Keywords: Homogeneity Methods for Variable Structure Systems & Sliding Mode Control, Higher Order Sliding Mode
Abstract: Homogeneity is a certain invariance of an object (a function, a set, a figure, etc) with respect to a class of transformations called dilations. All linear and a lot of essentially nonlinear models of mathematical physics are homogeneous (symmetric) in some sense. Homogeneous control laws appear as solutions of many control problems such as a minimum time feedback control for the chain of integrators or the high-order sliding mode design. Similarly to the linear case, an asymptotic stability of a homogeneous system implies its robustness (input-to-state stability) with respect to a certain class of parametric uncertainties and exogenous perturbations. In this talk we deal with the so-called linear geometric homogeneity, which allows many methods of linear control theory to be utilized for a non-linear control design. We study the problem of generalized homogeneous stabilization via sliding modes for linear and nonlinear plants and present a scheme for an “upgrade” of an exiting linear feedback to a generalized homogeneous sliding mode controller. The theoretical results are supported by real experiments.

Keywords: Application of Sliding Mode Control to other theoretical problems, Higher Order Sliding Mode, Chattering Analysis
Abstract: Standard problem of one-degree-of-freedom mechanical systems with Coulomb friction is revised for a relay-based feedback stabilization. It is recalled that such a system with Coulomb friction is asymptotically stabilizable via a relay-based output feedback, as formerly shown in [1]. Assuming an upper bounded Coulomb friction disturbance, a time-optimal gain of the relay-based feedback control is found by minimizing the derivative of the Lyapunov function proposed in [2] for the twisting algorithm. Furthermore, changing from the discontinuous Coulomb friction to a more physical discontinuity-free one, which implies a transient presliding phase at motion reversals, we analyze the residual steady-state oscillations. This is in the sense of stable limit cycles, in addition to chattering caused by the actuator dynamics. The numerical examples and an experimental case study accompany the provided analysis.

Keywords: Chattering Analysis, First Order Sliding Mode, Higher Order Sliding Mode
Abstract: A simple yet challenging benchmark problem is proposed inspired from a particular class of DC motors presenting an underdamped resonant mode. Such resonant mode causes significant limitation to standard PI control and leads to important chattering for both first-order sliding-mode (FOSM) and super-twisting algorithm (STA) controllers. A well tuned standard PI controller serves as a comparison basis. Then, two methods for chattering alleviation based on the introduction of an ideal sliding-mode loop into the controller are chosen. Their efficiency is discussed in simulation and experimental tests. The results suggest interesting challenges for developing more efficient chattering alleviation techniques, particularly so for higher-order sliding mode (HOSM) based control which cannot be considered as a chattering alleviation technique per se.

Keywords: Application of Sliding Mode Control to other theoretical problems, First Order Sliding Mode, Chattering Analysis
Abstract: The binary model reference adaptive control (B-MRAC) is a controller combining the good transient and robustness of Sliding Mode Control (SMC) with the smoothness of parameter adaptive control. The B-MRAC delivers continuous control signal being able to mitigate SMC chattering problems. As the adaptation gain increases, the B-MRAC tends to behave as the SMC. However, the residual set input perturbations was only shown to bounded but the bound was not shown to tend to zero as the gain increased without limit as expected for the SMC. In this paper we show that this property indeed holds and the residual error tends to zero as the adaptation gain increases to infinity. Simulation results illustrate the consistency of the theory presented.

Keywords: Higher Order Sliding Mode, Homogeneity Methods for Variable Structure Systems & Sliding Mode Control, Chattering Analysis
Abstract: The paper presents a discretization scheme for a homogeneous second order sliding mode (2-SM) controller, which preserves the finite-time stability of the closed-loop system even in the case the sampled-time implementation of the control. Numerical simulations confirm the efficiency of the proposed scheme for chattering reduction.

Keywords: Power Electronics, Chattering Analysis
Abstract: This paper presents an autotuning technique for the class of digitally-controlled PID voltage-mode dc-dc buck converters, based on the modified relay feedback test (MRFT). The autotuning is consists of short and simple test and tuning stages, where the tuning is done using tuning rules that are derived offline, once only, for a given class of plant dynamics. A major advantage of the presented autotuning is that it allows for the specification of the gain or phase margin. This paper includes a review of selected autotuning techniques for dc-dc buck converters and a background on autotuning using the MRFT. An explanation of how the test stage of the MRFT tuning method is adapted to switching dc-dc power converters is provided, as well as a detailed procedure for the derivation of tuning rules that provide near-optimal dynamic performance for the class of dc-dc buck converters. Experimental results are provided which show good dynamic performance of the autotuned controller as compared to a controller that is optimized using full knowledge of the parameters of the test converter.

