Nonlinear Control Research Articles

Nonlinear control of a half electric vehicle including an inverter, an in-wheel BLDC motor and Pacejka’s tire model

Nonlinear control of a half electric vehicle including an inverter, an in-wheel BLDC motor and Pacejka’s tire model

A Simple Controller Design for a Class of Uncertain Nonlinear Control Systems Guaranteed to Achieve Arbitrary Exponential Convergence Rates

This paper first proposes the concepts of high-efficiency stabilizable systems and high-efficiency controller. Then, using the time-domain analysis methodology, it is proved that a class of uncertain nonlinear systems can indeed become high-efficiency stabilizable systems under certain conditions; at the same time, we also provide its corresponding high-efficiency controller. Finally, some numerical simulation results are offered to illustrate and demonstrate the correctness of the main theorem and the design process of such a high-efficiency controller

Various duality models associated with some constrained robust nonlinear optimal control problems

This paper deals with various duality results for a new class of constrained robust nonlinear control problems. Concretely, we introduce a minimisation problem associated with a vector of functionals of multiple integral type. In addition, the considered multi-objective controlled optimisation problem is governed by several mixed constraints generated by partial derivatives of second order and uncertain data. For this new class of control problems, we establish and characterise Wolfe, Mond-Weir and mixed type robust dual models. To this aim, by using the notion of convex multiple integral functional, generated by a controlled second-order Lagrangian with uncertain data, and the concept of robust weak efficient solution to the problem under study, we build a new mathematical context to state and prove the duality theorems.

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Purpose To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems. Design/methodology/approach The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs. Findings In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis. Research limitations/implications Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task. Practical implications The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots. Social implications The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent. Originality/value A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

Output feedback control for hypersonic flight vehicles via distributed high-gain observer

During the hypersonic flight process of rigid hypersonic flight vehicles (HFVs), the flight-path angle and angle of attack are usually small and sensitive to flight condition variation, the accurate measurements are difficult, subsequently the formulation of states observers is an urgent issue. A distributed high-gain observer is proposed to reconstruct the admissible system state dynamics based on limited measured output. First, a distributed observer is proposed for the cascade strict-feedback system to ensure the global convergence of the state estimation errors between the estimated state in each local observer and system states, for the prescribed system initial values. Second, the distributed high-gain observer-based nonlinear control is investigated on the longitudinal dynamics of HFVs with partial measurable states. The rigid body system dynamic is divided into the altitude subsystem and the velocity subsystem. In the altitude subsystem, the proposed distributed high-gain observer is formulated to exact estimate the flight-path angle and angle of attack, and then the back-stepping design is proposed for constructing the controllers. The nonlinear dynamic inversion controller is introduced to accomplish the velocity tracking. Finally, simulation examples are served to verify that the proposed output feedback control possesses the superior properties of high tracking performance, fast convergence of state estimation error and easy-implementation.

Examining the performance of Laguerre-based and nonlinear predictive control models for wheeled mobile robots when facing obstacles

This focuses on the problem of controlling the formation of a team of rotating robots that are not homonomic and are not able to interact in a barrier environment. The virtual structure formation control strategy is obtained here to calculate each path of the robot separately while the reference path of the virtual center of the formation is generated by artificial potential fields. In this presentation, we will introduce a new control algorithm that utilizes Model predictive control and nonlinear system dynamics. Three traditional model prediction control controllers (MPC): logger-based MPC, nonlinear MPC, and traditional MPC are used to apply the control algorithm for the nonlinear system. Model predictive control is used to calculate the torques required to track the path by using the dynamic model of the Rotary moving robot. A proposed control rule is the most effective approach to solving the formation and tracking problems. Model Predictive Control will be introduced through the introduction of basic ideas and terms. Traditional MPC, logger-based MPC, and non-linear MPC are among the three MPC methods to be offered. The discrete time display of the power plant under control is taken into account by developing MPC methods for linear or nonlinear systems for practical implementation. The model predictor controller optimizes a cost function to calculate an optimal control sequence at any sampling point. While ignoring the rest, the system only achieves the first control action of this sequence. During subsequent sampling, the optimization problem is resolvable with the use of updated process measurements and a different horizon. The cost function formula is determined by the controller’s purpose. An error function often plays a role in determining the objective by revealing the difference between the desired and actual response. The shape of the formation can be preserved by the law of control by utilizing information from other robots, which can be assured through a new cost function. In the current conditions of disruption, the proposed controllers can also achieve the goal of tracking the path and maintaining formation, according to the results.

