Robustness Of Closed-loop System Research Articles

Decentralized Retrofit Model Predictive Control of Inverter-Interfaced Small-Scale Microgrids

In recent years, small-scale microgrids have become popular in the power system industry because they provide an efficient electrical power generation platform to guarantee autonomy and independence from the power grid, which is a critical feature in cases of catastrophic events or remote areas. On the other hand, due to the short distances among multiple distribution generation systems in small-scale microgrids, the interconnection couplings among them increase significantly, which jeopardizes the stability of the entire system. Therefore, this work proposes a novel method to design decentralized robust controllers based on a retrofit model predictive control scheme to tackle the issue of instability due to the short distances among generation systems. In this approach, the retrofit model predictive controller receives the measured feedback signal from the interconnection current and generates a control command signal to limit the interconnection current to prevent instability. To design a retrofit controller, only the model of a robust closed-loop system, as well as an interconnection line, is required. The model predictive control signal is added in parallel to the control signal from the existing robust voltage source inverter controller. Simulation results demonstrate the superior performance of the proposed technique as compared with the virtual impedance and retrofit linear quadratic regulator techniques (benchmarks) with respect to peak-load demand, plug-and-play capability, nonlinear load, and inverter efficiency.

Output regulation and tracking for linear ODE-hyperbolic PDE–ODE systems

This paper proposes a constructive solution to the output regulation — output tracking problem for a general class of interconnected systems. The class of systems under consideration consists of a linear 2 × 2 hyperbolic Partial Differential Equations (PDE) system coupled at both ends with Ordinary Differential Equations (ODEs). The proximal ODE system, which represents actuator dynamics, is actuated. Colocated measurements are available. The distal ODE system represents the load dynamics. The control objective is to ensure, in the presence of a disturbance signal (regulation problem), that a virtual output exponentially converges to zero. By doing so, we can ensure that a state component of the distal ODE state robustly converges towards a known reference trajectory (output tracking problem) even in the presence of a disturbance with a known structure. The proposed approach combines the backstepping methodology and frequency analysis techniques. We first map the original system to a simpler target system using an invertible integral change of coordinates. From there, we design an adequate full-state feedback controller in the frequency domain. Following a similar approach, we propose a state observer that estimates the state and reconstructs the disturbance from the available measurement. Combining the full-state feedback controller with the state estimation results in a dynamic output-feedback control law. Finally, existing filtering techniques guarantee the closed-loop system robustness properties.

Curved-Line Path-Following Control of Fixed-Wing Unmanned Aerial Vehicles Using a Robust Disturbance-Estimator-Based Predictive Control Approach

In this research, the design of a robust curved-line path-following control system for fixed-wing unmanned aerial vehicles (FWUAVs) affected by uncertainties on the latitude plane is studied. This is undertaken to enhance closed-loop system robustness under unknown uncertainties and derive the control surface deflection angle directly used to control FWUAVs, which has rarely been studied in previous works. The system is formed through the mass center position control (MCPC) and yaw angle control (YAC) subsystems. In the MCPC, the desired yaw angle, which is treated as the reference signal for the YAC subsystem, is calculated analytically using path-following errors, current flow angles, and the yaw angle. In the YAC, a disturbance estimator is designed to estimate uncertainties such as nonlinearities, couplings, time variations, model parameter perturbations, and unmodeled dynamics. Predictive functional controllers are designed to target nominal systems in the absence of uncertainties, such that the estimations of the uncertainties can be incorporated through feedback for closed-loop system robustness enhancement. The simulation results show that higher path-following precision and stronger robustness for the FWUAVs based on the proposed approach can be achieved using only rough model parameters compared with the conventional nonlinear dynamic inversion, which requires detailed model information.

Robustness of closed-loop glucose control systems

Robustness of closed-loop glucose control systems

Wind Tunnel System for Active Flutter Suppression Research: Overview and Insights

This paper describes the development of a new state-of-the-art large wind tunnel model for active flutter suppression studies as well as the supporting techniques used in tests focused on the effects of uncertainty. Design guidelines and the resulting aeroelastic characteristics of the model are covered together with representative test results. Those would allow other researchers working in this area to develop control laws for the new model and evaluate them. A number of important lessons and insight are reported regarding the design of the model, the level of success of commonly used mathematical modeling techniques to capture its behavior, sources of analysis/test correlation discrepancies, multifunction utilization of control surfaces for both system identification and flutter suppression, active flutter suppression testing safety, and techniques for estimating the robustness of closed-loop active aeroservoelastic systems by tests. The new system has made it possible to repeatedly push the actively controlled model, using various flutter suppression control laws (safely), to the actual flutter limit in tests numerous times. This capability is just one of the new experimental capabilities that the new system brings to the aeroelastic active control community.

