Vladimir Rasvan

Exponential stability analysis of the drilling system described by a switched neutral type delay equation with nonlinear perturbations

This paper deals with the exponential stability analysis of switched neutral systems under certain state-dependent switching rules with nonlinear perturbations bounded in magnitude. The proposal of an energy functional allow us to investigate the asymptotic and exponential stability of switched neutral systems through the solution of linear matrix inequalities. The results are illustrated with the exponential stability analysis of an oilwell drilling system allowing a significant reduction of the stick slip behavior.

Popov Theories and Qualitative Behavior of Dynamic and Control Systems

This paper is an attempt to summarize some problems that may be solved within the framework of the Popov and Popov-like theories. Besides classical absolute stability problem, problems as forced oscillations, systems with multiple equilibria, dissipativity (ultimate boundedness) are considered. The Popov theory and results are viewed as emerging in three stages: the first one is concerned with the discovery of the frequency domain inequality connected with integral equations, the second one corresponds to the generalization of Yakubovich Kalman lemma to the multivariable case as well as to hyper stability theory formulation, and the third stage incorporates results on various qualitative behavior for systems with multiple equilibria (mutability-dichotomy and gradient like behavior).

Three lectures on dissipativeness

This paper has at least two sources. The first one is that in spite of the quasi-obvious significance of the notion - at the physical level of rigor - there exist some three mathematical terms with different definitions and senses; all of them are connected to stability and oscillations and are important and useful in the case of nonlinear systems. The second one is the strong connection of dissipativeness and passivity to the hyperstability theory as developed by V. M. Popov. The presentation aims to include definitions of these dissipativeness concepts, criteria, applications and connections between them. The text is underlined by the idea that Liapunov, dissipation, hyperstability and other inequalities are the common basis for discovering various dissipativeness properties

Dynamics properties and control for oilwell drillstrings

It is considered the model with distributed parameters of the torsional vibrations for the drilling system. The basic model is obtained by using the generalized variational principle of Hamilton and it is completed by adding the dynamics of the driving motor in two cases: a d.c. motor and an induction motor. For this setup there is considered the steady state with constant rotating speed, the system in deviations and its stabilization using an energy like control Liapunov functional suggested by the energy identity which is specific to partial differential equations. The paper contains also comments on mathematical issues connected with the basics of the approach and suggestions for future research.

Current Control Of A VSI-FED Induction Machine By Predictive Technique.

The paper deals with a technique which uses the predictive concepts in order to obtain the pulse width modulation strategy of a voltage fed inverter. After the technique is briefly described, it is applied for the case when the inverter supplies an induction motor, the reference values of the currents being obtained from a classical vector control scheme. The described technique is then simulated and the waveforms are compared with ones obtained with preset currents (bangbang) pulse width modulation, as the behaviour of the two strategies are similar. Finally, the results are cross analysed and further actions are proposed for the work continuation.

Liapunov functionals for systems with time delay and propagation

Starting from some recently analyzed controlled models with propagation i.e. described by hyperbolic partial differential equations, it is shown that a Liapunov functional may be attached in a natural way by using development of the energy integral. As known from the general theory of the hyperbolic partial differential equations, the energy integral is a useful tool for obtaining uniqueness theorems. On the other hand, existence theorems may be obtained either starting from difference schemes (the approach of S.K. Godunov) but also by associating some functional differential equations (the approach of A.D. Myshkis, K.L. Cooke and their followers). Due to the one to one correspondence between the two mathematical objects, the counterpart of the Liapunov functional deduced from the energy integral is obtained for the functional differential equations. Using these mathematical tools some process applications are discussed: flexible beam (manipulator), flexible overhead crane and to applications of controlling the oil drilling plants. The outcome of the analysis is given by control structures and stability criteria.

