Presence Of Parametric Uncertainties Research Articles

A Comparative Study of Formulations and Algorithms for Reliability-Based Co-Design Problems

Abstract While integrated physical and control system co-design has been demonstrated successfully on several engineering system design applications, it has been primarily applied in a deterministic manner without considering uncertainties. An opportunity exists to study non-deterministic co-design strategies, taking into account various uncertainties in an integrated co-design framework. Reliability-based design optimization (RBDO) is one such method that can be used to ensure an optimized system design being obtained that satisfies all reliability constraints considering particular system uncertainties. While significant advancements have been made in co-design and RBDO separately, little is known about methods where reliability-based dynamic system design and control design optimization are considered jointly. In this article, a comparative study of the formulations and algorithms for reliability-based co-design is conducted, where the co-design problem is integrated with the RBDO framework to yield solutions consisting of an optimal system design and the corresponding control trajectory that satisfy all reliability constraints in the presence of parameter uncertainties. The presented study aims to lay the groundwork for the reliability-based co-design problem by providing a comparison of potential design formulations and problem–solving strategies. Specific problem formulations and probability analysis algorithms are compared using two numerical examples. In addition, the practical efficacy of the reliability-based co-design methodology is demonstrated via a horizontal-axis wind turbine structure and control design problem.

A robust active control scheme for automotive engine vibration based on disturbance observer

In this paper, a combination of robust active controller and disturbance observer for active engine mounts is proposed as an effective way to improve driver comfort for automotive vehicles. First, a robust controller based on μ-synthesis is designed for the engine mounting system in the presence of parametric uncertainty. The effectiveness of the μ-controller in satisfying robust stability and performance is demonstrated. To further improve the performance of vibration control, an observer is designed where all system states and unknown disturbances are estimated. The estimated disturbance forces are used as control signals to cancel the unwanted effects of these disturbances. The results of the system behavior at different engine speeds clearly demonstrate a significant improvement of the system performance as a result of applying the system observer.

Robust versus optimal control for the radius of spherical bubble in a perfect incompressible liquid, LMI optimization approach

Control of the bubble radius is essential in many medical and industrial applications. In this paper, the nonlinear governing dynamic of single spherical bubble in a perfect incompressible liquid is introduced. In continuation, the state space form of the nonlinear dynamic is presented and then observability and controllability are checked by Lie derivative concepts and finally the linearized state space is obtained around its equilibrium point. Second part of this paper is devoted to designing control strategies for the nonlinear governing dynamics of bubble, where the ultrasonic pressure plays the role of control input and the output is radius of bubble which is intended to follow desired radius in order to prevent from bubble collapse phenomenon. A novel robust control is proposed to ensure the desired level of performance in the presence of parametric uncertainty. In this method, the stability of the closed loop system is guaranteed by Lyapunov theorem and the stabilizing gain is achieved by Linear Matrix Inequality (LMI) optimization approach. For comparison, Linear Quadratic Regulator method is selected which is a very classical approach. The optimal feedback gain is also achieved through LMI approach. Simulation results indicate the effectiveness and efficiency of the robust over optimal controller.

Adaptive trajectory generation based on real-time estimated parameters for impaired aircraft landing

ABSTRACTThis paper is motivated by a need to address the challenge of securing a safe landing after suffering from inflight impairment. In this paper, a new adaptive generalised model predictive static programming (G-MPSP) is developed to generate a safe emergency landing trajectory for impaired aircraft. Utilising the computationally efficient G-MPSP framework, the proposed algorithm enables adaptation of model parameters based on the prediction errors to ensure reasonable guidance performance. Based on the estimated parameters, a feasible landing trajectory is then generated by the flexible finite-horizon G-MPSP with input constraints. The integrated approach features explicit closed-form solutions for both parameter estimation and trajectory generation. Its effectiveness is demonstrated by simulations in the presence of parameter uncertainties and noises and by comparison studies with the non-adaptive G-MPSP.