Robust Stabilization of Underactuated TORA System Based on Disturbance Observer and Fixed-Time Sliding Mode Control Method

A translational oscillator with a rotational actuator (TORA) is an underactuated nonlinear mechanical system with two degrees of freedom (DOF). This paper concerns the robust stabilization control problem for the system with multiple external disturbances. First, a disturbance observer is constructed based on the internal nonlinear dynamic behavior of the system. Second, a robust stabilization controller is designed by the estimated disturbances and the fixed-time sliding mode control method. The controller realizes the global robust stabilization control objective of the TORA system, and the stability of both disturbance observer and robust closed-loop control system are analyzed using the Lyapunov theorem. Finally, the effectiveness of the theoretical results are verified by numerical experiments.

An iterative strategy for robust integration of fault estimation and fault-tolerant control

This paper considers fault estimation (FE) and fault-tolerant control (FTC) for linear parameter varying systems with actuator and sensor faults, uncertainties, and disturbances. The inevitable coupling between the FE and FTC functions needs to be taken into account in the design to ensure the overall FE-based FTC closed-loop system performance and robustness. This paper proposes an iterative strategy to achieve the robust integration of FE and FTC by leveraging the concepts of Separation Principle and Small Gain Theorem. The iterative algorithm involves solving multi-objective linear matrix inequality optimisation problems at each iteration and has finite-step convergence guarantee. Efficacy of the proposed algorithm and its advantages over the existing works are illustrated through numerical simulations.

Robust Reduced-Order Active Disturbance Rejection Control Method: A Case Study on Speed Control of a One-Dimensional Gimbal

Usually, the order of active disturbance rejection control (ADRC) is equal to the relative order of the plant. To improve the control performance, a robust reduced-order method for ADRC is investigated in this paper. Firstly, frequency domain analysis shows that the lower-order extended state observer (ESO) has a smaller disturbance estimation error, so disturbance attenuation capability can be improved by reducing the order of ADRC. However, using only reduced-order ADRC will worsen the robustness of closed-loop systems. Therefore, a robust ADRC method based on a modified noise reduction disturbance observer (MNRDOB) is proposed. The main role of the MNRDOB is to improve the control performance of the closed-loop system by modifying the structure of the controlled object. In addition, the robust stability of the closed-loop control system based on the MNRDOB is discussed. Moreover, some simulations are used to demonstrate the robustness and noise suppression effects of the compound control method reduced-order ADRC with MNRDOB, and the parameter tuning method for the MNRDOB to improve the robustness of the system is given. Finally, some experiments on speed control of a one-dimensional gimbal are performed, and the results show that the proposed method is excellent in overshoot, tracking accuracy, and disturbance attenuation.

A method for robust quadratic pole assignment

A new method is proposed for robust quadratic pole assignment problem. We first give the results on the solution of quadratic pole assignment problem. Then the Schur form corresponding to closed-loop system is established and normality departure is used to measure the robustness of closed-loop system. On these grounds, a method for robust quadratic pole assignment problem is proposed by minimizing the normality departure of closed-loop system. The proposed method avoids to transform the second-order control system to the first-order control system. Moreover, it is implemented in real operations. Numerical experiments show that our method has good performance on the robustness of closed-loop system.

Design and Analysis of Two-Switch-Based Enhanced Gain Buck–Boost Converters

This article presents evolution of two-switch-based enhanced gain buck–boost converter (EGBBC) topologies. All these topologies exhibit quadratic buck–boost voltage transformation ratio together with common ground feature. The basis for these topological evolutions is the cascading of boost followed by restructured ZETA. Direct cascading of boost with ZETA yields a pseudo quadratic conversion ratio and an additional buck stage is mandatory to transform the gain to quadratic buck–boost form. Without adding additional stages and to yet realize the quadratic buck–boost transformation, a modified boost configuration at the front-end together with restructured cascading approach is adopted in the topological evolution. This evolution resulted in three different topologies exhibiting quadratic buck–boost voltage gain named as EGBBC Type-1, Type-2, and Type-3. Exhaustive steady-state and dynamic analysis is presented for Type-1, while brief formulations are listed for Type-2 and 3. Also, a comprehensive review of the reported buck–boost converters is made and compared with EGBBC features. A 10 ∼ 37 W, 15 to 10 V for bucking operation, and 75 V for boosting operation prototype is built for concept validation. A simple two-pole two-zero compensator is adopted for load voltage regulation. Measurement results demonstrate closed-loop system stability, robustness, and voltage regulation both in bucking as well as in boosting operation.

