Vinicius F. Montagner

Design and Implementation of a Robust Current Controller for VSI Connected to the Grid Through an LCL Filter

This paper describes the design and implementation of a discrete controller for grid-connected voltage-source inverters with an LCL filter usually found in wind power generation systems. First, a theorem that relates the controllability of the discrete dynamic equation of the inverter with LCL filter and the sampling frequency is derived. Then, a condition to obtain a partial state feedback controller robust to grid impedance uncertainties and based on linear matrix inequalities is proposed. This controller guarantees the stability and damping of the LCL filter resonance for a large set of grid conditions without requiring self-tuning procedures. Finally, an internal model controller is added to ensure asymptotic reference tracking and disturbance rejection, significantly reducing the impact of grid background voltage distortion on the output currents. Experimental results are presented to support the theoretical analysis and to demonstrate the system performance.

Convergent LMI Relaxations for Quadratic Stabilizability and

This paper investigates the quadratic stabilizability of Takagi-Sugeno (T-S) fuzzy systems by means of parallel distributed state feedback compensators. Using Finslers lemma, a new design condition assuring the existence of such a controller is formulated as a parameter-dependent linear matrix inequality (LMI) with extra matrix variables and parameters in the unit simplex. Algebraic properties of the system parameters and recent results of positive polynomials are used to construct LMI relaxations that, differently from most relaxations in the literature, provide certificates of convergence to solve the control design problem. Due to the degrees of freedom obtained with the extra variables, the conditions presented in this paper are an improvement over earlier results based only on Polyas theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms. An extension to cope with guaranteed H infin attenuation levels is also given, with proof of asymptotic convergence to the global optimal controller under quadratic stability. The efficiency of the proposed approach in terms of precision and computational effort is demonstrated by means of numerical comparisons with other methods from the literature.

{{\mathscr H}}_{\infty}

This paper proposes a sensorless vector control that combines two discrete-time observers to estimate the rotor speed and position of permanent magnet synchronous machines (PMSM). The first one is a sliding mode (DSM) current observer and the second one is an adaptive electromotive force (EMF) observer. Initially, the sliding conditions that assure the sliding motion around the sliding surface are derived and a design procedure to the DSM current observer is developed. Moreover, using discrete-time adaptive Lyapunov based EMF observer the rotor speed and position are obtained. Experimental results validate the theoretical analysis and demonstrate the very good performance of the proposed discrete-time sensorless vector control.

Control of Takagi–Sugeno Fuzzy Systems

This paper presents some general results concerning the existence of homogeneous polynomial solutions to parameter-dependent linear matrix inequalities whose coefficients are continuous functions of parameters lying in the unit simplex. These results are useful in the context of robust analysis and synthesis of parameter-dependent feedback gains (gain-scheduling) for uncertain linear systems in polytopic domains. A result showing the generality of the class of static gains with homogeneous polynomial dependence and a result dealing with the solutions of parameter-dependent linear matrix inequalities with slowly time-varying parameters are also given

Discrete-Time Sliding Mode Observer for Sensorless Vector Control of Permanent Magnet Synchronous Machine

This paper provides necessary and sufficient finite dimensional linear matrix inequality conditions to compute linearly parameter-dependent state feedback controllers ensuring quadratic stability for Takagi-Sugeno fuzzy systems. The proposed conditions are stated as progressively less conservative sets of linear matrix inequalities based on an extension of Polyas theorem, allowing to obtain a solution for the quadratic stabilizability problem whenever a solution exists. An additional design condition is also given, relying on the use of slack matrix variables to recover the control gains. Problems of decentralized control and control with a prescribed decay rate are also addressed, being the results illustrated by means of numerical examples.

Existence of Homogeneous Polynomial Solutions for Parameter-Dependent Linear Matrix Inequalities with Parameters in the Simplex

This paper presents a linear matrix inequality-based procedure for the design of state feedback current controllers that are robust to uncertainties on grid inductance for grid-connected converters with LCL filters. The state feedback control law includes the filter state variables, the states of resonant controllers, and considers also the delay from digital control implementation. As the main contribution here, the proposed strategy allows to deal with resonant controllers of arbitrary dimension, and provides results complying with IEEE Standard 1547 requirements. The control synthesis condition takes into account the assignment of the closed-loop eigenvalues in a circular region with radius r, located inside the unit circle, and the control design relies only on the choice of the value of the radius in the interval 0 <; r ≤ 1, providing all the state feedback gains in a simple and efficient procedure.

Necessary and sufficient LMI conditions to compute quadratically stabilizing state feedback controllers for Takagi-Sugeno systems

A new sufficient condition for the robust stability of linear systems with time-varying polytopic uncertainty is given in terms of linear matrix inequalities. The robust stability condition is assured by means of a parameter dependent Lyapunov function, taking into account bounds on the time derivatives of the uncertain parameters. Using line search, bounds on the magnitude as well as on the rates of change of the time-varying uncertain parameters can be determined solving a convex problem, encompassing quadratic stability results and providing less conservative evaluation than other similar methods from the literature. Moreover, constraints in the dynamic behavior of the uncertain parameters can be easily handled, providing a useful tool for the stability analysis of a class of nonideal switched systems.

LMI-Based Control for Grid-Connected Converters With LCL Filters Under Uncertain Parameters

This paper addresses the stability of discrete controlled grid connected voltage source inverters with LCL-filter usually found in wind power generation systems. First a theorem that relates the controllability of the discrete dynamic equation with the LCL-filter parameters and the sampling frequency is derived. Then, a robust partial state feedback design on the linear matrix inequalities framework guarantee the stability damping the LCL-filter resonance for a large set of grid conditions without requiring tuning procedures. Finally, an internal model controller is added to ensure asymptotic reference tracking and disturbance rejection, therefore reducing significantly the impact of grid background voltage distortion on the line currents. Simulation and experimental results are presented to support the theoretical analysis carried out and to demonstrate the system performance.

A new LMI condition for the robust stability of linear time-varying systems

The problems of robust stability analysis and state feedback control based on gain-scheduling for continuous-time systems with time-varying parameters that have bounded rates of variation and lie inside a polytope are addressed in this article. With respect to previous results in the literature, two main contributions of the article are: (i) the robust stability analysis conditions are less conservative and demand less computational effort than the existing ones; (ii) the conditions can be extended to cope with the problem of control design for this class of system. Parameter-dependent linear matrix inequality (LMI) conditions are given for the existence of a parameter-dependent Lyapunov function quadratic in the state and homogeneous polynomially of arbitrary degree in the parameter assuring robust stability. Two convex procedures based on LMIs exhibiting distinct complexities are proposed to solve the problem of robust stability. An extension to deal with the computation of a stabilising parameter-dependent state feedback gain for this class of time-varying systems is also provided, as a sequence of LMIs of increasing precision. Examples illustrate the results, including comparisons with other techniques from the literature.

Stability analysis of grid-connected voltage source inverters with LCL-filters using partial state feedback

A linear matrix inequality approach to compute 2 guaranteed costs by means of parameter-dependent Lyapunov functions is proposed. The uncertain linear systems are supposed to belong to convex-bounded domains (polytope type uncertainty). Both continuous- and discrete-time systems are investigated and the results are illustrated by means of numerical examples.