Exact Linearization Technique Research Articles

Intelligent ISSA-Based Non-Singular Terminal Sliding-Mode Control of DC–DC Boost Converter Feeding a Constant Power Load System

In response to the issue of system oscillations in direct current (DC) microgrid systems with constant power loads (CPL), this paper proposes a non-singular terminal sliding-mode control (NTSMC) strategy based on the improved salp swarm algorithm (ISSA). Firstly, the state-feedback exact linearization technique is employed to establish a linearized model of the converter system. Then, the NTSMC based on a composite sliding-mode surface is designed to achieve rapid convergence and effectively weaken the chattering issue in traditional sliding-mode control, ensuring a constant power supply to the load. The parameters of the proposed NTSMC are optimized using the ISSA, which introduces an intelligent NTSMC. Finally, a MATLAB/Simulink simulation model is established. The simulation results show that the ISSA-based composite sliding-mode surface NTSMC system designed for DC microgrid systems with CPL exhibits high robustness and guarantees ideal steady-state characteristics and dynamic responses when input voltage fluctuations and load disturbances occur.

Fractal control and synchronization of population competition model based on the T–S fuzzy model

It is of great significance to study the law of population change in species protection, resource utilization, ecological stability, and so on. The fractal behavior of the population competition model is discussed from the fractal viewpoint. By using the sector nonlinear method, the Takagi–Sugeno (T–S) fuzzy model of the population competition model is established, and the Julia set of the population competition model based on the T–S fuzzy model is introduced. The parallel distributed compensation (PDC) is used to design the corresponding fuzzy controller, and sufficient conditions for the stability of the system are given in the form of linear matrix inequalities (LMIs). The parameters of controller gain are obtained by solving LMIs, and the control of the Julia set of the population competition model based on the T–S fuzzy model is carried out. Using the exact linearization technique, the synchronization of the Julia sets of the population competition models is realized based on the T–S fuzzy model by the linear control method, and the Julia set diagram of the corresponding population competition model is analyzed.

Robust Stabilization for Uncertain Non-Minimum Phase Switched Nonlinear System under Arbitrary Switchings

This paper addresses the problem of stabilization of non-minimum phase switched nonlinear systems where the internal dynamics with symmetries or non-symmetries of each mode may be unstable. The authors initially build a stabilizing Lyapunov controller for each mode in order to stabilize its own unstable internal dynamics. The proposed approach is based on the exact input-output feedback linearization technique and the Lyapunov stability theory. The stability results for non-minimum phase switched nonlinear systems with arbitrary switching rules are then obtained using generalized Gronwall–Bellman inequalities. Finally, numerical examples are provided to demonstrate the efficacy of the achieved results.

A Single Phase Hybrid Multiport Microinverter for Photovoltaic Energy Controlled by Exact Linearization

Solar energy can be captured by Photovoltaics (PV) and converted into electrical power. This electrical power can then be connected to grids by power electronic converters, which can also operate the PV panels at around their maximum power point (MPP), maximizing the harvested energy. When the PV panels are connected in an array, the partial shading effect generates a distortion of the power curve can result in a power loss since tracking algorithms might not be able to detect the MPP. To solve this issue microinverters have been proposed, with a small power electronic converter being connected to each PV panel, this arrangement enables independence for maximum power point tracking and electrical isolation. This paper presents a double output multiport microinverter capable of feeding DC and AC loads or providing connection to a single-phase AC grid and energy storage. The proposed structure can be operated in grid-connected and islanded modes. This paper describes the microinverter controlled with the exact linearization technique on both the DC and AC sides, obtaining a lineal transfer function representation of the nonlinear and coupled power electronic converters. The operation of the proposed topology and its control strategy is validated using a laboratory proof-of-concept prototype.

