Robust Feedback Control Research Articles

Robust stability analysis and feedback control for networked control systems with additive uncertainties and signal communication delay via matrices transformation information method

The interval type-2 Takagi-Sugeno (T-S) fuzzy dynamic output feedback and H-infinity stability analysis is studied for a class of networked control systems with multiple time-varying additive uncertainties, time-varying signal communication delay and external disturbance. Firstly, the interval type-2T-S fuzzy is employed to denote the system plant. Secondly, the multiple time-varying additive uncertainties are introduced in the controller design and the state variables depending on additive uncertainties. Thirdly, the delay-dependent Lyapunov-Krasovskii functional with double integral terms is designed to derive the less conservative stability conditions in terms of linear matrix inequalities (LMIs). The characteristic of the state variables are reflected effectively by employing the controller with multiple time-varying additive uncertainties. The closed-loop system is asymptotically stable with prescribed H-infinity performance index γ by employing the matrices transformation information. The less conservative stability conditions are derived and extended into the networked control system without additive uncertainties. Finally, simulations are presented to show the effectiveness of the proposed methods.

Robust dynamic output feedback control of blood glucose level in diabetic rat with robust descriptor Kalman filter

This paper deals with the robust control problem for a model of blood glucose system in Type-1 diabetic rats with disturbances (food, physical activity, and insulin sensitivity parameter) and model uncertainties. The considered model has a special structure, which can be written as a descriptor model. The robust control law is designed such that the output of the system tracks the desired reference signal despite the parameter uncertainties. By utilizing the μ-synthesis-based and H∞ controller design methods, the desired input signals (insulin for injection) are designed for both approaches and compared with each other. Moreover, the control structure is considered in a way that the states are not essential to be directly measured, and instead, the states estimation is utilized which operates in the closed-loop system together with a control law. Due to the existence of the model uncertainties, external disturbances, and also the characteristics of the descriptor system, the robust descriptor Kalman filter is designed for this system. Finally, to demonstrate the efficiency of the proposed methods, they are applied to the model, and simulations are provided. The results show the closed-loop system including the descriptor model, robust controller, and robust descriptor Kalman filter can force the blood glucose level to maintain in the normal range successfully with an acceptable state estimation error.

Comparative Study of Trajectory Tracking Control for Automated Vehicles via Model Predictive Control and Robust H-infinity State Feedback Control

A comparative study of model predictive control (MPC) schemes and robust H_{infty } state feedback control (RSC) method for trajectory tracking is proposed in this paper. The main objective of this paper is to compare MPC and RSC controllers’ performance in tracking predefined trajectory under different scenarios. MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire, which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode. RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison. Then, three test cases are built in CarSim-Simulink joint platform. Specifically, the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions. Besides, the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability. Furthermore, an extreme curve test is built where the road adhesion changes suddenly, in order to test the performance of both controllers under extreme conditions. Finally, the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.

Adaptive robust output feedback control for attitude tracking of quadrotor unmanned aerial vehicles

SummaryThis work proposes a new adaptive robust output feedback control method for attitude reference tracking of a quadrotor unmanned aerial vehicle without using the angular velocity measurements. By using the K‐filters well known in the adaptive control community, the necessity of velocity measurements or estimating is avoided. The attitude system model is transformed into a second‐order model where the angular velocity measurements are not involved. However, the model includes mismatched uncertainties which should be estimated and compensated by the disturbance observers (DOBs). The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid the explosion of the controller complexity. For each Euler angle axis, the prescribed performance control technique is adopted to ensure a prescribed performance, the lumped disturbance is compensated by a DOB, and furthermore an adaptive law is introduced to adaptively update the corresponding uncertain inertia parameter which affects the control performance significantly. The control performance of the overall control system is analyzed rigorously from the viewpoint of input‐to‐state practical stability. In addition, it is shown how the adaptive laws contribute to improving the control performance. And simulation examples are provided to demonstrate the performance of the proposed method.

Variable structure robust controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

Diabetes mellitus type 1 occurs when β‐cells in the pancreas are destroyed by the immune system. As a result, the pancreas cannot produce adequate insulin, and the glucose enters the cells to produce energy. To elevate the glycaemic concentration, sufficient amount of insulin should be taken orally or injected into the human body. Artificial pancreas is a device that automatically regulates the level of body insulin by injecting the requisite amount of insulin into the human body. A finite‐time robust feedback controller based on the Extended Bergman Minimal Model is designed here. The controller is designed utilizing the backstepping approach and is robust against the unknown external disturbance and parametric uncertainties. The stability of the system is proved using the Lyapunov theorem. The controller is exponentially stable and hence provides the finite‐time convergence of the blood glucose concentration to its desired magnitude. The effectiveness of the proposed control method is shown through simulation in MATLAB/Simulink environment via comparisons with previous studies.