State Estimation of Slow-Rate Integrated Measurement Systems in the Presence of Parametric Uncertainties

In this paper, state estimation of integrated measurement systems in the presence of stochastic parametric uncertainties has been studied in the framework of the optimal filtering technique. Integrated measurement is common in chemical processes in which a small amount of material are gradually collected for a period of time from a few minutes to some hours. This material is transported to the laboratories for analysis and measurement. The goal is to estimate slow-rate and fast-rate instantaneous states out of this integrated measurement by using the Kalman filter while parametric uncertainties have been considered in the noise parameters. Also, convergence analysis of this filter has been studied. The effectiveness of this method has been evaluated through simulation on a distillation column model and implementation on a laboratory-scale pH neutralization pilot plant.

Nonlinear Robust $H_{\infty }$ Control for Spacecraft Body-Fixed Hovering Around Noncooperative Target Via Modified $\theta -D$ Method

This paper addresses the robust control problem of spacecraft body-fixed hovering near a noncooperative target in the presence of parametric uncertainties and disturbances. A closed-form nonlinear robust $H_{\infty }$ controller constructed by the solution of Hamilton–Jacobi–Isaacs (HJI) inequality is designed, which can stabilize the closed-loop system with the $H_{\infty }$ performance. To obtain the solution of HJI, an effective numerical approximation approach called the modified $\theta \text{--}D$ method is proposed, which can obtain a numerical approximation solution of HJI by only solving one algebraic Riccati inequality and several Lyapunov equations rather than a partial differential inequality. The detailed numerical calculation processes of solving the HJI are presented, which shows that the modified $\theta \text{--}D$ method can be implemented offline with less computational burden. Finally, the effectiveness of the designed robust control scheme is demonstrated via a numerical example.

Robust Predictive Speed Regulation of Converter-Driven DC Motors via a Discrete-Time Reduced-Order GPIO

Converter-driven direct current (dc) motors exhibit various advantages in industry, but impose several challenges to higher precision speed regulation in the presence of parametric uncertainties and exogenous, time-varying load torque disturbances. In this paper, the robust predictive speed regulation problem of a generic dc–dc buck converter-driven permanent magnet dc motors is addressed by using an output feedback discrete-time model predictive control algorithm. A new discrete-time reduced-order generalized proportional-integral observer (GPIO) is proposed to reconstruct the virtual system states as well as the lumped disturbances. The estimates of GPIO are then collected for output speed prediction. An optimized duty ratio law of the converter is obtained by solving a constrained receding horizon optimization problem, where the operational constraint on control input is explicitly taken into account. Finally, the effectiveness of the proposed new algorithm is demonstrated by various experimental testing results.

Distributed Consensus for Multiple Lagrangian Systems With Parametric Uncertainties and External Disturbances Under Directed Graphs

In this paper, we study the leaderless consensus problem for multiple Lagrangian systems in the presence of parametric uncertainties and external disturbances under directed graphs. To achieve asymptotic behavior, a robust continuous term with adaptive varying gains is added to alleviate the effects of the external disturbances with unknown bounds. In the case of a fixed directed graph, by introducing an integrate term in the auxiliary variable design, the final consensus equilibrium can be explicitly derived. We show that the agents achieve weighted average consensus, where the final equilibrium is dependent on three factors, namely, the interactive topology, the initial positions of the agents, and the control gains of the proposed control algorithm. In the case of switching directed graphs, a model-reference-adaptive-consensus-based algorithm is proposed such that the agents achieve leaderless consensus if the infinite sequence of switching graphs is uniformly jointly connected. Motivated by the fact that the relative velocity information is difficult to obtain accurately, we further propose a leaderless consensus algorithm with gain adaptation for multiple Lagrangian systems without using neighbors' velocity information. We also propose a model-reference-adaptive-consensus-based algorithm without using neighbors' velocity information for switching directed graphs. The proposed algorithms are distributed in the sense of using local information from its neighbors and using no common control gains. Numerical simulations are performed to show the effectiveness of the proposed algorithms.