Input-output Feedback Linearization Control for SM-PMSM

This paper introduces a velocity control strategy for Surface-Mounted Permanent Magnet Synchronous Motors SM-PMSM using exact linearization and input-output decoupling techniques, which are rooted in the principles of differential geometry. The primary aim of this control approach is to establish a static state feedback mechanism and to convert the nonlinear PMSM model into a linear, decoupled, and controllable system. Initially, the state model that represents the PMSM dynamics within the d-q reference frame is defined. Subsequently, the process of designing the control through linearization and input-output decoupling is outlined. Lastly, the synthesis of the compensator is grounded in the pole placement method, aiming to drive the direct current towards zero and ensure optimal torque operation. Simulation outcomes conducted on Matlab/Simulink demonstrate the efficacy of the speed control strategy, which is facilitated by a straightforward algorithm for practical implementation. However, it is inadequate against variations in machine parameters and load torque disturbances.

Expansion planning of a price-maker virtual power plant in energy and reserve markets

This paper addresses the expansion planning problem of a virtual power plant considering the possibility of building new assets such as conventional, renewable, and energy storage units. The VPP is modeled as a price-maker player that strategically participates in energy and reserve markets by altering the prices of these markets to its own benefit. The VPP includes flexible demands, conventional and renewable generating units, and energy storage units. Variabilities in renewable production levels are modeled using a modified clustering K-medoids method, while the uncertain reserve request coefficients are represented using a set of scenarios. The present problem is formulated as a two-stage stochastic bi-level model, where the upper-level problem represents the expected profit of the VPP to be maximized by building new assets, while the lower-level problems model the clearing of the energy and reserve electricity markets for different market conditions, which aim to maximize the social welfare and reduce the cost of the ancillary systems, respectively, and determine the market prices of both markets. The stochastic bi-level model is converted to a single-level mixed-integer linear programming problem by replacing the lower-level problems by their Karush-Kuhn–Tucker optimality conditions and by applying exact linearization techniques. Numerical results show that considering the VPP as a price-maker player influences its expansion decisions and allows the VPP to increase its profit up to 108.8% in comparison with a price-taker behavior. Also, the numerical results indicate that the participation in the reserve market increases a 26.76% the expected profit achieved by the VPP.

Stability and Safety of Cooperative Adaptive Cruise Control Vehicular Platoon under Diverse Information Flow Topologies

For the cooperative adaptive cruise control (CACC) vehicular platoon, apart from decentralized controllers, the dynamics of a platoon can be affected substantially by the information flow among connected and automated vehicles (CAVs). Existing research studies mainly focus on the stability analysis of platoons where CAVs only adopt the predecessor-following (PF) communication scheme; however, when CAVs “look” further ahead or behind than one vehicle, the stability of platoons might change. To this end, this study seeks to explore the stability and investigate the rear-end collision risk of CACC vehicular platoon under diverse information flow topologies. The research first comprehensively reviews typical information flow topologies for CAV platoons and platoon stability criteria for analyzing local and string stability of platoons. Moreover, the CACC longitudinal dynamic model is derived using the exact feedback linearization technique, which accommodates the inertial delay of powertrain dynamics. Accordingly, sufficient conditions of stability are mathematically derived to guarantee distributed frequency-domain-based control parameters. Simulation experiments are conducted to verify the correctness of derived sufficient stability conditions. The results show that platoons could better maintain stability with more vehicle information taken into consideration. However, when assessing the safety, it is found that the bidirectional type information flow topology would increase rear-end collision risk for CAV platoon. Further, the information flow topology of two-predecessor-leader following is the most recommended to enhance fully CAV platoon stability.

Investigating How the Equilibria of the Electricity Market are Affected by Modeling the Strategic Behavior of Consumers

The paper proposes a formulation for a generalized Nash equilibrium model which incorporates the strategic biddings of some consumers capable of providing reserve and balancing services in the day-ahead and balancing markets, respectively. The strategic bidding in the electricity market is modelled using a bilevel optimization programming, where the electricity cost of consumers is minimized at the Upper Level (UL), and the energy and reserve costs in the market clearing process are co-optimized at the lower level (LL). By means of the strong duality theorem, the original bilevel model is transformed into an equivalent single-level Mathematical Problem with Equilibrium Constraints (MPEC). The joint problem of all MPECs, one per consumer, constitutes an Equilibrium Problem with Equilibrium Constraints (EPEC). The resulting EPEC is finally formulated as an auxiliary Mixed-Integer Linear Programming (MILP) problem. To this end, an exact linearization technique and Fortuny-Amat transformation are adopted to substitute the nonlinear terms and the complementarity conditions. In addition, a parametrization technique is used to replace the dual variable associated with the strong duality equation which appears in the EPEC problem. The diagonalization method is also adopted in this part as an ex-post analysis to verify the obtained solutions of the resulted MILP. Finally, a 3-bus illustrative example and the IEEE RTS 24-Bus System and 118-Bus System are considered to investigate the performance of the proposed approach.

