Antonio Rosales

Performance margins in conventional and second order sliding mode controllers

A concept of the performance margins for systems controlled by conventional and second order sliding mode controllers is proposed. These margins are based on the systems tolerance to self sustained oscillations with certain amplitude and frequency. The practical performance margins are introduced as the maximal gain increase or/and the maximal phase lag added to the frequency characteristic of the linear part of the open loop system that yield acceptable loss of systems performance in terms of admissible parameters of self-sustaining oscillations. The method to compute the performance margins is presented. Examples and simulations which verify the utility of the concept are shown.

Chattering Analysis of HOSM Controlled Systems: Frequency Domain Approach

In this article, a methodology of chattering analysis of Sliding Mode/Higher Order Sliding Mode (SM/HOSM) control systems in the frequency domain is presented. A numerical method for computing the Describing Functions (DFs) of HOSM control algorithms is given. The algorithm for predicted chattering parameters in dynamically perturbed system via the Describing Function-Harmonic Balance (DF-HB) technique is proposed. The stability conditions for limit cycles in dynamically perturbed HOSM control systems are presented. The concepts of Practical Stability Phase Margin ( PSPM) and Practical Stability Gain Margin (PSGM) as the robustness metrics to unmodeled dynamics in HOSM control systems are introduced. The methodologies for computing PSPM and PSGM via DF-HB technique are provided. The accuracy of the proposed chattering analysis techniques is confirmed via computer simulations.

Analysis and design of systems driven by finite-time convergent controllers: practical stability approach

ABSTRACT A concept of the practical stability margins for systems driven by finite-time convergent (FTC) controllers, including sliding-mode/higher order sliding-mode (HOSM) controllers, is proposed. These margins are based on the systems tolerance to self-sustained oscillations with certain amplitude and frequency limits. The practical stability margins are introduced as the maximal gain increase or/and the maximal phase lag added to the frequency characteristic of the linear part of the open-loop system that yields acceptable loss of systems stability/performance in terms of admissible parameters of self-sustaining oscillations. It is proposed using the describing function-harmonic balance technique for the identification of the practical stability margins. To ensure the desired practical stability margins, linear dynamics compensators are designed and added in cascade to FTC controllers. The proposed approach is verified on numerous examples.

Stator-flux-oriented sliding mode controller for DFIG with variable hysteresis loop for limiting switch frequency of rotor-side power converter

Doubly fed induction generator (DFIG) is the most implemented electric machine in wind energy conversion systems (WECS) due to reduced size converter, active and reactive power control and economic factors. However, the power electronic stage needs an accurate controller that allows to follow the stator power regulation. As a result, Sliding-Mode Control (SMC) has been successfully implemented in DFIG because the natural discontinuous control signals arising from the controller can be used for direct switching of power electronic devices. Yet, switching frequency of SMC depends on the sample rate, controller parameters and electric machine dynamics; this conditions produce a control signal with a variable switching frequency hindering implementation. In this paper a stator-flux-Oriented sliding-mode controller with a hysteresis band that limits the switching frequency of power electronic devices to a set value is presented. This methodology improves previous proposals by limiting switching frequency making implementation more feasible. Simulation results are presented to validate the control methodology.

Frequency domain analysis of HOSM systems

The frequency domain analysis of dynamically perturbed Higher Order Sliding Mode (HOSM) systems is tackled using Describing Function (DF) and Harmonic Balance (HB) techniques. The goal of this analysis is to study possible limit cycles in such systems. DFs of Nested 3rd and 4th order algorithms are obtained for the first time. Then, HB equation is used to analyze the real sliding motion in the HOSM system, where the sliding set converges to a limit cycle. Chattering (limit cycle) in the HOSM systems is studied, and the chattering parameters (amplitude and frequency) are computed. A definition of Tolerance Limits, which characterizes the acceptable performance in the real HOSM system, is applied to verify if the chattering parameters fit the amplitude and frequency limits. Next, Performance Phase Margin and Performance Gain Margin definitions, which give the metrics for robustness of real HOSM to unmodeled dynamics, are applied to assess the robustness of the limit cycle emerged in the real HOSM system. Examples and simulations that validate the obtained results are presented.