Discrete-Time Sliding Mode Energy Control of sine-Gordon Chain with Adaptive Augmentation*

The present paper focuses on the robustness issues of the speed-gradient energy control design for the one-dimensional sine-Gordon system. The energy stabilization of a non-zero level is addressed as the energy reference tracking problem. In the paper, the “relay” speed gradient algorithm, using state feedback with in-domain actuators, is designed and its adaptive augmentation is proposed. The properties of the closed-loop energy feedback for sampling-in-time control algorithms are studied numerically. In the PDE setting, such an adaptive adjustment of the sliding mode control gain has not been investigated so far. This modification is demonstrated to ensure the closed-loop system robustness with respect to the time sampling.

Real-Time Sensorless Robust Velocity Controller Applied to a DC-Motor for Emulating a Wind Turbine

The wind power systems of variable velocity using a doubly-fed induction generator dominate large-scale electrical generation within renewable energy sources. The usual control goal of the wind systems consists of maximizing the wind energy capture and streamlining the energy conversion process. In addition, these systems are an intermittent energy source due to the variation of the wind velocity. Consequently, the control system designed to establish a reliable operation of the wind system represents the main challenge. Therefore, emulating the operation of the wind turbine by means of an electric motor is a common strategy so that the controller design is focused on the induction generator and its connection to the utility grid. Thus, we propose to emulate the dynamical operation of a wind turbine through a separately excited DC motor driving by a sensor-less velocity controller. This controller is synthesized based on the state-feedback linearization technique combined with the super-twisting algorithm to set a robust closed-loop system in the presence of external disturbances. A robust velocity observer is designed to estimate the rotor velocity based on the armature current measuring. Furthermore, a robust differentiator is designed for estimating the time derivative of the velocity error variable, achieving a reduction in the computational calculus. Experimental tests were carried using a separately excited DC motor coupled with a dynamometer to validate the proposed wind turbine emulator.

Multi-Objective Model Predictive Control for Vehicle Active Suspension System

This paper puts forward a multi-objective model predictive control scheme in order to address the conflicting control objectives of a vehicle active suspension system. The key problem in designing an active suspension controller is that the controller has to realize a feasible control input that can satisfy the competing control requirements such as ride comfort, suspension travel and road handling. Hence, in this work, these constraints are integrated into an optimal control framework and a finite horizon model predictive controller is used to solve the multi-objective cost function. The key advantage of the proposed scheme is that the model predictive control design finds the optimal control input by solving the discrete time algebraic Riccati equation. This guarantees not only a robust closed loop system but also a realizable control effort, without violating the hard constraints of the active suspension system. The proposed model predictive control design is experimentally validated on a laboratory scale quarter car suspension system using hardware-in-loop testing. The performance of the model predictive control scheme is compared with the one of the unconstrained linear quadratic regulator and tested for four realistic road profiles. The experimental results substantiate that the suspension system controlled by the model predictive controller offers better ride comfort and road handling features when compared to the conventional linear quadratic regulator.

Fractional order controllers increase the robustness of closed-loop deep brain stimulation systems.

We studied the effects of using fractional order proportional, integral, and derivative (PID) controllers in a closed-loop mathematical model of deep brain stimulation. The objective of the controller was to dampen oscillations from a neural network model of Parkinson's disease. We varied intrinsic parameters, such as the gain of the controller, and extrinsic variables, such as the excitability of the network. We found that in most cases, fractional order components increased the robustness of the model multi-fold to changes in the gains of the controller. Similarly, the controller could be set to a fixed set of gains and remain stable to a much larger range, than for the classical PID case, of changes in synaptic weights that otherwise would cause oscillatory activity. The increase in robustness is a consequence of the properties of fractional order derivatives that provide an intrinsic memory trace of past activity, which works as a negative feedback system. Fractional order PID controllers could provide a platform to develop stand-alone closed-loop deep brain stimulation systems.

A new robust closed-loop control system for electrosurgical generators

Commercially available electrosurgical generator (ESG) depends on circuit topologies that are responsive to changes in resistance of the tissue. This change in resistance varies the amount of power delivered, especially amid arcing. Changes in resistance along the body make it even harder to keep the power delivery and voltage in limits. An important property of ESG is to be able to keep the output power constant in the constant power region. In this work, a closed-loop control system is designed and tested for ESG to improve its performance in the nonlinear constant power region. A quantitative study of a buck converter and boost inverter is presented along with the closed-loop response for the ESG unit. A comparative analysis of two control methods, i.e., proportional integral derivative (PID) and proportional integral derivative sliding mode control (PIDSMC), is presented for the ESG unit. Results confirm that the presented closed-loop system can highly improve the performance of the ESG system and PIDSMC is found to be a more suitable choice.

