on the chosen particles number). This is due to the exponential dependence of needed particles number to the object dimension. It has been also observed that the particle filter, in comparison to the Extended Kalman filter, better estimates the state variables which are well metered, and simultaneously worse estimates the state variables which are worse metered. Possible approaches for objects with a greater number of state variables also have been adduced, including the dispersed particle filter.