Phase and Gain Margins with Third Order Sliding Mode Control: An Integrated Guidance Application

Department of Defense Regulation requires designers to evaluate the robustness of their designs using phase and gain margin criteria. Given that such criteria are applicable to linear designs, their inapplicability in their current definition to Higher Order Sliding Mode (HOSM) control designs; non-linear designs techniques in the time domain appeared to constitute a major hindrance to the application of HOSM techniques to aircraft and missiles. This paper illustrates the usage of new phase and gain margin techniques applicable to HOSM designs for providing measures of robustness such designs. The technique consists in replacing the -1 singularity point used with linear designs with describing function based representations of the HOSM controller. It is applied here to general problem of guidance of aerospace vehicles steered with aerodynamic lift that is, to a control problem with relative degree = 3. In the application case we assume the unavailability of attitude measurements. Results show that whether the guidance enforces the collision condition or a proportional integral linear manifold has little effect on the robustness. The concept of practical Relative Degree is introduced and applied instead of the strict definition thereof.

Practical Stability Phase and Gain Margins Concept

A new concept of chattering characterization for the systems driven by finite-time convergent controllers (FTCC) in terms of practical stability margins is presented. Unmodeled dynamics of order two or more incite chattering in FTCC driven systems. In order to analyze the FTCC robustness to unmodeled dynamics the novel paradigm of Tolerance Limits (TL) is introduced to characterize the acceptable emerging chattering. Following this paradigm a new notions of Practical Stability Phase Margin (PSPM) and Practical Stability Gain Margin (PSGM) as a measure of robustness to cascade unmodeled dynamics is introduced. Specifically, PSPM and PSGM are defined as the values that have to be added to the phase and gain of dynamically perturbed system driven by FTCC so that the characteristics of the emerging chattering reach TL. For practical calculation of PSPM and PSGM, the Harmonic Balance (HB) method is employed and a numerical algorithm to compute Describing Functions (DFs) for families of FTCC (specifically, for nested, and quasi-continuous Higher Order Sliding Mode (HOSM) controllers) was proposed. A database of adequate DFs was developed. A numerical algorithm for solving HB equation using the Newton–Raphson method was suggested to obtain predicted chattering parameters. Finally, computational algorithms that identify PSPM and PSGM for the systems driven by FTCC were proposed. The algorithm of a cascade linear compensator design that corrected the FTCC, making the values of PSPM and PSGM to fit the prescribed quantities, was presented. In order to design the flight-certified FTCC for attitude for the F-16 jet fighter, the proposed technique was employed in a case study. The prescribed robustness to cascade unmodeled dynamics was achieved.

Grid-Voltage-Oriented Sliding Mode Control for DFIG Under Balanced and Unbalanced Grid Faults

Doubly fed induction generators (DFIGs) are widely used in variable-speed wind turbines. Despite the well-accepted performance of DFIGs, these generators are highly sensible to grid faults. Hence, the presence of grid faults must be considered in the design of any control system to be deployed on DFIGs. Sliding mode control (SMC) is a useful alternative for electric machinery control since SMC offers fast dynamic response and less sensitivity to parameter variations and disturbances. Additionally, the natural outputs of SMC are discontinuous signals allowing direct switching of power electronic devices. In this paper, a grid-voltage-oriented SMC is proposed and tested under low voltage grid faults. Unlike other nonmodulated techniques such as direct torque control, there is not a necessity of modifying the controller structure for withstanding low depth voltage dips. For stator natural flux cancelation, the torque and reactive power references are modified to inject a demagnetizing current. Simulation results demonstrate the demagnetization of the natural flux component as well as a robust tracking control under balanced and unbalanced voltage dips.

Frequency domain characterization of stator-flux-oriented SMC for DFIG using Tsypkin's method

Sliding Mode Control (SMC) has been successfully implemented in power converters applications since the discontinuous nature of the controller output allows direct switching of power electronic devices. However, due to physical limitations of power converter, the switching frequency must be maintained at low levels in order to prevent overheating and hazardous conditions of the semiconductors, therefore, hysteresis loops are typically included in the switching logic. In this work, a the Doubly Fed Induction Generator (DFIG) controlled by a stator flux oriented SMC is analyzed in the frequency domain using Tsypkins method in order to obtain the hysteresis width that ensures a maximum switching frequency value covering all the operational conditions of the electric machine. The results are tested and evaluated by means of simulation studies of a DFIG controlled by a two level power converter.

An adaptive sliding mode control with self-regulated boundary layer

In this paper an adaptive sliding mode control (SMC) law with self-regulated boundary layer is proposed. The design of the adaptive SMC considers practical issues as actuator limitation/saturation and error tolerance, which is given in terms of the boundary layer presented in real sliding mode. The existence of sliding motion is proved via Lyapunov analysis. Self-regulation to the best value of boundary layer (minimum value) associated with the discrete step size and systems response speed is guarantee. Furthermore, a methodology to estimate the minimum boundary layer involving the sliding surface is given as well as an estimation of the frequency of the sliding surface on steady state. An example and simulations validate the proposed adaptive SMC law are presented.