Strategic Biddings of a Consumer demand in both DA and Balancing Markets in Response to Renewable Energy Integration

This paper proposes strategic biddings for a consumer demand that participates in both the day-ahead and balancing markets. The strategic behavior of the consumer is represented by the bilevel optimization programming with minimization of consumer costs at the upper level (UL) subject to the co-optimization of energy and reserve in the market clearing process at the lower level problem (LL). Using the Karush-Kuhn-Tucker (KKT) optimality constraints to replace the LL problem, the bilevel model is recast into a single-level mathematical program with equilibrium constraints (MPEC). The resulted model is finally formulated as a mixed-integer linear programming (MILP) problem using the exact linearization technique and Fortuny-Amat transformation to replace bilinear terms and the complementarity constraints, respectively. The results demonstrate a reduction in the electricity consumption payment for the strategic consumer and a decline in social welfare.© 2017 Elsevier Inc. All rights reserved.

Implementation of Exact Linearization Technique for Modeling and Control of DC/DC Converters in Rural PV Microgrid Application

The inclusion of solar systems in rural microgrids is becoming increasingly important to supply energy for irrigation, electric motors, lighting and other. This paper presents the implementation of an exact linearization technique for the modeling and control of a DC/DC converter for use in a microgrid based on a photovoltaic (PV) generation system where non-linear converters are used. The basic advantage of this technique is in linearizing the converter model, thus allowing different operating points to be considered under different conditions. This paper presents a general description of the implemented microgrid topology. The exact linearization theory adapted for power converters is applied to both a Single-Ended Primary-Inductor converter (SEPIC) to extract energy from PV modules and to a Boost converter to increase the voltage. Experimental results are also presented to validate the effectiveness of the proposed control.

Super-Twisting Algorithm Applied to Velocity Control of DC Motor without Mechanical Sensors Dependence

A DC motor velocity control in feedback systems usually requires a velocity sensor, which increases the controller cost. Additionally, the velocity sensor used in industrial applications presents several disadvantages such as maintenance requirements and signal conditioning. In this work, we propose a robust velocity control scheme applied to a DC motor based on estimation strategies using a sliding-mode observer. This means that measurements with mechanical sensors are not required in the controller design. The proposed observer estimates the rotational velocity and load torque of the motor. The controller design applies the exact-linearization technique combined with the super-twisting algorithm to achieve robust performance in the closed-loop system. The controller validation was carried out by experimental tests using a workbench, which is composed of a control and data acquisition Digital Signal Proccessor board, a DC-DC electronic converter, an interface board for signals conditioning, and a DC electric generator connected to an adjustable resistive load. The simulation and experimental results show a significant performance of the proposed control scheme. During tests, the accuracy, robustness, and speed response on the controller were evaluated and the experimental results were compared with a classic proportional-integral controller, which uses a conventional encoder.

Prescribed Performance Controller Design for DC Converter System With Constant Power Loads in DC Microgrid

In this paper, a composite prescribed performance control strategy is developed for stabilizing dc/dc boost converter feeding constant power loads. First, by employing the exact feedback linearization technique, the nonlinear uncertain dc converter system is first transformed into the Brunovsky’s canonical form. Then, a nonlinear disturbance observer is utilized to evaluate the dynamic change of load power and the accuracy of output voltage regulated by feedforward compensation. Next, the prescribed performance controller is elaborately designed to ensure that the tracking error of output voltage is always within the margin of predefined error bounds. Based on the backstepping design approach, the composite nonlinear controller with prescribed performance is determined. Finally, the numerical simulation results are presented to demonstrate the tracking performance of the proposed controller.