Predictive Versus Vector Control Of The Induction Motor

The paper deals with the vector control and predictive control of the induction motor. For the vector control, the rotor flux oriented one is pointed out, with highlight on the voltage source inverter type. The influence of the most important parameter variations (e.g. stator resistance) is discussed. A simple (and practical) method for avoiding these influences is presented, based on proper simulation models. Following the basics of the predictive control, a simulation model for this type of command is presented, together with simulations results. Finally, the results are cross analysed and further actions are proposed the work continuation. INTRODUCTION On one hand, since the basic work concerning torque and field control due to Leonhard, Blaschke and their followers in the 1970s, the AC drives became a competitive technology with respect to the traditional one, based on DC drives. In rotating references, solidar with the rotor flux, stator flux or magnetizing flux respectively, there is an obvious decoupling between the two components of the stator current: while the direct component acts on the flux modulus only and produces the reactive component, the quadrature component generates the torque, being the active component. The two components of the stator current may be thus controlled independently and the flux and torque generation are thus decoupled, similarly to the DC motor. Due to results simplicity, the rotor flux orriented control has imposed almost as a standard. From here, two types of control were engineered. On one hand we have the direct control drives, where flux position and modulus are known while the reactive and active components of the stator current are computed in the proper reference frame using the set-point torque and flux. On the other hand we have the indirect control drives, where the slip frequency is computed and imposed without direct knowledge of the flux, while the reference system change from the flux-reference to stator-reference one is performed by integration of the sum of the motor speed and the speed corresponding to the computed slip (Casadei et al. 2002, Vas 1998). A very simple method for the toque control is also the Direct Torque Control (DTC), suited for electrical traction applications (Takahashi and Noguchi 1986, Baader et al. 1992, Ehsani et al. 1997, Faiz et al. 1999, Haddoun et al. 2007, Ivanov 2009, Ivanov 2010). On the other hand, the increased computational capabilities of the existing DSP allow the implementation of the predictive control at the level of the converters which induce the hybrid character of the overall control system of the drive. We infer that predictive control has established itself in the last 5-7 years as a very proficient form of controlling highly nonlinear and uncertain systems; moreover the most recent results show its applicability to fast processes among which drives and their converters have a central position (Seo et al. 2009, Prieur and Tarbouriech 2011, Geyer et al. 2008, Mariethoz et al. 2010, Geyer et al. 2009, Trabelsi et al. 2008, Shi et al. 2007, Rodriguez et al. 2007, Larrinaga et al. 2007, Richter et al. 2010, Almer et al. 2010). The paper will briefly present in the first section the basics of the vector control for the rotor flux oriented control for voltage source inverter, with highlight on the influence of the parameters variations on the drive performance. A simple method for reducing these influences will be discussed based on appropriated models. The basics of the predictive control will be presented in Section 2. Section 3 will analyse the predictive control applied to the induction motor, based also on a Simulink model. Finally, conclusions will be issued and ideas for continuation will be pointed out. VECTOR CONTROL OF INDUCTION MOTOR As stated above, the vector control strategy most often used is the rotor flux oriented one. The reasons reside in the simplicity of the expressions resulted from the rotor voltage equation which mainly gives the rotor flux speed and further, by integration, the rotor flux position, used at its turn for the transformation of the reference currents/voltages from the rotary frame to the stationary one. For the squirrel cage induction motor, the rotor voltages equation in terms of phasors is ( ) 0 r r r mr r r r r r d R i j P dt Ψ Ψ Ψ Ψ = + + ω − ω Ψ , (1) where Rr is the rotor resistance, r r i Ψ is the rotor current, m ω is the rotor flux speed, ω is the mechanical speed of the rotor and P is the number of pairs of poles. The Ψ subscript highlights that (1) is expressed in the rotary frame synchronous with the rotor flux r r Ψ Ψ . By assuming unsaturated operation (realistic hypothesis when the stator currents are precisely controlled), the rotor flux expressed in terms of magnetizing inductance Lm and rotor magnetizing current mr i is m r mr L i Ψ = ⋅ Consequently, (1) becomes ( ) 0 mr r m mr r m r r mr d i R i L j P i L dt Ψ = + + ω − ω ⋅ ⋅ . (2) The rotor current r r i Ψ , being immeasurable for the squirrel cage motor, is expressed in terms of the stator current s r i Ψ and the magnetizing one. By denoting the rotor time constant / r r r T L R = , (2) becomes ( ) mr r mr r r mr s r mr d i T i i j P T i dt Ψ + = − ω − ω , (3) Lr being the total rotor inductance which includes the leakages ( r m r L L Lσ = + ). By identifying the terms on each of the axes d, q, the following two expressions result which are the simplest among all the vector control types mr r sd mr d i T i i dt + = , (4) sq mr r r mr i P T i ω = ω + . (5) We notice from (4) that if the flux is kept constant ( ct. mr i = ), then = ct. sd mr i i = As the electromagnetic torque expressed in the rotor flux oriented frame is 2 3 2 m e sd sq r L t P i i L = ⋅ , (6) from (5) and (6) results that the slip speed (term 2 in (5)) is proportional with the torque and further, the mechanical characteristic of the induction motor are straight lines, quite similar to the DC motor. When the motor is supplied by a voltage source inverter, the necessary voltages are obtained by considering the stator voltages equation expressed in the same rotary frame synchronous with the rotor flux r r Ψ Ψ : s r r r s s m s r s r mr s r m s r r r d i di u R i L L dt dt j L i j L i Ψ Ψ Ψ Ψ

Frequency domain stability inequalities for nonlinear time delay systems

Motivated by various applications, among which one can mention the problem of PIO - P(ilot)-I(n-the-loop)-O(scillations), it is considered the problem of the absolute (global asymptotic) stability of the zero equilibrium for systems with slope restricted nonlinearities. Since the linear part incorporates also time delay, it is taken the approach of integral equations subject to the so-called IQC - Integral Quadratic Constraints. It is thus obtained an early stability inequality due to V.A. Yakubovich, but valid for time delay systems in the basic (stable) case - when the linear part is exponentially stable.

IMPROVED DYNAMIC PROPERTIES BY FEEDBACK FOR SYSTEMS WITH DELAY IN CONTROL

It is considered a linear controlled system with delay in control and subject to constant exogeneous signals, for which the following problems are discussed: feedback stabilization and exact regulation by finite pole assignment using a linear control law deduced by applying finite assignment and Artstein transform for a system that is extended by integrators; the same extended system is then stabilized subject to a quadratic performance index. The theorems are illustrated by simulation results. In simulation there are considered other effects: saturation of the actuators and intelligent integrators.

Stabilization and Decoupling Control Applied in Vehicle Dynamics

Abstract The classical one-mass model for road vehicle dynamics in lateral motion is considered as basic for such actual problems as: 4-wheel steering or fully automatic steering of cars. Starting from the robustness problem a decoupling scheme based on controlled servo has been proposed. This paper provides a stability analysis of this algorithm based on frequency methods for the classical problem of absolute stability. This approach is motivated by the uncertainty introduced by the tire-road characteristics: it leads to consider a class of nonlinear functions satisfying sector-type and slope restrictions. This stability analysis is directed finally to estimate a rather important merit figure of a road vehicle - the critical speed-introduced from stability considerations for the lateral motion.