Robust Nonlinear Control Research Articles

Reduction of Effect of Waves Disturbance on Ship Roll Motion by Using Robust Nonlinear Control

Reduction of Effect of Waves Disturbance on Ship Roll Motion by Using Robust Nonlinear Control

Overcome uncertainties of vertical take-off and landing aircraft based on optimal sliding mode control

<span>This study aims to design a robust and optimal controller to overcome the problems related to the existence of disturbances and uncertainties during takeoff and landing operations of vertical take-off and landing (VTOL) aircraft. The dynamics are decomposed into two phase’s parts which are the minimum phase and the non-minimum phase. These two-part are controlled by proposing a robust nonlinear controller represented by sliding mode control (SMC). Also, the chattering effect due to the fast-switching surface in SMC is eliminated by utilizing a proposed sigmoid function which acts as the sigmoid function. The controller's main parameters are tuned optimally based on the particle swarm optimization (PSO) algorithm. In addition, the controller guaranteed the system stability based on the Lyapunov and Routh theories. The main output parameter responses represented by the positioning of the centre of mass and angle of rolling are determined with bounded control inputs. The performance of the proposed controller is tested by tracking VTOL parameters to the desired trajectories. The simulated results not only showed a significant tracking trajectory but also system stability guaranteed. In addition, the results showed an improved rate of 72% and 84% compared with those results obtained from the literature.</span>

Robust control designs for microalgae cultivation in continuous photobioreactors

Abstract Microalgae are used to produce renewable biofuels and high-value components and in bioremediation and CO2 sequestration tasks. These increasing applications, in conjunction with a desirable constant large-scale productivity, motivate the development and application of practical controllers. This paper addresses the application of robust control schemes for microalgae cultivation in continuous photobioreactors. Due to the model uncertainties and external perturbations, robust control designs are required to guarantee the desired microalgae productivity. Furthermore, simple controller designs are desirable for practical implementation purposes. Therefore, two robust control designs are applied and evaluated in this paper for two relevant case studies of microalgae cultivation in photobioreactors. The first control design is based on an enhanced simple-input output model with uncertain estimation. The second control design is the robust nonlinear model predictive control considering different uncertain scenarios. Numerical simulations of two case studies aimed at lipid production and CO2 capture under different conditions are presented to evaluate the robust closed-loop performance.

Simplified Nonlinear Current-Mode Control of DC-DC Cuk Converter for Low-Cost Industrial Applications.

This paper presents a robust nonlinear current-mode control approach for a pulse-width modulated DC-DC Cuk converter in a simple analog form. The control scheme is developed based on the reduced-state sliding-mode current control technique, in which a simplified equivalent control equation is derived using an averaged power converter model in continuous conduction mode. The proposed controller does not require an output capacitor current sensor and double proportional-integral compensators as in conventional sliding-mode current controllers; thus, the cost and complexity of the practical implementation is minimized without degrading the control performance. The simplified nonlinear controller rejects large disturbances, provides fast transient response, and maintains a constant switching frequency. The nonlinear control scheme is developed using an analog circuit with minimal added components, which is suitable for low-cost industrial applications. The control law derivation, control circuit design, controller gains selection, and stability analysis are provided. The proposed control methodology is verified via simulating the closed-loop nonlinear power converter model in MATLAB/SIMULINK under abrupt changes in load current and input voltage. The simulation results show that the proposed control scheme provides robust tracking performance, a low percentage overshoot, fast transient response, and a wide operating range. The maximum percentage overshoot and settling time of the closed-loop power converter response during line disturbance are 5.6% and 20 ms, respectively, whereas the percentage overshoot and settling time during load disturbance are 2.8% and 15 ms, respectively.

Distributed time‐varying optimization control for multirobot systems with collision avoidance by hierarchical approach

AbstractIn this article, a distributed time‐varying optimization problem for multirobot systems with collision avoidance is studied. A hierarchical control framework is employed to simplify the complex problem into two subproblems in two layers. One is the network layer where a novel distributed time‐varying finite‐time optimal control protocol as a signal generator is proposed for each robot. The signal generator ignores the model constraint and uncertainty. The other is the real‐time layer, which mainly contains a sampling module and a robust nonlinear model predictive control (NMPC) module. The former samples the optimal signal from the signal generator as a series of sampling tracking points with proper distance to improve tracking performance, and the latter searches for the optimal control protocol for the robot system to track these sampling tracking points in sequence with the model constraint and uncertainty. Furthermore, considering the collision between each robot, a give‐way strategy is designed that the robot with a low priority has to stop to wait for the other with a high priority to move first. And a primary‐secondary judgment technology determines the priorities of robots adaptively according to the current state of the robots. If the way forward of the moving robot is blocked by the stopping one, an auxiliary point is introduced as a temporary transfer station to avoid collision further. Finally, the effectiveness of the proposed methods is verified by a simulation example.