A Novel Assorted Nonlinear Stabilizer for DC–DC Multilevel Boost Converter With Constant Power Load in DC Microgrid

The multilevel boost converter (MBC) has been widely adopted in the dc microgrid systems due to its high voltage gain and simple structure. In recent years, the power electronic loads, which usually behave as constant power loads (CPLs), are penetrating in microgrids. The incremental negative impedance of CPLs degrades the stability of microgrid systems. To ensure effective power flow and guarantee system stability, eliminating the undesired effects of CPLs is a necessity. In this article, a novel assorted nonlinear stabilizer, which is integrated with an extended nonlinear disturbance observer (NDO) and an adaptive backstepping controller, is proposed for stabilizing the MBC-fed microgrid system with CPLs. First, the reduced-order MBC model is transformed into the Brunovsky's canonical form using the exact feedback linearization technique. Second, owing to the NDO, fast system dynamic responses are achieved. Using the estimations of NDO, an adaptive backstepping controller is developed to strictly guarantee the microgrid bus voltage stability in the sense of a large signal. Simulation and experiment results are presented to verify the effectiveness and feasibility of the proposed stabilizer.

Consensus Based Control Algorithm for Nonlinear Vehicle Platoons in the Presence of Time Delay

The platoon control problem for nonlinear vehicles in the presence of time delay is investigated in this paper, where both constant time delay and time-varying delay cases are considered. A linearized third-order vehicle dynamic model is firstly derived by deploying the exact feedback linearization technique and the vehicle platoon control problem is converted into a consensus-seeking problem. Then, a consensus based vehicle platoon control algorithm with time delay is proposed, which drives vehicles to form an equally spaced platoon with the same velocity. By deploying the Lyapunov-Razumikhin theorem, the upper bound of time delay for vehicle platoon with constant time delay is derived and the sufficient conditions that guarantee the stability of the vehicle platoon are obtained. Meanwhile, the sufficient conditions that ensure the stability of vehicle platoon with time-varying delay are acquired via the Lyapunov-Krasovskii theorem. Numerical demonstrations verify the feasibility and correctness of the theoretical results.

A Novel Composite Nonlinear Controller for Stabilization of Constant Power Load in DC Microgrid

Transportation electrification involves the wide utilization of power electronics based dc distribution networks and the integration of a large amount of power electronic loads. These power electronic loads, when tightly controlled, behave as constant power loads (CPLs) and may cause system instability when interacting with their source converters. In this paper, a composite nonlinear controller is proposed for stabilizing dc/dc boost converter feeding CPLs by integrating a nonlinear disturbance observer (NDO)-based feedforward compensation with backstepping design algorithm. First, the model is transformed into the Brunovsky’s canonical form using the exact feedback linearization technique, to handle the nonlinearity introduced by the CPL. Second, the NDO technique is adopted to estimate the load power variation within a fast dynamic response, serving as a feedforward compensation to increase the accuracy of output voltage regulation. Then a nonlinear controller is developed by following the step-by-step backstepping algorithm with strictly guaranteed large signal stability. The proposed controller not only ensures global stability under large variation of the CPL but also features fast dynamic response with accurate tracking over wide operating range. Both simulations and experiments are conducted to verify the proposed strategy.

Modeling of DC–DC Converter Using Exact Feedback Linearization Method: A Discussion

ABSTRACTDC–DC converter finds widespread use in variety of applications. DC–DC converter inherently possess nonlinear dynamics, therefore different linearization schemes are used to get a linearized model of the converter. The classical state-space averaging method is one of the most widely used linearizing method for DC–DC converter. But the said linearization method has some inherent limitation which limits the accuracy of the developed linearized model. This paper provides a discussion of mathematical modeling of DC–DC converter operating in continuous conduction mode as well as in discontinuous conduction mode using exact feedback linearization (EFL) technique which is based on Lie algebra. A linearized model of the converter is obtained using EFL and the effect of change in duty cycle and change in circuit parameters on the frequency response has been studied. The frequency response of the EFL model and nonlinear model is matching within the range of duty cycle and load resistance considered in this paper.

