Nonlinear Backstepping Control Research Articles

Robust control design of an air‐breathing engine for a supersonic vehicle using backstepping and UKF

AbstractThis paper presents an efficient robust control design approach for an air‐breathing engine for a supersonic vehicle using the Lyapunov stability theory based nonlinear backstepping control, augmented with unscented Kalman filter (UKF). The primary objective of the control design is to ensure that the thrust produced by the engine tracks the commanded thrust by regulating the fuel flow to the combustion chamber. Moreover, as the engine operates in a supersonic range, an important secondary objective is to manage the shock wave location in the intake for maximum pressure recovery with adequate safety margin by varying the throat area of the nozzle simultaneously. To estimate the states and parameters as well as to filter out the process and sensor noises, a UKF has been incorporated for robust output feedback control computation. Furthermore, independent control designs for the actuators have been carried out to assure satisfactory performance of the engine. Additionally, a guidance loop is designed to generate a typical flight trajectory of the representative vehicle using a nonlinear suboptimal input constrained model predictive static programming formulation for testing the performance of the engine. Simulation results clearly indicate quite successful robust performance of the engine during both climb and cruise phases.

Nonlinear Coordinated Steering and Braking Control of Vision-Based Autonomous Vehicles in Emergency Obstacle Avoidance

This paper discusses dynamic control design for automated driving of vision-based autonomous vehicles, with a special focus on the coordinated steering and braking control in emergency obstacle avoidance. An autonomous vehicle is a complex multi-input and multi-output (MIMO) system, which possesses the features of parameter uncertainties and strong nonlinearities, and the coupled phenomena of longitudinal and lateral dynamics are evident in a combined cornering and braking maneuver. In this work, an effective coordinated control system for automated driving is proposed to deal with these coupled and nonlinear features and reject the disturbances. First, a vision algorithm is constructed to detect the reference path and provide the local location information between vehicles and reference path in real time. Then, a novel coordinated steering and braking control strategy is proposed based on the nonlinear backstepping control theory and the adaptive fuzzy sliding-mode control technique, and the asymptotic convergence of the proposed coordinated control system is proven by the Lyapunov theory. Finally, experimental tests manifest that the proposed control strategy possesses favorable tracking performance and enhances the riding comfort and stability of autonomous vehicles.

Backstepping flux observer for nonlinear control of the direct-drive permanent magnet synchronous generator wind turbines

This article described a backstepping flux observer and a backstepping control strategy applied to the wind energy conversion system based on synchronous generator. The proposed control technique is developed for both converters: the stator-side converter and the grid-side converter. The stator flux is recovered by the backstepping flux observer, and simultaneously, we introduce stator resistance variations to test the robustness of nonlinear backstepping control strategy. Then, MATLAB simulation works show high performances in terms of tracking, stability, and robustness against parameter variations.

Comparative study between the rotor flux oriented control and non‐linear backstepping control of a five‐phase induction motor drive – an experimental validation

Multiphase variable speed electric drives are employed in applications where the reduction in the total power per phase and the highest level of overall system reliability is required. Most of the literature on five-phase induction motor (IM) drive deals with field oriented control, direct torque control, and other non-linear control such as backstepping method. This study deals with the theoretical concept and experimental implementation of indirect rotor flux oriented control (IRFOC) and backstepping control (BSC) of a five-phase IM drive. A comprehensive comparison is done between the most popular IRFOC and non-linear BSC. Backstepping control offers high performance in both steady state and transient operations even in the presence of parameters variations. However, this strategy (BSC) allows the synthesis of the speed and the flux control for a five-phase IM, nevertheless this strategy is asymptotically stable in the context of Lyapunov. The comparison is done using experimental approach. The two control approaches are compared in different terms such as their stability proprieties, achievable dynamic performances, online computational effort, the possibilities of controller design and the complexity of their implementation.

Online Adaptation of Rotor Resistance based on Sliding Mode Observer with Backstepping Control of A Five-Phase Induction Motor Drives

Multiphase electric drives have been developed due to numerous advantages offered by those machines when it compared with the conventional three-phase machines. Multiphase motor drives are considered for applications, where the reduction of power per phase for both motor and inverter and high reliability are required. High performance control techniques are developed for multi-phase drives. The performances of the high performance controller and flux observers may be degraded during the operation. Since the parameters of Induction Motor (IM) varies continuously due to temperature variation and heating. Thus it is significantly important that the value of rotor resistance is continuously observed online and adapted by the control algorithm in order to avoid detuning effects. The efficiency and performance of an induction motor drive system can be improved by online observation of the critical parameters, such as the rotor resistance and stator resistance. Among the parameters of IM, rotor resistance is a decisive one for flux estimation, and also the stator resistance becomes critical in the low-speed operation condition. This paper presents a new online estimation method for the rotor resistance of the IM for sliding mode observer. This method generally based on theories of variable structure and is useful in order to adjust online unknown parameters (load torque and rotor resistance). The presented non-linear compensator afford a voltage inputs on the articulation of stator current and rotor speed measurements, and engender an estimates for the unknown parameters simultaneously, the non-measurable state variables (rotor flux and derivatives of the stator current and voltage) that converge to the corresponding true values. Under the persistent excitation condition, the proposed method estimates the actual value of rotor resistance, which guarantees the exact estimation of the rotor flux. Non-linear Backstepping control and adaptive sliding mode observer of a five-phase induction motor drive is presented. The accuracy and validity of the method is verified by MATLAB simulation model.