Observer‐based controller design for blood glucose regulation for type 1 diabetic patients with disturbance estimation: A backstepping approach

AbstractIn this paper, an observer‐based nonlinear controller is proposed to regulate blood glucose concentration (BGC) in type 1 diabetes mellitus (T1DM). The considered virtual patient model is the extended Bergmann minimal model, which is augmented by a meal disturbance and adapted to represent the insulin–glucose homeostasis of T1DM. The backstepping (BS) technique is used to design a closed‐loop feedback controller. The proposed controller does not need to measure insulin, plasma concentrations, and external disturbances while improving control performance and robustness against uncertainty. Insulin concentrations and plasma levels are estimated using state observers and disturbance using a disturbance estimator. These estimations are used as feedback to the controller. The asymptotic stability of the observer‐based controller is proved using the Lyapunov theorem. Furthermore, it is proven that the system is bounded input–bounded output (BIBO) stable in the presence of uncertainties caused by uncertain parameters and external disturbances. For real situations, we consider only the BGC available for measurement, and in addition, inter‐ and intra‐patient variability of system parameters is considered. The results confirm that the proposed controller can asymptotically regulate BGC through appropriate injection of insulin under meal disturbance and of variations in system parameters.

Sliding dynamics of a Filippov ecological system with nonlinear threshold control and pest resistance

Sliding dynamics of a Filippov ecological system with nonlinear threshold control and pest resistance

Neural critic learning with accelerated value iteration for nonlinear model predictive control

Neural critic learning with accelerated value iteration for nonlinear model predictive control

Planar curved path following controller for a small fixed-wing unmanned aerial vehicle with constrained parameters optimized by nonlinear model predictive control

Planar curved path following controller for a small fixed-wing unmanned aerial vehicle with constrained parameters optimized by nonlinear model predictive control

An Improved Nonlinear Droop Control Strategy in DC Microgrids

An Improved Nonlinear Droop Control Strategy in DC Microgrids

Robust Smith Predictor-Based Internal Model Nonlinear Control With Lead Compensation Extended State Observer for PMLSM Servo Systems Considering Time Delay

Robust Smith Predictor-Based Internal Model Nonlinear Control With Lead Compensation Extended State Observer for PMLSM Servo Systems Considering Time Delay

An Adaptive Extended Kalman Filter With Passivity-Based Control for DC-DC Converter in DC Microgrids Supplying Constant Power Loads

This paper proposes an adaptive nonlinear control strategy to eliminate the instability problem of buck converters in DC microgrids (DCMG) considering constant power load (CPL). The strategy includes an Adaptive Passivity-Based Controller (PBC) and an Adaptive Extended Kalman Filter (AEKF). The proposed AEKF performs faster and more accurately than the conventional EKF and adjusts the covariance matrices adaptively. Furthermore, this AEKF directly estimates the unknown CPL power supplied by the converter and prevents the number of measurement sensors from increasing. Hence, PBC ensures system stability alongside AEKF. The controller guarantees Lyapunov stability and fast dynamic response in the presence of uncertainties and perturbations compared to other nonlinear methods. MATLAB simulations and laboratory implementation are provided to confirm the performance and robustness of the proposed control strategy and validate the analysis.

Simultaneous robust model predictive control and state estimation for nonlinear systems with state‐ and input‐dependent uncertainties

AbstractThe convergence and stability of uncertain nonlinear systems is a challenging problem in the nonlinear control area. Besides, in many practical cases, all states are not measurable and are affected by measurement noise. Based on this motivation, the first objective of this paper is to design a novel output feedback robust model predictive control approach for nonlinear systems with state‐ and input‐dependent uncertainties and measurement noise. This approach combines state estimation and robust model predictive control (MPC) into one min–max optimization and by solving the optimization, these two tasks are performed simultaneously. The studied nonlinear system comprises a linear part, a nonlinear part, and a function that denotes the state‐ and input‐dependent uncertainties. Therefore, the other objective is to reduce the computational complexity; thus, the system's nonlinear term and the aforementioned uncertainties are converted into additional disturbances. Subsequently, the optimization problem becomes a quadratic form, which leads to global convergence with the appropriate selection of objective function weights. Besides, this paper explores the convergence of the closed‐loop system states and the sufficient synthesis conditions to guarantee input‐to‐state stability. The implementation on a numerical example and a CSTR process demonstrate the applicability and reliability of the proposed approach.

Adaptive robust control of electromagnetic actuators with friction nonlinearity and uncertainty compensation

Friction nonlinearity and uncertainty are the main factors affecting the highly performance control of electromagnetic actuators. In this paper, a nonlinear adaptive robust control strategy is proposed of electromagnetic actuators with friction nonlinearity and uncertainty compensation. First, the dynamical model of the electromagnetic actuator is established considering nonlinearity and uncertainty. Then, an adaptive robust controller is designed based on the continuously differentiable friction model to ensure that the control input is continuously and bounded. In the design of the controller, the unfavorable effects of unknown parameters in the electromagnetic actuator are eliminated by constructing a parameter adaptive law. Meanwhile, in order to improve the tracking accuracy of the electromagnetic actuator, a nonlinear robust control law is designed to ensure the robustness of the controller. The stability analysis by Lyapunov function shows that the asymptotic tracking effect can be obtained when only parameter uncertainty exists in the closed-loop system of the electromagnetic actuator, and the consistent bounded stability can be ensured when the system also exists uncertain nonlinearity. Extensive comparative results verify the effectiveness of the proposed control method.