A Simple High-Performance Current Control Strategy for V2G Three-Phase Four-Leg Inverter With LCL Filter

Electric vehicles (EVs) can behave as distributed energy storage devices for providing on-demand smart grid support service, that is, an emerging vehicle-to-grid (V2G) technology. A high-performance and easy-implementation current control strategy for V2G three-phase four-leg inverter with LCL filter is proposed. It consists of a deadbeat (DB) controller and a paralleled repetitive controller (RC). The DB controller is based on the weighted average inductor current (WAIC) scheme, which simplifies the third-order LCL filter to be an equivalent first-order $L$ filter. The stability of the DB-controlled inverter with the unmodeled system time delay is analyzed. The DB controller is of very fast response and easy implementation but is not immune to system time delay and various uncertainties. To overcome the disadvantages, a plug-in RC is added to reinforce the DB controller to remove harmonic distortion from the feed-in current in the presence of parameter uncertainties. A lab prototype of 10-kW grid-connected three-phase four-leg inverter has been built up to validate the proposed current control strategy. The simulations and experiments are provided to demonstrate the validity of the proposed control strategy.

An enhanced state convergence architecture incorporating disturbance observer for bilateral teleoperation systems

To bilaterally control an nth-order teleoperation system modeled on state space, state convergence methodology provides an elegant way to design control gains through a solution of 3 n + 1 equations. These design conditions are obtained by allowing the master–slave error to evolve as an autonomous system and then assigning the desired dynamic behavior to the slave and error systems. The controller, thus obtained, ensures the motion synchronization of master and slave systems with adjustable force reflection to the operator. Although simple to design and easy to implement, state convergence method suffers from its dependence on model parameters, and thus the performance of the controller may degrade in the presence of parametric uncertainties. To address this limitation, we propose to integrate an extended state observer in the existing state convergence architecture which will not only compensate the modeling inaccuracies by treating them as a disturbance but will also provide the estimates of the master and slave states. These estimated states are then used to construct the bilateral controller which is designed by following the method of state convergence. In this case, 2 n + 2 additional design equations are required to be solved to fix the observer gains. To validate the proposed enhancement in the state convergence architecture, simulations and semi-real-time experiments are performed in MATLAB/Simulink environment on a single degree-of-freedom teleoperation system.

Nonlinear adaptive sliding-mode control of the electronically controlled air suspension system

Recent years, electronically controlled air suspension has been widely used in vehicles to improve the riding comfort and the road holding ability. This article presents a new nonlinear adaptive sliding-mode control method for electronically controlled air suspension. A nonlinear dynamical model of electronically controlled air suspension is established, where the nonlinear dynamical characteristic of the air spring is considered. Based on the proposed nonlinear dynamic model, an adaptive sliding-mode control method is presented to stabilize the displacement of electronically controlled air suspension in the presence of parameter uncertainties. Parameter adaptive laws are designed to estimate the unknown parameters in electronically controlled air suspension. Stability analysis of the proposed nonlinear adaptive sliding-mode control method is given using Lyapunov stability theory. At last, the reliability of the proposed control method is evaluated by the computer simulation. Simulation research shows that the proposed control method can obtain the satisfactory control performance for electronically controlled air suspension.

Adaptive Nonlinear Hierarchical Control for a Rotorcraft Transporting a Cable-Suspended Payload

Rotorcrafts, with satisfactory maneuver performance and ability under complex terrains unreachable for ground robots, are playing important roles for goods transportation. In this article, we focus on the control of the cable-suspended transportation way due to its lower costs and more agility of the rotorcraft's rotational motion. Compared with traditional crane systems and single rotorcrafts without loads, the aerial transportation system presents “double” underactuated property, stronger system nonlinearity, and more complex dynamic coupling, which are huge challenges for control schemes design. Meanwhile, aerial transportation usually suffers from external disturbances and uncertainties presented with aerodynamic damping coefficients and rope length. Additionally, overshoots of the rotorcraft's position are potential threats for flight safety, especially in confined and complex environments. To address these problems, a novel adaptive control scheme is designed, which ensures effective rotorcraft positioning and payload swing suppression with restricted overshoot amplitudes. Asymptotic results are obtained with rigorous theoretical derivations provided by the Lyapunov-based stability analysis and LaSalle's invariance theorem. Real-time experiments are performed to validate the effectiveness of the proposed control scheme even in the presence of external disturbances. To the best of our knowledge, this is the first method designed for aerial transportation systems which achieves simultaneous rotorcraft positioning and swing suppression, together with insurance for overshoot restriction even in the presence of parametric uncertainties.