On the steady motions control of viscoelastic joined robotic manipulators

In this paper, the control problem of the serial multi-link robotic manipulators with rigid and viscoelastic joints is considered. The manipulators structure is such that only the rigid joints are controlled by DC motors. It is shown that such robotic manipulators can make so called stationary motions wherein the part of the generalized coordinates does’t change in time and the others change according to a linear law. The robust output feedback controllers are obtained for the robotic manipulators such that the stationary motion is locally, semi-globally, and globally asymptotically stable.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

Output feedback synchronization control for supply vessels during underway replenishment with unknown dynamics and disturbances under input saturation

ABSTRACT This paper investigates the synchronization control problem for a supply vessel during underway replenishment with unknown dynamics, unknown disturbances, input saturation and unavailable velocities. A virtual trajectory shifted by a distance at an angle relative to the trajectory of the supplied vessel is planned. A high-gain observer observer is employed to estimate unavailable vessel velocities and an auxiliary design system is constructed to address the effect of input saturation. Then, the adaptive radial basis function neural networks are employed to approximate unknown dynamics and the adaptive laws are derived to estimate bounds of unknown disturbances. Incorporating the above into the dynamic surface control method, an output feedback robust adaptive neural synchronization control law is developed to force the supply vessel to track the virtual trajectory such that the synchronization navigation between the supply and the supplied vessels is realized. The theoretical analysis and simulation results validate our developed control scheme.

Output feedback robust distributed model predictive control for parallel systems in process networks with competitive characteristics

The parallel structure is one of the basic system architectures found in process networks. This paper formulates control strategies for such parallel systems when the states are unmeasured. The competitive coupling and competitive constraints are addressed in the control design. A distributed buffer and pre-estimator are proposed to solve problems relating to coupling and timely communication whilst a distributed moving horizon estimator is employed to further improve the estimation accuracy in the presence of the constraints. An output feedback robust distributed model predictive control algorithm is then developed for such parallel systems. The Lyapunov method is used for the theoretical analysis which produces tractable linear matrix inequalities (LMI). Simulations and experimental results are provided to validate the effectiveness of the proposed approach.

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either or measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller—which was jointly optimized with a linear derivative estimator—with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

Robust Output Feedback Control of Single-Link Flexible-Joint Robot Manipulator with Matched Disturbances Using High Gain Observer.

This article focuses on the output feedback control of single-link flexible-joint robot manipulators (SFJRMs) with matched disturbances and parametric uncertainties. Formally, four sensing elements are required to design the controller for single-link manipulators. We have designed a robust control technique for the semiglobal stabilization problem of the angular position of the link in the SFJRM system, with the availability of only a position sensing device. The sliding mode control (SMC) based output feedback controller is devised for SFJRM dynamics. The nonlinear model of SFJRM is considered to estimate the unknown states utilizing the high-gain observer (HGO). It is shown that the output under SMC using HGO-based estimated states coincides with that using original states when the gains of HGO are sufficiently high. Finally, the results are presented showing that the designed control technique works well when the SFJRM model is uncertain and matched perturbations are expected.

Estimation and rejection of sinusoidal disturbance with unknown frequency using cascade disturbance observer

A disturbance rejection approach is presented for a class of uncertain systems subject to sinusoidal disturbance with unknown frequency. The proposed disturbance estimation method includes two types of observers that are connected in cascade form. The disturbance property is excited through an auxiliary filter, and then a frequency factor observer is constructed to generate the information required by full-order state observer. Thus, with the disturbance and system state estimation values, the composite control structure including a cascade disturbance observer (CDO) and a robust feedback controller is designed. As a result, the uncertain system with unknown-frequency sinusoidal component can be controlled within the disturbance observer-based control (DOBC) framework, where the asymptotic stability performance can be guaranteed.

Robust Output Feedback Control Design for Inertia Emulation by Wind Turbine Generators

Wind generation has gained widespread use as a renewable energy source. Most wind turbines and other renewables connected to the grid through converters result in a reduction in the natural inertial response to grid frequency changes. The doubly-fed induction generator (DFIG) can be controlled to compensate for this reduction and, in fact, provide faster response than traditional synchronous machines. This paper proposes to design observer based output feedback linear quadratic regulator (LQR) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control laws to realize the inertia emulation function and deliver fast frequency support. The aim is to track the reference speed by a diesel synchronous generator (DSG) in order to reach the desired inertia. The control signal is computed based on a reduced order model using the balanced truncation technique. A comparison with selective modal analysis (SMA) and balanced truncation model reduction techniques is presented. Comprehensive results show the effective emulation of synthetic inertia by implementing the control laws on a nonlinear three-phase diesel-wind system. The proposed technique is analyzed for different short circuit ratio (SCR) scenarios.