Keywords: Power Electronics, Chattering Analysis, First Order Sliding Mode
Abstract: Design and analysis of a cascade control DCDC boost converter is proposed in this paper using the locus of a perturbed relay system (LPRS). The output voltage is regulated using a PI controller in the outer-loop and a sliding mode controller in the inner-loop. The chattering amplitude and frequency is analyzed using the LPRS method. The use of the LPRS method also allows one to exactly evaluate the equivalent gain, necessary for the disturbance (slow motion) analysis. Moreover, the stability analysis is evaluated in terms of two aspects: the orbital stability of the oscillations in the inner-loop (chattering stability), and the stability of the overall averaged dynamics. Besides, the SM controller is designed to operate at a specified switching frequency through the proper selection of the hysteresis value using the LPRS method. The theoretical analysis is verified through simulations and hardware implementation.

Keywords: Adaptive Sliding Mode, Power Electronics
Abstract: Bidirectional Electric Vehicle (EV) charger technology becomes all the more important. The energy stored in the EV battery can flow from Vehicle to Grid (V2G), Home (V2H), Load (V2L), or Vehicle (V2V), this is known as V2X mode. The EV onboard charger comprises AC-DC converter and DC-DC converter. This paper discusses the bidirectional DC-DC LLC resonant converter, motivated by an industry partnership, in order to improve control performance in V2X mode over both battery voltage and power variation. The new challenge is twofold. Firstly, it leads to develop a LLC converter model based on the Phase Shift Modulation (PSM) in order to cover more operating points and to provide the DC bus voltage control. Secondly, it ensures the DC bus request tracking with robustness against disturbances in the LLC converter. To attain the second objective, a non-linear Adaptive Super Twisting Sliding Mode (ASTSM) control law is proposed. The control gain is adaptive to deal with unknown boundaries of the disturbances. A comparison of the ASTSM control and the classic control laws is conducted with respect to the DC bus current disturbance and DC bus voltage request variation. The results highlight the advantages of the proposed control strategy.

Keywords: Sliding Mode based Observation, Electric Drives And Actuators, Higher Order Sliding Mode
Abstract: In this paper, a sensorless control strategy for permanent magnet synchronous motor (PMSM) is proposed. The main contribution of this work is the extraction of the angular error (theta-hat{theta}) of the PMSM, from the measurable currents i_{alpha} and i_{beta}. Then, thanks to the robustness in the presence of disturbances, and to the convergence in finite time of the control and observation strategies based on sliding mode techniques; first, an observer is designed by using the extraction of (theta-hat{theta}) in order to estimate rotor position, speed and disturbance of PMSM under a wide speed range. After that, the estimates of the observer are implemented in a super-twisting controller to track a desired speed reference and a current-i_{d} reference. Moreover, the gains of the observer and controller are parameterized in terms of only one parameter in order to reduce tuning time. In addition, based on a Lyapunov approach, a convergence analysis of the observer and a stability analysis for the closed-loop system are introduced. Finally, the proposed observer-control scheme has been validated experimentally in an PMSM in order to show its effectiveness.

Keywords: Higher Order Sliding Mode, Power Electronics
Abstract: This paper presents a novel predefined-time convergent control algorithm, which enables one to explicitly set the convergence time in advance, independently of initial conditions. The proposed algorithm utilizes linear time-varying control input terms instead of previously employed exponential ones. The algorithm performance is verified by simulations for a full-scale 4D Permanent-Magnet Synchronous Motor (PMSM) system with completely and incompletely measurable states. The numerical simulations confirm the algorithm efficiency in each considered case. To the best of our knowledge, this is the first attempt to design a predefined-time convergent control law for multi-dimensional systems with incompletely measurable states, using a linear time-varying control input.

Keywords: Power Electronics, Automotive Systems, Sliding Mode based Observation
Abstract: This work presents the preliminary findings of a feasibility study for a class of sliding mode differentiators to be used in an on-line parameter estimation methodology for vanadium redox flow batteries (VRFB). Specifically, three high-order continuous differentiators are considered: a Standard Differentiator; a Filtering Differentiator, which excels the former by incorporating rejection to large noises small in average; and a Tracking Filtering Differentiator, which produces smooth consistent derivatives while inheriting the noise rejection capabilities from the previous one.