A new robust nonlinear controller for fractional model of wind turbine based DFIG with a novel disturbance observer

A new robust nonlinear controller for fractional model of wind turbine based DFIG with a novel disturbance observer

Design of intelligent nonlinear robust controller for hydro-turbine governing system based on state-dynamic-measurement hybrid feedback linearization method

Due to the stochastic grid loads and intermittent renewable energy sources in today’s power grid, hydro-generator and grid system stability is increasingly dependent on the hydro-turbine governing system (HTGS). For the HTGS with external disturbances and system uncertainties, an intelligent nonlinear robust controller (INRC) based on state-dynamic-measurement feedback linearization (SDMFL) is proposed to enhance the HTGS’s control performance in this paper. This strategy establishes a dynamic output function including actuator displacement, generator rotor angle, and turbine parameters. The relationship between dynamic output and control input is derived based on this function to establish the corresponding linear state-space model. Then, the mixed H2/H∞ robust controller based on the linear model is designed to suppress the effects of external disturbances and system uncertainties on the system performance. In addition, the controller performance is optimized by levy flight and chaos theory-based gravitational search algorithm (LCGSA), resulting in the INRC. Simulations are performed in MATLAB, and the results are compared with the nonlinear robust controller (NRC) and PID controller. The results show that the proposed controller INRC improves the control performance of nonlinear HTGS with smaller overshoot and shorter adjustment time in all cases.

Robust Nonlinear Adaptive Control for Power Quality Enhancement of PMSG Wind Turbine: Experimental Control Validation

Due to the intense penetration of wind energy into the power grid, grid quality and stability have become a crucial necessity in this type of power generation. It is in this context that this article has just designed an Adaptive Nonlinear Control strategy applied to the Permanent Magnet Synchronous Generator (PMSG) of 1.5 MW power, in order to generate good quality and cleanly usable energy. Interestingly, this robust control algorithm mainly uses the Lyapunov stability theory, which ensures the stability of the Wind Energy Conversion System (WECS), and therefore offers excellent results in the presence of system parametric uncertainties and changes in the elements of the external environment. To this end, the methodology followed in this in-depth study focuses on the application of the Adaptive Backstepping Control algorithm for WECS by exploiting the MATLAB/Simulink toolbox. The theoretical study and simulation of the WECS was supported by the Processor-in-the-Loop (PIL) implantation of the control in the dSPACE DS1104 embedded board to approve the effect of the control in terms of robustness against different wind profiles and parametric changes. ST-LINK communication is used to connect the embedded board and the host computer. The results obtained revealed a fast response of the different signals, a practically low ripple rate of the order of 0.1% and minor overshoots for the different electrical quantities. Operation with a unity power factor is well ensured via this control strategy. Therefore, the adaptive control applied to the WECS has verified the high performance offered and benefits from additional robustness properties.

Controllability of networked systems with heterogeneous dynamics

Hao et al. (Int J Robust Nonlinear Control 28(5):1778–1788, 1976) established necessary and sufficient conditions for the controllability of homogeneous networked systems where the individual nodes are linear time-invariant (LTI) systems and the network topology matrix is diagonalizable. In this paper, we consider a class of heterogeneous networked systems having triangularizable network topology. Here, we establish a result which gives necessary and sufficient conditions for controllability of a class of heterogeneous systems, which generalizes the result of Hao et al. (Int J Robust Nonlinear Control 28(5):1778–1788, 1976). Also, we provide some necessary conditions for the controllability of general heterogeneous networked systems having some restrictions on the network topology matrix. Theoretical results are illustrated with numerical examples.

Dual‐mode robust model predictive control for the tracking control of nonholonomic mobile robot

AbstractIn this article, a novel dual‐mode robust model predictive control (MPC) approach is proposed for solving the tracking control problem of nonholonomic mobile robot with additive bounded disturbance. To reduce the negative effects of disturbance, and drive the state of real system closer to the one of nominal system, a robust reference signal is introduced into the cost function of MPC. In order to reduce the computation burden caused by online optimization of MPC and further improve the tracking accuracy, a dual‐mode control strucuture consisting of the robust MPC and the local nonlinear robust control is developed, in which the local nonlinear robust control law is applied within a specified terminal region. Finally, simulation results on the nonholonomic mobile robot are presented to show the validity of the proposed control approach.