Output feedback robust disturbance rejection tracking control design for a bipedal robotic system with articulation constraints

The design of an output-based robust disturbance rejection controller, aimed to solve the state tracking for the articulations of an experimental biped robot, was the main outcome of this study. The robust disturbance rejection controller included an auxiliary hybrid observer entailed to recover the angular velocity for each articulation. The estimated states served to perform the approximation of disturbances and non-modeled parts in the biped robot dynamics by implementing an extended state observer structure. The observer used the tracking position errors as input information, as well as considering the limb articular constraints, which are natural for biologically inspired biped robots. The effect of state constraints motivated the implementation of a hybrid observer with saturated output error injection. The controller design used the estimation of constraint velocity for solving the design of a tracking trajectory control to resolve the reproduction of the gait cycle by the bipedal robotic system. The Lyapunov stability theory served to obtain the laws which adjust the observer gains as well as to prove the ultimate boundedness of the tracking error as well. The evaluation of the suggested controller was realized on a numerical representation of the biped robot. These simulations illustrated the tracking performance of the hybrid robust disturbance rejection controller for all biped robot articulations in a decentralized structure. Experimental evaluations were also considered to validate the robust disturbance rejection controller design. A fully actuated biped robot was constructed and controlled by the robust disturbance rejection controller. The tracking results obtained by the robust disturbance rejection controller (in both the numerical and experimental evaluations) overcame the classical approach performances of diverse controllers as state feedback (proportional-derivative form) and regular robust disturbance rejection controller which did not consider the articulation constraints.

Optimal Trajectory Planning and Robust Tracking Using Vehicle Model Inversion

This article deals with the issue of tracking a reference optimal trajectory for an autonomous nonlinear vehicle model by designing both lateral and longitudinal robust feedback control and a suited feedforward control. In previous works, a strategy based on a human-driver field of view was used to plan an optimal trajectory reference. The optimization has been made using a Genetic Algorithm (GA), and the obtained trajectory has been injected into a Potential Field (PF) so as to be reactive to unforeseen events by using a point mass model. Here, the previously developed GA-PF planification process is integrated in a new complete global planning and tracking method and applied to a validation nonlinear vehicle model. This control tracking method is developed in two strategies: a bicycle model is used as model inversion for feedforward design and a robust control is designed as feedback control in order to take the vehicle (mass and velocity) and road (slope and adherence) parameter variations into account. A lateral nonlinear control and a longitudinal robust control are designed. Realistic autonomous car simulation results are provided on an overtaking scenario and a round-about scenario.

Adaptive robust feedback control of moving target tracking for all - Electrical tank with uncertainty

A moving target tracking control problem for marching tank based on adaptive robust feedback control scheme is addressed. A series of preparations is needed for tank gun before shooting a target, the purpose of this paper is to design a control system to fulfill two requirements in this process: the turret-barrel system of tank needs to be adjusted from off-target position to command position and point to the moving target stably when there are strong uncertainties (modeling error, uncertain disturbance with unknown boundaries and road excitation) in the system. Considering the characteristic of coupled interaction, the first thing we do in this paper is to build a coupled analysis model of turret - barrel system with uncertainty term in state-space form. Second, an adaptive robust feedback control scheme is proposed by adding adaptive law to overcome the uncertainty. Third, multi-body dynamics software is used to establish the mechanical mechanism of the tank, and DC-motor module is established in SIMULINK environment, thus the target information and tracking error of the control system is collected and transferred, the gear-ball screw is derived directly by the output torque of the DC-motor module. Finally, the control system and the 3D model are combined together by means of RecurDyn/SIMULINK co-simulation, the turret-barrel system of tank can approximately track the moving target in a certain range. With the adaptive robust feedback control, the target action is completely followed when the target location is constantly changing.

Robust non-fragile memory feedback control for multi-weighted complex dynamical networks with randomly occurring gain fluctuations

This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results.

Time-Varying Tube-Based Output Feedback Robust MPC for T–S Fuzzy Systems

For Takagi–Sugeno fuzzy systems subject to inexact membership functions, bounded disturbances, and noises, an output feedback robust model predictive control (RMPC) approach with time-varying robust tubes is investigated. The membership functions errors are bounded within convex sets via the properties of zonotopes and interval matrices. An offline table stores a series of structures that include nested robust positive invariant sets with the corresponding nominal feedback controller gains, ancillary controller gains, and observer gains. According to bounds of real-time estimation error sets, the time-varying structures in the offlined table are searched. Then, the output feedback RMPC problem with time-varying tightened constraints on inputs and states is optimized to stabilize the nominal system. The output feedback RMPC approach can not only update bounds of the estimation errors and uncertain terms resulting from inexact membership functions, but also reduce the computational burden. The proposed RMPC algorithm with recursive feasibility guarantees the robust stability of the controlled systems.

Fully Distributed Dynamic Event-Triggered Semiglobal Consensus of Multi-agent Uncertain Systems with Input Saturation via Low-gain Feedback

This paper investigates the event-triggered consensus problem of multi-agent systems with uncertainties and input saturation. First, a fully distributed robust consensus low-gain feedback control strategy is proposed, in which some global information, such as the communication graph and the scale of network, is not needed. Then, by defining an internal dynamic variable to memory the past state, an adaptive dynamic event-triggering mechanism is proposed, which contributes to reducing the usage of communication resources and also does not rely on any global information. Furthermore, Lyapunov-based consensus analysis results are presented, and it is also formally shown that Zeno behavior can be excluded with the proposed consensus protocols. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.