Non-linear backstepping control of five-phase IM drive at low speed conditions–experimental implementation

In this paper non-linear backstepping control (BSC) is employed for high performance five-phase induction motor drive for low speed operation. The traditional control approaches such as direct torque control and indirect rotor field oriented control introduces stability problem at low speed. The proposed BSC is shown to offer stable operation in the sense of Lyapunov and high dynamics at low speed. Experimental results are provided to present the proprieties of the proposed approach at low speed in terms of stability, torque ripple, desired control performance, achievable dynamics and complexity of implementation etc.

Near minimum-time feedback attitude control with multiple saturation constraints for agile satellites

Agile satellites are of importance in modern aerospace applications, but high mobility of the satellites may cause them vulnerable to saturation during attitude maneuvers due to limited rating of actuators. This paper proposes a near minimum-time feedback control law for the agile satellite attitude control system. The feedback controller is formed by specially designed cascaded sub-units. The rapid dynamic response of the modified Bang–Bang control logic achieves the near optimal property and ensures the non-saturation properties on three-axis. To improve the dynamic performance, a model reference control strategy is proposed, in which the on-line near optimal attitude maneuver path is generated by the cascade controller and is then tracked by a nonlinear back-stepping controller. Furthermore, the accuracy and the robustness of the control system are achieved by momentum-based on-line inertial identification. The rapid attitude maneuvering can be applied for tasks including the move to move case. Numerical simulations are conducted to verify the effectiveness of the proposed control strategy in terms of the saturation-free property and rapidness.

A new balancing three level three dimensional space vector modulation strategy for three level neutral point clamped four leg inverter based shunt active power filter controlling by nonlinear back stepping controllers

In this paper is proposed a new balancing three-level three dimensional space vector modulation (B3L-3DSVM) strategy which uses a redundant voltage vectors to realize precise control and high-performance for a three phase three-level four-leg neutral point clamped (NPC) inverter based Shunt Active Power Filter (SAPF) for eliminate the source currents harmonics, reduce the magnitude of neutral wire current (eliminate the zero-sequence current produced by single-phase nonlinear loads), and to compensate the reactive power in the three-phase four-wire electrical networks. This strategy is proposed in order to gate switching pulses generation, dc bus voltage capacitors balancing (conserve equal voltage of the two dc bus capacitors), and to switching frequency reduced and fixed of inverter switches in same times. A Nonlinear Back Stepping Controllers (NBSC) are used for regulated the dc bus voltage capacitors and the SAPF injected currents to robustness, stabilizing the system and to improve the response and to eliminate the overshoot and undershoot of traditional PI (Proportional-Integral). Conventional three-level three dimensional space vector modulation (C3L-3DSVM) and B3L-3DSVM are calculated and compared in terms of error between the two dc bus voltage capacitors, SAPF output voltages and THDv, THDi of source currents, magnitude of source neutral wire current, and the reactive power compensation under unbalanced single phase nonlinear loads. The success, robustness, and the effectiveness of the proposed control strategies are demonstrated through simulation using Sim Power Systems and S-Function of MATLAB/SIMULINK.

Backstepping control of a wind turbine for low wind speeds

The aim of this paper was the control of active and reactive powers exchanged between the doubly fed induction generator (DFIG) and the grid in the presence of uncertainty. To achieve this objective, we use the nonlinear backstepping control to command the mechanical and the electrical part and them maximum power point tracking algorithm based on fuzzy logic theory to extract optimal power for low wind speeds. In order to determine the optimal parameters for the backstepping controller we use the genetic algorithm. The simulation results are presented, using a 660 kW DFIG, to demonstrate the effectiveness of the proposed approach.