Robust nonlinear observer-based controller design for one-sided Lipschitz switched systems with time-varying delays

The core objective of this paper is to investigate the problem of robust nonlinear observer-based controller design for one-sided Lipschitz (OLS) switched systems. This work considers nonlinear switched systems with norm-bounded uncertainties, time-varying delays, and external disturbances. By selecting appropriate Lyapunov-Krasovskii functions and applying the OSL condition together with the quadratic inner boundedness property, we drive certain necessary and sufficient conditions for the observer-based control of the underlying system that assure the exponential convergence of the system states, the observer states, and the error states to zero, in respect of linear matrix inequalities via average dwell-time approach. The devised scheme offers necessary robustness against L2-norm bounded perturbations. In the end, the proposed scheme has been validated a suitable practical example.

On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case

The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this literature dealing with Kelly Betting. With this as the high-level motivation, we study the potential for use of nonlinear control in this framework. To this end, we consider a “demonstration case” which is one of the simplest scenarios encountered in this line of research: repeated flips of a biased coin with probability of heads p, and even-money payoff on each flip. First, we formulate a new robust nonlinear control problem which we believe is both simple to understand and apropos for dealing with concerns about distributional robustness; i.e., instead of assuming that p is perfectly known as in the case of the classical Kelly formulation, we begin with a bounding set P0,1 for this probability. Then, we provide a theorem, our main result, which gives a closed-form description of the optimal robust nonlinear controller and a corollary which establishes that it robustly outperforms linear controllers such as those found in the literature. A second, less significant, contribution of this paper bears upon the computability of our solution. For an n-flip game, whereas an admissible controller has 2n-1 parameters, at the optimum only O(n2) of them turn out to be distinct. Finally, it is noted that the initial assumptions on payoffs and the use of the uniform distribution on p are made mainly for simplicity of the exposition and compliance with length requirements for a Letter. Accordingly, the paper also includes a new section with a discussion indicating how these assumptions can be relaxed.

Modeling and Robust Control for Tendon–Sheath Artificial Muscle System Twist With Time-Varying Parameters and Input Constraints: An Exploratory Research

Tendon–sheath artificial muscle (TSAM) is a type of artificial muscle, which is widely used in robotic flexible endoscopies. The characteristics of the tendon force/position transmission were studied recently, but the control issue of the TSAM <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> twist <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> is still barely concerned. In this article, an effective robust control scheme is proposed for the TSAM <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> twist <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> , which achieves satisfactory tracking performance. First, a rigorous model was developed for the TSAM <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> twist <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> with consideration of parameters uncertainty and actuator input constraints, moreover, the disturbance of the discontinuous friction (Coulomb friction) was analyzed. Next, by applying some signal operation methods, a nonlinear robust controller was designed. In addition, the stability of the control strategy was proven theoretically by utilizing Lyapunov-based theory. Finally, a series of hardware experiments were conducted on a robotic flexible ureteroscope test-bed. The feasibility of the proposed model, the effectiveness and robustness of the designed control method were extensively validated.

Design and implementation of a nonlinear robust controller based on the disturbance observer for the active spray boom suspension

Spray boom vibrations are one of the main causes of the uneven distribution of agrochemicals. Using active suspension to maintain the correct height of nozzles is critical for obtaining a uniform spray pattern and minimizing the possibility of spray drift. However, the electro-hydraulic active pendulum boom suspension has nonlinear uncertain factors such as parameter uncertainties, external disturbances, model error, etc., which complicate the design of the controller. Therefore, this paper proposes a nonlinear robust feedback control method with disturbances compensation, which integrates a robust controller and disturbance observers through the backstepping method. Initially, to verify the performance of the controller, the Lyapunov stability theory is used to prove that the proposed controller can guarantee the given transient performance and the final tracking accuracy. Furthermore, taking the active suspension of a 28 m wide boom driven by a single-rod hydraulic actuator as an implementation case, the proposed NRCDC controller was compared with a variety of control schemes through a rapid control prototype of a pendulum active suspension. Finally, the proposed control scheme is implemented on a self-propelled sprayer with a boom of 12 m in length. The field test results show that all the performance indicators of the NRCDC controller are better than the other three conventional controllers. Both laboratory and field tests have verified the effectiveness and high performance of the proposed controller. Keywords: robust control, sprayer boom, boom suspension, hydraulic control system, disturbance observer DOI: 10.25165/j.ijabe.20231601.7007 Citation: Cui L F, Xue X Y, Kong W, Ding S M, Gu W, Le F X. Design and implementation of a nonlinear robust controller based on the disturbance observer for the active spray boom suspension. Int J Agric & Biol Eng, 2023; 16(1): 153–161.