Affine nonlinear control for an ultra-supercritical coal fired once-through boiler-turbine unit

The ultra-supercritical once-through boiler (OTB) unit is an advanced power generation technology with high plant efficiency, high coal utilization, and low emission. However, it is difficult to realize a coordinate control for the ultra-supercritical OTB unit to achieve fast and stable dynamic response during load tracking and grid frequency disturbances, and its complexity and nonlinearity result in the ultra-supercritical OTB unit becoming a multiple-input and multiple-output system filled with severe coupling and interference. According to the affine nonlinear system theory, a nonlinear control method is developed to solve nonlinear decoupled optimal control problems of a nonlinear ultra-supercritical OTB unit. Firstly, the exact linearization technique is used to transform the nonlinear ultra-supercritical OTB system into a linear one and an optimal LQR is designed for the corresponding nominal system. The optimal nonlinear control law can be derived by coordinate conversion and condition feedback and the study can be conducted for reasonable experiments and analysis. Then, compared with the linear PID control and model predictive control, the effectiveness and superiority of the proposed nonlinear optimal control have been verified through different loads disturbances from 50% to 100% using the Matlab/Simulink Toolbox.

An approach of the exact linearization techniques to analysis of population dynamics of the mosquito Aedes aegypti

Dengue fever, chikungunya and zika are caused by different viruses and mainly transmitted by Aedes aegypti mosquitoes. These diseases have received special attention of public health officials due to the large number of infected people in tropical and subtropical countries and the possible sequels that those diseases can cause. In severe cases, the infection can have devastating effects, affecting the central nervous system, muscles, brain and respiratory system, often resulting in death. Vaccines against these diseases are still under development and, therefore, current studies are focused on the treatment of diseases and vector (mosquito) control. This work focuses on this last topic, and presents the analysis of a mathematical model describing the population dynamics of Aedes aegypti, as well as present the design of a control law for the mosquito population (vector control) via exact linearization techniques and optimal control. This control strategy optimizes the use of resources for vector control, and focuses on the aquatic stage of the mosquito life. Theoretical and computational results are also presented.

Switching Control for Aero-Engines Based on Switched Equilibrium Manifold Expansion Model

This paper investigates the switching control problem for aero-engines. An event-triggered switching control strategy is presented based on the proposed switched equilibrium manifold expansion (EME) model of the aero-engine in order to enhance the speed regulation performance. First, a switching law is given using an optimization index for the candidate EME models, which utilize different mappings based on the off-line data of the aero-engine so that the switched EME model has higher accuracy than general EME models. Then, controllers for the subsystems of the switched EME model are designed using the exact feedback linearization technique. Asymptotic stability of the closed-loop switched system is ensured for arbitrary switching with the given condition. This enables us to pursue other performances via design of switching law with stability guaranteed. An event-triggered switching law is constructed for the controllers to get a better performance. Finally, a case study for a two-spool turbofan engine is performed to verify the effectiveness and superiority of the proposed control strategy.

Resource allocation in shared spectrum access communications for operators with diverse service requirements

In this paper, we study inter-operator spectrum sharing and intra-operator resource allocation in shared spectrum access communication systems and propose efficient dynamic solutions to address both inter-operator and intra-operator resource allocation optimization problems. For inter-operator spectrum sharing, we present two competent approaches, namely the subcarrier gain based sharing and fragmentation based sharing, which carry out fair and flexible allocation of the available shareable spectrum among the operators subject to certain well-defined sharing rules, traffic demands and channel propagation characteristics. Subcarrier gain based spectrum sharing scheme has been found to be more efficient in terms of achieved throughput. However, fragmentation based sharing is more attractive in terms of computational complexity. For intra-operator resource allocation, we consider resource allocation problem with users' dissimilar service requirements, where the operator supports users with delay-constraint and non-delay constraint service requirements, simultaneously. This optimization problem is a mixed integer nonlinear programming problem and nonconvex, which is computationally very expensive, and the complexity grows exponentially with the number of integer variables. We propose less-complex and efficient suboptimal solution based on formulating exact linearization, linear approximation and convexification techniques for the nonlinear and/or non-convex objective functions and constraints. Extensive simulation performance analysis has been carried out that validates the efficiency of the proposed solution.