To model the vanadium redox flow batteries an equivalent circuit model is employed, whose time varying parameters are estimated by a recursive least squares algorithm with forgetting factor, that requires the VRFB measured voltage and current, together with their derivatives. To assess the performance of the different differentiation algorithms in obtaining reliable values of the VRFB parameters, the storage system is excited with standardised current demand profiles. Finally, representative simulation results are presented and discussed.

Keywords: Power Electronics, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Electric Drives And Actuators
Abstract: The use of DC-DC converters has been increasing in recent years in several applications. This paper proposes the application of a robust switched control strategy for DC-DC converters, primarily focuses on the reduction of the H_{infty} norm improving the transient response under disturbances. In order to achieve this, the Takagi-Sugeno (T-S) fuzzy model for nonlinear systems as a convex combination of linear systems is used, thereafter is proposed another relaxed design procedure for the switching controller with the use of Linear Matrix Inequalities (LMI's). The H_{infty} norm constraint is introduced into the switched control and then the first condition is relaxed with the use of the Finsler's Lemma. For the verification of the proposed conditions, the control strategy is applied to a Buck DC-DC converter, obtaining an improvement in the dynamic response against disturbances compared to switched control without H_{infty} norm restriction.

Keywords: Adaptive Sliding Mode
Abstract: This paper proposes a Barrier Function-based Adaptive Super-Twisting Algorithm (BF-ASTA) for Tensioned Leg Platform (TLP)-based floating offshore wind turbines (FOWT). The barrier function allows the gain adaptation to ensure, in a finite time, the convergence of the system states to their references in a predefined range with two main advantages: it does not need the knowledge of the upper bound of perturbations and it does not overestimate the control gain. The proposed BF-ASTA is designed based on a control-oriented model of the 5MW TLP-based FOWT and is validated on the high-fidelity code OpenFAST. The simulation results show the capacity of the controller to regulate the rotor speed at its nominal value and to reduce the platform pitch angle white less blade stresses compared to the proportional integral gain-scheduling (GSPI) controller.

Keywords: Adaptive Sliding Mode, Higher Order Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control
Abstract: In this paper, a new self-tuning strategy for super-twisting sliding mode controller is applied for offshore wind turbine system operating in region III. An algorithm is used to provide self-tuning gains for the purpose of improving the performance of the controller in the presence of unknown perturbations. Adaptive protocols are designed with reduced parameters (only one tuning parameter known as targeted accuracy in the controller part) without having knowledge of the system's uncertain bounds. The floating wind turbine is a highly nonlinear system and the main objectives are the limitation of platform pitch motion, blade fatigue load reduction, and power regulation. Here, by using the FAST simulator the designed controller has been tested, and achieved results demonstrate the capabilities of the proposed method.

Keywords: Adaptive Sliding Mode, Higher Order Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control
Abstract: This paper proposes a novel Adaptive Super-Twisting Algorithm (STA) to cope with bounded and unbounded disturbances. The proposed adaptive multilayered scheme does not require the knowledge of upper bounds for the matched disturbances and their derivatives. The only requirement is that the m-th derivative is bounded by an unknown constant. Using a modified low-pass filter we can estimate the disturbance and its derivatives so that both gains of the STA can be adapted in a non-conservative way, enforcing a second-order sliding mode and reducing the undesirable effects of chattering.

Keywords: Adaptive Sliding Mode
Abstract: This paper presents a solution to the problem of adaptive sliding-mode control for systems whose control gain presents zero-crossings. The approach is based on the so called barrier function-based adaptive sliding-mode control to avoid the problem of gain over-estimation, while achieving convergence to a predefined neighborhood of the origin. The theoretical properties of the scheme are proven by means of Lyapunov functions and its application to quasi-periodic systems and the problem of orbital stabilization of mechanical systems is demonstrated by means of simulations.

Keywords: Adaptive Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Application of Sliding Mode Control to other theoretical problems
Abstract: This paper proposes event-triggered adaptive supertwisting algorithm (ETASTA) based guidance law for a planar relative motion, where the line-of-sight (LOS) rate converges to zero or a small neighborhood of zero in finite time before guidance termination. The guidance law is proposed by taking into account both the maneuvering and non-maneuvering target. Further, a triggering condition is provided using an event-based approach that uses the minimum amount of control while meeting the stability requirements. Using Lyapunov theorem, the stability of the system is guaranteed. Moreover, it is shown that the proposed theory does not exhibit the Zeno phenomenon, since the inter-event time is bounded by a positive quantity. Finally, numerical example;s demonstrate the efficacy of the proposed guidance law.