Automatic Scenario Generation for Robust Optimal Control Problems*

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 214+3x192 boundary scenarios are considered. A validation with randomly drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used.

Robust Nonlinear Self-Triggered Control Policy for a Novel Fully Actuated UAVs

This paper proposes a self-triggered control policy for a general kind of nonlinear system, ensuring robust performance under various perturbations and alleviating communication burden simultaneously. A novel fully actuated multirotors applied this method shows great robustness to perturbations and is able of tracking six dimensional decoupled trajectories without continuous background sensor monitoring. Rigorous input-to-state stability analysis is deduced and numerical simulations confirm the validity of the policy.

A non-linear backstepping control of Permanent Magnet Synchronous Motor (PMSM)

In the industry, the permanent magnet synchronous motors are one of the most widely used motors and have superior performance compared to the other types of motors. The principal objective of this paper is to ameliorate the performance of PMSMs by implementing a robust non-linear backstepping control. The first part deals with the vector control of mechanical sensors using PI controller. In the second part, we shed the light on the non-linear backstepping control, using Lyapunov function, of PMSM from the point of view of stability and robustness. The results are validated by MALTAB/SIMULINK. The results obtained show the good stability and good dynamic of PMSM’s control by backstepping controller, also the PI is very sensitive to parameter’s machine variation compared with the backstepping controller.

Robust Nonlinear Control for the Fully Actuated Hexa-Rotor: Theory and Experiments

This letter addresses a fully-actuated Hexa-rotor’s control under exogenous position and attitude disturbances. For that aim, we propose a nonlinear and robust control based on a backstepping technique for position dynamics and a geometric control for attitude dynamics. We demonstrate that the closed-loop system is globally exponentially stable. To validate the reached stability, we present simulation results using MATLAB/Simulink and software in the loop simulations using the well-known PX4 firmware in a realistic scenario on a virtual environment in Gazebo. Finally, to ultimately demonstrate the effectiveness of our algorithm, we implement it on an own-developed fully-actuated Hexa-rotor platform. Our contributions can be summarized as 1) the design of a robust controller for the fully-actuated Hexa-rotor not presented in the literature, 2) the publication of the controller’s code for the PX4 autopilot software, and 3) drone’s construction and presentation of real flight experiments.

Control of a DFIG based wind turbine using modified Conditional Servo-compensator

This paper presents the control of a wind turbine composed by a doubly fed induction generator (DFIG), which provides power to the main grid through a feeder. The control algorithm is designed following the modified Conditional Servo-Compensator (mCS) theory. This control technique was recently developed to a broad class of nonlinear systems, and this paper brings the first result applied to wind turbines. The mCS theory has several advantages compared to others, as it is a robust nonlinear control scheme. First, it provides rigorous stability analysis, that allows explicit definition of performance and operating conditions. Secondly, it is a robust controller, and only needs lump values and bounds for parameters and dynamics. Finally it is very simple and easy to implement, and does not need heavy computer burden, it is only based on standard local measurements, and represents a promising solution for real applications. The theoretical results are verified by simulations using detailed Simpower models. These simulations show very good results facing a Low Voltage Ride Through scenario, which is one of the most severe tests used for practical applications. The proposed scheme could easily be adapted to the control of other applications based on power converters, as the control of the interconnection of a full wind farm to the main grid, or the control of a terminal in a DC grid.

Sliding Mode Controllers Design based on Control Lyapunov functions for uncertain LTI systems

In this paper, a design method of sliding controllers based on control Lyapunov functions for uncertain LTI systems is proposed. Systems with matched non-vanishing disturbances, unmatched uncertainties and uncertain control coefficient matrix are considered. It is shown that whenever a robust nonlinear controller exists that renders the system quadratically stabilizable, in the absence of matched non vanishing disturbances, there is also an appropriate First-Order Sliding-Mode controller stabilizing the origin, that also renders the equilibrium point robustly stable in presence of perturbations. This shows that Sliding-Mode controllers are not more restrictive than other controllers, at least for the class of uncertain systems considered. Moreover, the design based on control Lyapunov functions provides a natural sliding surface, having an asymptotically stable sliding dynamics, so that with the corresponding sliding mode controller ensures global asymptotic stability of the uncertain system. The efficiency of the proposed SMC control is validated experimentally on a Furuta pendulum benchmark.