Investigation on the Effect of Parasitic Elements on PID Control of DC-DC Buck Converter

DC-DC converter circuits are used in many electronic devices to adjust the voltage to a certain level such as Electric Vehicle. DC-DC Buck converters, which are the most used type of DC-DC converters, reduce the input voltage and keep the output voltage constant at a desired reference voltage value. In this study, the effect of parasitic elements in Buck DC-DC converters is examined on the PID controllers. Parasitic elements cause a non-linear effect on the Buck converter system model. Studies in the literature generally control the output voltage by designing controllers on the Buck converter model without parasitic elements. Alternatively, linear controllers such as PID are designed according to the linearizing model, taking into account the effect of parasitic elements. In addition, nonlinear controllers are designed on the full model with the effect of parasitic elements. In this study, the effect of parasitic elements on linear controllers, especially PID, is examined.

Characteristics analysis and nonlinear control of a digital hydraulic pressure tracking system for high-speed helicopter wet friction clutch

The reliability and control precision of the engagement and disengagement of wet friction clutch are crucial to the transmission of high-speed helicopters. In contrast to the traditional proportional hydraulic system, the digital hydraulic system provides a viable solution due to the use of several fast switching valves (FSVs). In this research, a digital hydraulic pressure tracking system using two fast switching valve arrays (DHPTS-FSVA) is proposed and its nonlinear model is established. Firstly, the static and dynamic characteristics of the DHPTS-FSVA are deeply analyzed by virtue of the half-bridge resistance theory. Moreover, a novel pressure control strategy is proposed, which consists of nonlinear adaptive control method, differential PWM with pressure compensation, and logic allocation strategy of PWM duty ratio. Finally, comparative simulation and experimental results indicate that the maximum, average, and standard deviation of the errors are reduced by at least 16.1%, 45.1%, and 39.5%, respectively, at the tracking frequencies of 1Hz and 2Hz, which proves that the proposed controller exhibits better tracking performance at low frequencies.

Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems

Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a mesh-free data-based approximation method for the value function of optimal control problems, which partially mitigates the dimensionality problem. The method is based on a greedy Hermite kernel interpolation scheme and incorporates context knowledge by its structure. Especially, the value function surrogate is elegantly enforced to be 0 in the target state, non-negative and constructed as a correction of a linearized model. The algorithm allows formulation in a matrix-free way which ensures efficient offline and online evaluation of the surrogate, circumventing the large-matrix problem for multivariate Hermite interpolation. Additionally, an incremental Cholesky factorization is utilized in the offline generation of the surrogate. For finite time horizons, both convergence of the surrogate to the value function and for the surrogate vs. the optimal controlled dynamical system are proven. Experiments support the effectiveness of the scheme, using among others a new academic model with an explicitly given value function. It may also be useful for the community to validate other optimal control approaches.

A passivity control and developed nonlinear disturbance observer for boost converter with constant power load in DC microgrid

SummaryThis paper presents an adaptive nonlinear control scheme to ensure the stability of a boost converter in a DC microgrid that supplies a constant power load (CPL) and a resistive load. The proposed controller comprises a passivity‐based control (PBC) and a Nonlinear Disturbance Observer‐Based Robust Control (NDOBRC). The PBC guarantees the overall stability of the proposed controller, whereas the NDOBRC compensates for various sources of disturbances and uncertainties in the system, such as CPL power. The large‐signal stability of the PBC is established using the Lyapunov function. Simulation and experimental results demonstrate the effectiveness of the proposed controller in terms of superior performance compared to the PI method.

ESO-based and FTDO-based anti-swing control for overhead cranes with external disturbance

Overhead cranes play a pivotal role in various industrial applications. This paper presents two methodologies for suppressing the payload’s swing and completing the accurate positioning. The original crane model is initially transformed into a chained form. Two nonlinear controllers are devised to regulate the trolley’s position and achieve the payload’s anti-swing control. The first approach utilizes backstepping, extended state observer, and filter technique to effectively estimate system state and disturbance and make the closed-loop system uniformly ultimately bounded. In contrast, the second method involves sliding mode control and finite-time disturbance observer to ensure the finite-time convergence of the resulting closed-loop system and the accurate disturbance estimation. Finally, simulation results are provided to validate the effectiveness of the proposed methods.