Stefan Domek

Active vibration control in milling flexible workpieces

During milling of flexible workpieces a regenerative chatter vibration may become a critical factor that limits productivity. It is shown in this paper that a selection of cutting parameters based on a stability lobes diagram may not always be a remedy for low productivity due to increased forced vibration level. Additionally, other factors such as tool wear may limit the selection of stable spindle speeds. This paper presents an active control system that counteracts the development of chatter vibration. The proposed active control system employs Linear Quadratic Gaussian (LQG) algorithm and piezoelectric actuator to suppress vibration during cutting. The Kalman filter is used to estimate the state of the system required by LQG algorithm. The active control introduces damping into the system, thereby raising the critical depth of cut and reducing forced vibration amplitude. It enables stable cutting under a much wider range of cutting parameters than for the uncontrolled system. Cutting tests are performed to demonstrate an effectiveness of the control system. Practical issues limiting applications of the proposed technique are discussed.

Hybrid model-following control algorithm within the motion control system

The goal of this paper is to present a new robust hybrid method that ensures stiffness of the mechanical characteristic of the direct current motor servo drive, which means lack of influence of the varying load torque on quality of the velocity control, what extends the concept of the MFC-V (Model-Following Velocity Control) system that allows one to shape the servo drive transient response, ensuring, among other things, an overshoot free step response in the velocity control loop. The proposed multi-loop-controller solution exemplifies a possible approach to designing a motor servo drive within the motion control system of a CNC (Computer Numerical Control) machines.

Calibration of Cameras and Fringe Pattern Projectors in the Vision System for Positioning of Workpieces on the CNC Machines

Application of machine vision in automation, robotics and mechatronic systems is one of the most rapidly developing areas of industrial and applied computer science. The vision system presented in the paper can be used for automatic positioning of the workpieces on the numerically controlled machines. The idea of the system is based on the 3D scanning using the fringe patterns approach [ but its accuracy strongly depends on the lighting conditions and the proper calibration of the whole vision system. The most crucial elements for the calibration are both cameras and structural light projectors, as well as the overall geometrical configuration (external parameters in the common coordinate system) and the compensation of the brightness nonlinearities introduced by the structural light sources. In the paper some methods used for the calibration of the experimental system and obtained results are presented.

Improving stability and regulation quality of nonlinear MIMO processes

Abstract The paper presents results of comparative analysis of the control system introducing dynamic decoupling and the robust two-degrees of freedom control system with the use of the decoupled nominal model of the linearized MIMO process. First the design method of the control system with dynamic decoupling of MIMO processes has been replayed. Next, basic advantages of the model following control structure for MIMO systems, its stability and robustness properties are presented. Finally, a MFC-MIMO robust control system has been proposed. The presented control structure has been tested for its performance on the tracking processes of yaw angle and position of the drillship. Results of simulation tests lend support to the view that the proposed MIMO-MFC control method may find wide application to robust control of nonlinear plants with time-varying or perturbed parameters.

Fractional-Order Model Predictive Control with Small Set of Coincidence Points

In the paper the possibility and conditions for employing the fractional-order differential calculus theory in the model predictive control are analyzed. First, the principle of the integer-order linear predictive control and theoretical foundations of the fractional-order differential calculus are reminded. Using the presented theoretical foundations attention is focused further on the possibility of employing the fractional-order calculus for model predictive control with a small set of coincidence points. The introduction of the fractional-order differential calculus at the stage of synthesizing the control algorithm offers an additional degree of freedom in tuning a control loop. The discussion is illustrated with results of simulation tests.

Piecewise Affine Representation of Discrete in Time, Non-integer Order Systems

The multi-model approach has been often used for modeling and control of physical processes in recent years, leading to a class of so-called switched systems. Their properties, particularly the stability, observability and controllability analysis, have become one of active research topics in control theory and applications. In the paper a method of modeling nonlinear, discrete in time, non-integer order systems by means of piecewise affine multi-models is proposed, and then the special cases of such models are described. The discussion is illustrated with results of simulation tests.

Approximation and stability analysis of some kinds of switched fractional linear systems

Many systems appearing in practice exhibit a hybrid nature, that is, a coupling between continuous dynamics and discrete events. Special cases of such systems are those in which the linear subsystems are switched according to time or according to state and/or input. In the paper a method for approximation of some kinds of switched fractional linear systems is proposed and their stability is analyzed.

Model-Plant Mismatch in Fractional Order Model Predictive Control

The effectiveness of model predictive control (MPC) depends on the accuracy of the process model, which is utilized directly to compute the manipulated variable. The effect of various model-plant mismatches on the performance of the classic predictive controller is well known. However, many industrial processes exhibit very complex properties, and determining an adequate model for them is not an easy task. In recent years it has been suggested to employ non-integer order models to describe difficult processes. This leads to fractional order model predictive control (FOMPC) systems. Their properties, e.g. stability, robustness, control quality, have become one of the active research topics in control theory and applications. In the paper, the effect of various plant-model mismatches on the performance of FOMPC is illustrated through a simulation experiment.

Multiple use of the fractional-order differential calculus in the model predictive control

In the paper a multiple use of the fractional-order differential calculus theory in the model predictive control is proposed. First, the principle of the integer-order linear predictive control and theoretical foundations of the fractional-order differential calculus are reminded. Using the presented theoretical foundations attention is focused further on the possibility of developing the fractional-order model predictive control with an internal process model and a fractional-order cost function. The introduction of the fractional-order differential calculus at the stage of synthesizing the control algorithm offers an additional degree of freedom in tuning a control loop. The discussion is illustrated with results of some laboratory experiments.

Fractional Linear Systems with Memory Deficiency and Their State-Space Integer-Order Approximation

The current state vector in non-integer order systems depends on large number of previous states, i.e. on the memory efficiency of the system. If a memory impairment occurs, the current fractional order system switches to the system with another behavior. In the paper some non-integer order models of biological-like systems with memory deficiency are defined and a state-space integer-order approximation of such models is introduced. Some numerical examples of such approximation are shown.