Extended-state-observer-based output feedback adaptive control of hydraulic system with continuous friction compensation

This paper presents an extended state observer-based output feedback adaptive controller with a continuous LuGre friction compensation for a hydraulic servo control system. A continuous approximation of the LuGre friction model is employed, which preserves the main physical characteristics of the original model without increasing the complexity of the system stability analysis. By this way, continuous friction compensation is used to eliminate the majority of nonlinear dynamics in hydraulic servo system. Besides, with the development of a new parameter adaption law, the problems of parametric uncertainties are overcome so that more accurate friction compensation is realized. For another, the developed adaption law is driven by tracking errors and observation errors simultaneously. Thus, the burden of extended state observer to solve the remaining uncertainties is alleviated greatly and high gain feedback is avoided, which means better tracking performance and robustness are achieved. The designed controller handles not only matched uncertainties but also unmatched dynamics with requiring little system information, more importantly, it is based on output feedback method, in other words, the synthesized controller only relies on input signal and position output signal of the system, which greatly reduces the effects caused by signal pollution, measurement noise and other unexpected dynamics. Lyapunov-based analysis has proved this strategy presents a prescribed tracking transient performance and final tracking accuracy while obtaining asymptotic tracking performance in the presence of parametric uncertainties only. Finally, comparative experiments are conducted on a hydraulic servo platform to verify the high tracking performance of the proposed control strategy.

Parametric Robust Control of the Multivariable 2 × 2 Looper System in Steel Hot Rolling: A Comparison between Multivariable QFT and H∞

Two robust mutlivariable controllers, H∞ and a decentralized quantitative feedback theory (QFT), are designed in the frequency domain for the 2 × 2 looper system in a steel hot rolling mill to keep stability in the presence of parametric uncertainties. The H∞ controller is designed by using the mixed sensitivity approach, while the multivariable decentralized QFT is designed by the extension of the sequential loop closing method presented elsewhere. Stability robustness conditions are verified in the frequency domain, while simulations in time domain are carried out to evaluate the controllers and compare their performance along with that of proportional + integral (PI) and single input single output (SISO) QFT controllers designed earlier. The QFT controller shows the best balance among the performance indicators analyzed here; however, at the expenses of using higher power in one of the control inputs.

Robust adaptive backstepping fast terminal sliding mode controller for uncertain quadrotor UAV

The problem of controlling the quadrotor orientation and position is considered in the presence of parametric uncertainties and external disturbances. Previous works generally assume that the flight controller parameters are constants. In reality, these parameters depend on the desired trajectory. In this article, a complete mathematical model of a quadrotor UAV is presented based on the Euler-Newton formulation. A robust nonlinear fast control structured for the quadrotor position and attitude trajectory tracking is designed. The position loop generates the actual thrust to control the altitude of the quadrotor and provides the desired pitch and roll angles to the attitude loop, which allow the control of the quadrotor center of gravity in the horizontal plane. The attitude loop generates the rolling, pitching and yawing torques that easily allow the insurance of the quadrotors stability. The outer loop (position loop) uses the robust adaptive backstepping (AB) control to get the desired Euler-angles and the control laws. The inner loop (attitude loop) employs a new controller based on a combination of backstepping technique and fast terminal sliding mode control (AB-ABFTSMC) to command the yaw angle and the tilting angles. In order to estimate the proposed controller parameters of the position and the upper bounds of the uncertainties and disturbances of the attitude, online adaptive rules are proposed. Furthermore, the Lyapunov analysis is used to warranty the stability of the quadrotor UAV system and to ensure the robustness of the controllers against variation. Finally, different simulations were performed in the MATLAB environment to show the efficiency of the suggested controller. The sovereignty of the proposed controller is highlighted by comparing its performance with various approaches such as classical sliding mode control, integral backstepping and second order sliding mode controls.