Interval Analysis of the Eigenvalues of Closed-Loop Control Systems with Uncertain Parameters

Uncertainty caused by a parameter measurement error or a model error causes difficulties for the implementation of the control method. Experts can divide the uncertain system into a definite part and an uncertain part and solve each part using various methods. Two uncertainty problems of the control system arise: problem A for the definite part—how does one find out the optimal number and position of actuators when the actuating force of an actuator is smaller than the control force? Problem B for the uncertain part—how does one evaluate the effect of uncertainty on the eigenvalues of a closed-loop control system? This paper utilizes an interval to express the uncertain parameters and converts the control system into a definite part and an uncertain part using interval theory. The interval state matrix is constructed by physical parameters of the system for the definite part of the control system. For Problem A, the paper finds out the singular value element sensitivity of the modal control matrix and reorders the optimal location of the actuators. Then, the paper calculates the state feedback gain matrix for a single actuator using the receptance method of pole assignment and optimizes the number and position of the actuators using the recursive design method. For Problem B, which concerns the robustness of closed-loop systems, the paper obtains the effects of uncertain parameters on the real and imaginary parts of the eigenvalues of a closed-loop system using the matrix perturbation theory and interval expansion theory. Finally, a numerical example illustrates the recursive design method to optimize the number and location of actuators and it also shows that the change rate of eigenvalues increases with the increase in uncertainty.

RISE Feedback Control of Cable-Driven Parallel Robots: Design and Real-Time Experiments

Control of Cable-Driven Parallel Robots (CDPRs) is considered as a challenging task due to their highly nonlinear dynamic behavior, abundant uncertainties, low-stiff cables, parameters variation, cable tensions, and actuation redundancy. Hence, a robust controller is needed to obtain higher performance despite the above mentioned issues. In this paper, we propose a Robust Integral of the Sign of the Error (RISE) control scheme to solve the problem of reference trajectory tracking. RISE feedback control is a robust nonlinear continuous controller which can guarantee a semi-global asymptotic tracking under limited assumptions on the system’s structure. RISE ensures the closed-loop system robustness towards parametric uncertainties and external disturbances. The proposed control solution is designed and implemented in real-time experiments on a fully constrained 4-DOF Cable-Driven Parallel Robot (CDPR) named PICKABLE. The obtained experimental results show that the proposed controller outperforms the classical PID controller and the first-order Sliding Mode Control (SMC) in terms of tracking performances and robustness towards payload variations.

Adaptive backstepping second-order sliding mode fuzzy control for three-phase active power filter

Because of the heavy use of electrical equipment, harmonic pollution is becoming more and more serious, which brings potential safety risks to our lives. In view of the fact that active power filters can effectively eliminate harmonics, an adaptive second-order sliding mode fuzzy control based on the backstepping method is proposed to eliminate harmonics in this article. The second-order sliding mode control can eliminate chattering in the system and results in a smoother controller. The uncertainties in the system are approximated by a fuzzy control system, and the adaptive laws are designed to ensure the stability of the system. Backstepping control can improve the stability and robustness of closed-loop systems. Simulation results show that the proposed method has better tracking effect, strong robustness, and stability and can effectively eliminate harmonics.

Adaptive synchronization of uncertain fractional-order chaotic systems using sliding mode control techniques

In this article, an adaptive nonlinear controller is designed to synchronize two uncertain fractional-order chaotic systems using fractional-order sliding mode control. The controller structure and adaptation laws are chosen such that asymptotic stability of the closed-loop control system is guaranteed. The adaptation laws are being calculated from a proper sliding surface using the Lyapunov stability theory. This method guarantees the closed-loop control system robustness against the system uncertainties and external disturbances. Eventually, the presented method is used to synchronize two fractional-order gyro and Duffing systems, and the numerical simulation results demonstrate the effectiveness of this method.

A New Synthetic Minmax Optimization Design of ${H_{\infty} }$ LQ Tracking Control for Industrial Processes Under Partial Actuator Failure

To cope with the control problem of industrial processes with partial actuator failure and disturbance, an improved synthetic minmax optimization design-based ${H_{\infty} }$ linear quadratic (LQ) tracking control strategy is presented in this paper. A new state space model that integrates the dynamics of the process states and the tracking error is first formulated as the basic dynamic process representation. By introducing the new state space model formulation, a new minmax optimization of the ${H_{\infty} }$ norm of the system performance is presented for LQ tracking control design, where more degrees of freedom are offered through the simultaneous adjusting of the tracking dynamics and the state regulation in the cost function, resulting in the enhanced control performance over traditional ${H_{\infty} }$ LQ tracking control. Meanwhile, the nominal closed-loop system stability and robustness under uncertainty are discussed and the monotonicity conditions that are sufficient for both nominal and robust system stability are derived. The case studies on an injection molding process and a nonlinear batch reactor under partial actuator failures and disturbance show the effectiveness of the proposed strategy.