Francisco Salas

Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties

Min-max model predictive control (MPC) is one of the control techniques capable of robustly stabilize uncertain nonlinear systems subject to constraints. In this paper we extend existing results on robust stability of min-max MPC to the case of systems with uncertainties which depend on the state and the input and not necessarily decaying, i.e. state and input dependent bounded uncertainties. This allows us to consider both plant uncertainties and external disturbances in a less conservative way. It is shown that the input-to-state practical stability (ISpS) notion is suitable to analyze the stability of worst-case based controllers. Thus, we provide Lyapunov-like sufficient conditions for ISpS. Based on this, it is proved that if the terminal cost is an ISpS-Lyapunov function then the optimal cost is also an ISpS-Lyapunov function for the system controlled by the min-max MPC and hence, the controlled system is ISpS. Moreover, we show that if the system controlled by the terminal control law locally admits certain stability margin, then the system controlled by the min-max MPC retains the stability margin in the feasibility region.

Bifurcation Analysis of Five-Phase Induction Motor Drives With Third Harmonic Injection

The interest in variable-speed multiphase induction- motor drives has substantially increased in recent years and novel proposals show good prospects for industrial implementation in high-power applications. The additional degrees of freedom existing in multiphase machines have allowed for new applications with high torque density by current harmonic injection in concentrated winding machines. This paper addresses, for the first time, the bifurcation analysis of a five-phase induction-motor drive when a third harmonic is injected for torque-enhancement purposes. The main focus of this paper is to present a mathematically based study of the nonlinear dynamics of the proposed drive with torque enhancement. The overall bifurcation analysis for both concentrated and distributed winding machines confirms that the harmonic injection provides not only torque enhancement but also more robust controllers. This further advantage offers improved performance of multiphase drives compared to their three-phase counterparts.

On the stability of constrained MPC without terminal constraint

The usual way to guarantee stability of model predictive control (MPC) strategies is based on a terminal cost function and a terminal constraint region. This note analyzes the stability of MPC when the terminal constraint is removed. This is particularly interesting when the system is unconstrained on the state. In this case, the computational burden of the optimization problem does not have to be increased by introducing terminal state constraints due to stabilizing reasons. A region in which the terminal constraint can be removed from the optimization problem is characterized depending on some of the design parameters of MPC. This region is a domain of attraction of the MPC without terminal constraint. Based on this result, it is proved that weighting the terminal cost, this domain of attraction of the MPC controller without terminal constraint is enlarged reaching (practically) the same domain of attraction of the MPC with terminal constraint; moreover, a practical procedure to calculate the stabilizing weighting factor for a given initial state is shown. Finally, these results are extended to the case of suboptimal solutions and an asymptotically stabilizing suboptimal controller without terminal constraint is presented.

Brief Hopf bifurcation in indirect field-oriented control of induction motors

The appearance of self-sustained oscillations in high performance AC drives, and in particular, in induction motors whose speed is regulated with the industry standard field-oriented control, is a well-documented but little understood phenomenon. It is well known that the oscillations may be quenched by returning the outer-loop PI speed control, but no precise rules to carry out this task, which may be time consuming, are known. In this paper, we show that these oscillations may arise due to the existence of Hopf bifurcations. Some simple rules for selecting the gains of the PI controller are obtained as a result of our analysis.

Bogdanov-Takens bifurcation in indirect field oriented control of induction motor drives

We explore further the occurrence of bifurcations in the indirect field oriented control of induction motors. This study is a continuation of previous publications. New results reveal the occurrence of codimension-two bifurcation phenomena, such as a Bogdanov-Takens bifurcation.

Voltages balance control in three phase three-level NPC rectifiers

In this work, several strategies to control a three phase three-level Neutral Point Clamped (NPC) rectifiers are presented. This type of converter has two operation modes, as rectifier or as inverter. As rectifier, the dc-link is split in two, being two capacitors placed at the output. The objective of control the dc-link capacitors voltages balance is the goal of this paper. This capacitors voltages difference should be stabilized at zero so that no unbalance appears in the system. Under the assumption of a two-time-scale, the equation of the capacitors voltages balance dynamic is studied and it is shown that it is linear except for an exogenous term, which can be considered as a disturbance. Analyzing this term, it is shown that its expression takes the form of a sinusoidal signal. This fact is used to design the controller by cancellation of the sinusoidal disturbance. Some methods of control using this idea are proposed in this paper and their results are also presented.

CODIMENSION-TWO BIFURCATIONS IN INDIRECT FIELD ORIENTED CONTROL OF INDUCTION MOTOR DRIVES

This paper provides further results on bifurcation analysis of indirect field oriented control of induction motors. Previous results presented on this subject [Bazanella & Reginatto, 2000, 2001; Go...

On Modeling and Parameter Estimation of Brushless DC Servoactuators for Position Control Tasks

Abstract Brushless DC (BLDC) servomotors have become a popular choice when implementing high–precision position controllers for mechatronic systems. A motor of this kind requires a drive that can be configured in different operation modes, according to the internal controllers it utilizes. This paper first describes the main features and the complete electromechanical model of a BLDC motor/drive system, including some procedures for the identification of its parameters. Three common schemes for implementing position control using this kind of actuators are also presented, and the equivalence among them is employed to determine the drives internal control gains. Finally, experimental results in a typical BLDC servoactuator allow us to show the significance of the estimated parameters in real position control tasks.

ZERO-HOPF BIFURCATION IN INDIRECT FIELD ORIENTED CONTROL OF INDUCTION MOTORS

Abstract In this paper we explore the occurrence of zero-Hopf bifurcation in indirect field oriented control (IFOC) of induction motors. Codimension-two Bogdanov-Takens bifurcations as well as codimension-one saddle-node and Hopf bifurcations have been reported earlier. In this paper the occurrence of codimension-two zero-Hopf bifurcation in IFOC is analyzed and proven to occur under certain parameter settings. Bifurcations diagrams are also reported illustrating such bifurcations for a particular IFOC drive.

Fuzzy-Tuned PD Tracking Control of a 3-RRR Parallel Manipulator: Stability Analysis and Simulations

In this work we propose a variable gains PD tracking controller, in which the gains are tuned by a Fuzzy controller, for a parallel robot. The stability analysis of the closed-loop system is performed by using the Lyapunov-based perturbed systems theory. The closed-loop system is formed by the PD with variable gains control law and a so-called reduced model of the robot, which exhibits some properties similar to those found on the model of a serial robot. As a result, we demonstrate that, under a proper selection of the bounds of the variable gains, the tracking errors are uniformly ultimately bounded. Simulation results of the Fuzzy-tuned PD controller, applied to a 3-RRR planar parallel manipulator, are presented. The superior performance of the proposed approach is validated when compared with a classic PD controller.