Robust Adaptive Saturated Fault-tolerant Control of Autonomous Rendezvous with Mismatched Disturbances

This paper investigates the robust adaptive relative pose control design for spacecraft rendezvous and docking missions in the presence of parametric uncertainty, matched and mismatched disturbances, actuator saturation and faults. An adaptive saturated fault-tolerant controller is developed by incorporating the anti-windup compensator to adaptive backstepping technique. In contrast to traditional saturated fault-tolerant controllers for the spacecraft systems, the advantage of the proposed control approach can deal with the mismatched disturbances in the model. Also this approach does not require exact knowledge of the actuator faults and is implemented with uncertain value of fault information. Lyapunov analysis is employed to prove the ultimately uniformly bounded stability of the closed-loop system, where relative pose and velocities converge to adjustable small neighborhoods of zero. Numerical simulation results demonstrate the effectiveness of the proposed control approach.

Robust $$\mathcal{H}_\infty$$ Observer-based Stabilization of Linear Discrete-time Systems with Parameter Uncertainties

This paper addresses the problem of observer-based stabilization of discrete-time linear systems in presence of parameter uncertainties and l2-bounded disturbances. We propose a new variant of the classical two-step LMI approach. In the first step, we use a slack variable technique to solve the optimization problem resulting from stabilization by a static state feedback. In the second step, a part of the slack variable obtained is incorporated in the $$\mathcal{H}_\infty$$ observer-based stabilization problem, to calculate simultaneously the Lyapunov matrix and the observer-based controller gains. The effectiveness of the proposed design methodology is demonstrated using the dynamic model of a quadruple-tank flow process system. Additional numerical illustrations are presented to show the superiority of the proposed Modified Two-Step Method (MTSM) from a LMI feasibility point of view.

Koopman Operator Approach to Airdrop Mission Planning Under Uncertainty

Mission planning for ballistic airdrop requires the selection of optimal control inputs under uncertainty. While significant uncertainty usually exists in airdrop scenarios, current mission planning algorithms use only nominal parameters to compute a deterministic solution. This paper introduces an optimal control algorithm in which the Koopman operator is used to solve for the probabilistically optimal input in the presence of parametric uncertainty. The proposed approach offers unique computational advantages over alternative uncertainty quantification techniques, providing a practical method to compute a probabilistically optimal input. In the context of the airdrop problem, these inputs are the optimal package release point and aircraft run-in. Given an objective function defined over the drop zone and a joint probability density accounting for uncertainty in the system parameters, the objective function is pulled back to the drop altitude using the Koopman operator, and an expected value is computed with the joint probability density. The optimal release point and run-in is then selected to optimize this expected value. Following a general description of the Koopman operator approach to probabilistic decision making, the airdrop-specific implementation is described. Simulation examples are presented, highlighting the performance of the algorithm in real-world scenarios. Results compare favorably with those achieved through deterministic methods.

Integrated condition-based track maintenance planning and crew scheduling of railway networks

We develop a multi-level decision making approach for optimal condition-based maintenance planning of a railway network divided into a large number of sections with independent stochastic deterioration dynamics. At higher level, a chance-constrained Model Predictive Control (MPC) controller determines the long-term section-wise maintenance plan, minimizing condition deterioration and maintenance costs for a finite planning horizon, while ensuring that the deterioration level of each section stays below the maintenance threshold with a given probabilistic guarantee in the presence of parameter uncertainty. The resulting large MPC optimization problem containing both continuous and discrete decision variables is solved using Dantzig-Wolfe decomposition to improve the scalability of the proposed approach. At a lower level, the optimal short-term scheduling of the maintenance interventions suggested by the high-level controller and the optimal routing of the corresponding maintenance crew is formulated as a capacitated arc routing problem, which is solved exactly by transforming it into a node routing problem. The proposed approach is illustrated by a numerical case study on the optimal treatment of squats of a regional Dutch railway network. Simulation results show that the proposed approach is robust, non-conservative, and scalable.

Nonlinear adaptive control of microbial fuel cell with two species in a single chamber

Microbial fuel cells are emerging devices with an ability to harvest electrical energy from wastewater. We develop an integrated control-oriented model with uncertain parameters and a nonlinear adaptive control scheme that can estimate parameters on-line so as to provide robustness against parametric uncertainties with influent substrate concentration as an input variable for a single chamber unit with two bacterial species. In presence of parametric uncertainties, the closed-loop characteristics of the substrate concentration and influent substrate concentration are analyzed through lyapunov stability analysis and validated through appropriate simulation work. The results indicate that the suggested adaptive compensation scheme provides satisfactory performance in presence of parametric uncertainties.