Low speed control and implementation of permanent magnet synchronous motor for mechanical elastic energy storage device with simultaneous variations of inertia and torque

The spiral torsion spring-based mechanical elastic energy storage (MEES) device presented previously with inherent characteristic of simultaneous variations of inertia and torque is disadvantage to be actuated by conventional control method. This study proposes an improved non-linear backstepping control scheme based on combination of recursive least squares (RLS) and differential evolution (DE) optimisation to regulate permanent magnet synchronous motor (PMSM) at a very low speed and control MEES device effectively. For this presented control scheme, first, a single RLS method with forgetting factor is presented to simultaneously estimate the time-varying inertia and torque of MEES device. Second, on the basis of estimation results, an improved non-linear backstepping control algorithm considering parameter variations in derivation process is proposed to drive PMSM to operate at a very low speed. Finally, a self-adaptive parameter DE method is designed to optimise the several control parameters. The performance of the proposed methodology is verified through simulations and experiments.

Observer-based Adaptive Fuzzy Backstepping Tracking Control of Quadrotor Unmanned Aerial Vehicle Powered by Li-ion Battery

In this paper, an Adaptive Fuzzy Backstepping Control (AFBC) approach with state observer is developed. This approach is used to overcome the problem of trajectory tracking for a Quadrotor Unmanned Aerial Vehicle (QUAV) under wind gust conditions and parametric uncertainties. An adaptive fuzzy controller is directly used to approximate an unknown nonlinear backstepping controller which is based on the exact model of the QUAV. Besides, a state observer is constructed to estimate the states. The stability analysis of the whole system is proved using Lyapunov direct method. Uniformly Ultimately Bounded (UUB) stability of all signals in the closed-loop system is ensured. The proposed control method guarantees the tracking of a desired trajectory, attenuates the effect of external disturbances such as wind gust, and solves the problem of unavailable states for measurement. Extended simulation studies are presented to highlight the efficiency of the proposed AFBC scheme.

DSP-based adaptive backstepping using the tracking errors for high-performance sensorless speed control of induction motor drive

This paper presents a modified structure of the backstepping nonlinear control of the induction motor (IM) fitted with an adaptive backstepping speed observer. The control design is based on the backstepping technique complemented by the introduction of integral tracking errors action to improve its robustness. Unlike other research performed on backstepping control with integral action, the control law developed in this paper does not propose the increase of the number of system state so as not increase the complexity of differential equations resolution. The digital simulation and experimental results show the effectiveness of the proposed control compared to the conventional PI control. The results analysis shows the characteristic robustness of the adaptive control to disturbances of the load, the speed variation and low speed.

An energy-saving nonlinear position control strategy for electro-hydraulic servo systems

The electro-hydraulic servo system (EHSS) demonstrates numerous advantages in size and performance compared to other actuation methods. Oftentimes, its utilization in industrial and machinery settings is limited by its inferior efficiency. In this paper, a nonlinear backstepping control algorithm with an energy-saving approach is proposed for position control in the EHSS. To achieve improved efficiency, two control valves including a proportional directional valve (PDV) and a proportional relief valve (PRV) are used to achieve the control objectives. To design the control algorithm, the state space model equations of the system are transformed to their normal form and the control law through the PDV is designed using a backstepping approach for position tracking. Then, another nonlinear set of laws is derived to achieve energy-saving through the PRV input. This control design method, based on the normal form representation, imposes internal dynamics on the closed-loop system. The stability of the internal dynamics is analyzed in special cases of operation. Experimental results verify that both tracking and energy-saving objectives are satisfied for the closed-loop system.

High‐gain observer‐based output feedback control of single‐rod electro‐hydraulic actuator

In this study, a non-linear backstepping control method based on a high-gain observer design is presented for a single-rod electro-hydraulic actuator, which is not a strict feedback non-linear system. An equivalent model transformation is used for load pressure to establish the relationship between displacement command and virtual command of load pressure. So the convergence analysis of the single-rod electro-hydraulic servo (EHS) model can be divided into two parts. Since the EHS has only one measured output state, a high-gain observer is developed to estimate the full-state of EHS, which can be used in the design of backstepping control. Furthermore, the convergence of this proposed controller is proved by Lyapunov technique. The experimental results verify the dynamic behaviour of this controller varying the observer parameters. In comparison to proportional-integral controller, the proposed controller is more suitable for this EHS in some critical conditions with high response frequency and large unknown external load.

Model-based Predictive and Backstepping controllers for a state coupled four-tank system with bounded control inputs: A comparative study

This paper investigates the problem of global tracking control design for a state coupled four-tank liquid level system with bounded control inputs. For this MIMO system׳s dynamics, motivated by a desire to provide precise liquid level control, two radically different control approaches are presented and compared: the nonlinear generalized predictive control (NGPC) and the Backstepping control. First, an analytical solution of the NGPC is developed based on the nominal model. Then, a nonlinear Backstepping controller is designed in order to ensure globally asymptotical stabilization for this nonlinear system. To ensure a suitable basis for their comparison, the two different control methods are designed and verified with the same test setup under the control input saturation imposed by the system’s actuators. To highlight the efficiency and applicability of the proposed control schemes, simulation as well as experimental results are provided and discussed.

Experimental evaluation of automatically-generated behaviors for USV operations

The performance of four automatically-generated path planning behaviors is evaluated through field-testing. Experiments were conducted using a model-referenced trajectory planner, which was implemented on unmanned surface vehicles (USVs) of different size, thrust, and maneuverability characteristics. The planner combines a local search based on the Velocity Obstacles (VO) concept with a global, lattice-based search for a dynamically feasible trajectory (determined using models of the nonlinear dynamics, nonholonomic constraints, and low-level control of each system). Multiple low-level USV heading and speed controllers, varying in complexity from proportional control to nonlinear backstepping control, were tested with the planner. High planning performance is achieved by searching within a resolution-adaptive space of the USV׳s candidate motion goals. Sampling is constrained to ensure that the International Regulations for the Prevention of Collisions at Sea (COLREGs) are followed. Prior to on-water implementation, the system was fine-tuned in simulation. Four automatically-generated USV behaviors were demonstrated in on-water tests within a complex, static obstacle field: 1) Approach (USV approaches a fixed target); 2) Follow (USV approaches a moving target); 3) Single COLREGs-Compliant Crossing (USV approaches a fixed target while avoiding another vessel); and 4) Multiple COLREGs-Compliant Crossings (USV approaches a fixed target while avoiding an interference vessel multiple times).

Biomimetic Design for Unmanned Aerial Vehicle Safe Landing in Hazardous Terrain

Unmanned aerial vehicles capable of hazardous terrain landing are desirable for intelligence collection. A crucial point is the landing gear's autonomous adaptation to the rough surface, which is especially difficult in an unknown and constrained environment. To enable this capability, this paper proposes a novel biomimetic system that ascertains terrain appearances like large obstacles and precipitous slope using a monocular camera and adjusts the mechatronics landing structure according to the terrain. A dynamic model including the ground effect is provided and a time-to-contact theory-based backstepping nonlinear controller is designed to reject uncertainty disturbances as well as implement a bio-inspired guidance strategy for soft landing in hazardous terrain. The mechatronic architecture and cascade control structure using custom-built unmanned air vehicle platform are presented. Experimental results and video footage demonstrate this biomimetic approach efficiently controls a vehicle successfully landing in an unknown and unstructured constrained environment.

Coordinated Switching Control of the Excitation and Steam Valve System Based on State and Input Constraints

A single unit infinite system of the excitation and steam valve control was proposed based on Barrier Lyapunov theory of restrictive log type. The input amplitude constraint of the steam valve control was considered, and the coordinated nonlinear backstepping controller was designed by switching mechanism. At the same time, the generator rotor effect was considered to be an external unknown large disturbance on the output system, and the conservativeness of the simple estimates for the upper and lower bounds and scaling disturbance was reduced by Minimax. The Minimax method also ensured that the output of the controller and the power angle were within the prescribed range and inhibited the system output effect of disturbance as much as possible. Finally, simulation results of the generator disturbance of mechanical power in the single unit infinite system show that the control scheme effectively improves the transient stability of the dynamic processes of power systems.

Research of Robust Flight Control Algorithm for Quadrotor UAV

For quadrotor unmanned air vehicles (UAVs) nonlinear control problems under disturbance conditions, a nested loop control approach is presented to realize robust control. The robust control approach is proposed to solve the stabilization and navigation problems in the quadrotor. The robust control strategy is composed of two controllers. A nonlinear backstepping controller is designed for the inner loop to stabilize the attitude angle. A PID controller based on BP neural network is designed for the outer loop in order to generate the reference path for the inner loop. Numerous simulations and flight test experiments have been made to study the performance of controller based on the independently developed quadrotor UAV. The results illustrate that the proposed controller has good stability, maneuverability and robustness.

FPGA-Based Implementation Nonlinear Backstepping Control of a PMSM Drive

In this paper, we present a new contribution of FPGAs (Field-Programmable Gate Array) for control of electrical machines. The adaptative Backstepping control approach for a permanent magnet synchronous motor drive is discussed and analyzed. We present a Matlab&Simulink simulation and experimental results from a benchmark based on FPGA. The Backstepping technique provides a systematic method to address this type of problem. It combines the notion of Lyapunov function and a controller procedure recursively. First, the adaptative and no adaptative Backstepping control approach is utilized to obtain the robustness for mismatched parameter uncertainties. The overall stability of the system is shown using Lyapunov technique. The simulation results clearly show that the proposed scheme can track the speed reference. Secondly, some experimental results are demonstrated to validate the proposed controllers. The experimental results carried from a prototyping platform are given to illustrate the efficiency and the benefits of the proposed approach and the various stages of implementation of this structure in FPGA. DOI: http://dx.doi.org/10.11591/ijpeds.v4i1.4645