Robust Feedback Control Research Articles

Robust maximum power point tracking scheme for PV systems based on attractive ellipsoid method

Abstract The Photovoltaic (PV) systems have arisen as one of the best alternatives to electrical power generation based on renewable sources. However, such systems lack on energy transformation efficiency that gets worse in weather changing conditions. Hence, the application of Maximum Power Point Tracking (MPPT) methods that can extract the maximum power even for varying weather conditions is an essential task in PV systems. This paper proposes the design of a robust MPPT system composed by a regression plane to generate the voltage references that obtain the maximum PV power and a robust feedback controller based on the Attractive Ellipsoid Method (AEM) to track such reference applied to a PV array that supplies a load through a buck-boost converter. AEM is a methodology to design robust controllers for a specific class of systems satisfying a boundedness condition even in the case of incomplete system information. The stability of the system even under uncertainties and external disturbances is guaranteed by solving an optimization problem which generates the optimal controller gains using Linear Matrix Inequalities (LMI).

Robust control of q-profile and βp using data-driven models on EAST

• A novel H ∞ robust control scheme is developed for the current profile control using data-driven models. • A decoupling technique enables the control scheme to exhibit multi-functional characteristics. • An anti-windup technique can compensate the effects from moderate time-delays and actuator dynamics. • An efficient procedure is provided to support the H-mode steady-state operation on EAST. • Three general performance indexes are proposed to characterize the current profile control performance. A new robust feedback controller for the safety factor profile and poloidal plasma pressure parameter has been developed using a two-time-scale data-driven model. The model describes the linear plasma responses of the ι profile and β p with respect to auxiliary heating & current drive (H&CD) powers, around a typical plasma equilibrium in an H-mode steady-state plasma discharge on EAST. The feedback controller comprises a carefully designed low-pass filter for the timescale separation, a decoupling module and three local controllers synthesized from the H ∞ norm optimization and the singular value decomposition. The actuators are the lower hybrid current drive (LHCD) system at 4.6 GHz and the ion cyclotron resonance heating (ICRH) system at 33 MHz. Taking into account the actuation dynamics, an anti-windup technique is employed to condition the controller online aiming to attenuate the negative effects from moderate time delays and power saturations. Extensive nonlinear closed-loop simulations with the METIS code suggest that high β p and negative central magnetic shear that characterize advanced tokamak plasma scenarios can be achieved and sustained on EAST with good tracking performance and reasonable robustness via the proposed control scheme. The feedback control of the core ι profile and β p with a range of time delays, power saturations and varying weighting functions are evaluated numerically, compared and discussed. The control robustness to plasma parameter uncertainties including the line-averaged plasma density 〈 n ¯ e 〉 , the H-mode enhancement factor H factor and the effective charge number Z eff are assessed and analyzed.

Robust Output Feedback Tracking Control for Flexible-Joint Robots Based on CTSMC Technique

This brief considers a robust finite-time output feedback control scheme for the tracking problem of flexible-joint (FJ) robotic systems subject to unknown matched and mismatched time-varying disturbances. For this purpose, a novel dynamic terminal sliding mode surface is firstly constructed base on a sliding mode observer. Then, a continuous finite-time control scheme is developed to cope with these disturbances. Besides, the proposed controller guarantees the finite-time convergence of the closed-loop system and requires only the measurements of link positions. Finally, a two-link FJ robot as an example is provided to illustrate the effectiveness of the proposed control scheme.

Robust Output Feedback Control for Input-Saturated Systems Based on a Sliding Mode Observer

This paper designs a robust output feedback controller for input-saturated systems with parametric uncertainties and external disturbances based on the parametric Riccati equation and the sliding mode observer. The stability of the closed-loop system is ensured by the designed controller. The main advantages of the approach proposed in this paper are as follows: (a) the designed sliding mode observer can estimate unknown external disturbances and parametric uncertainties; (b) the designed output feedback controller can increase the state convergence speed; and (c) the control gain can be obtained from the solution of the parametric Riccati equation. The simulation results for a spacecraft rendezvous system illustrate the feasibility of the designed controller.

Robust Control of a Variable-Speed BLDC Motor Drive

This article deals with the design of a digital current control applied to a variable-speed low inductance brushless dc (BLdc) motor drive. A robust static full-state feedback control law is determined by means of a convex optimization problem, subject to linear-matrix-inequality constraints. The optimization is used to achieve a fast time response with reduced overshoot under the parametric variation. Results from a 5 kW/48 V BLdc motor prototype is used to validate the proposed approach with a superior performance when compared to two other control strategies.

Iterative LMI approach to robust static output feedback control of uncertain polynomial systems with bounded actuators

This paper presents a novel static output feedback stabilization of polynomial systems with bounded actuators. We propose a new sufficient condition for static output feedback design for nominal polynomial systems with constraints on input magnitudes. In the proposed stabilization condition, the system matrices and the Lyapunov matrices are separated, and hence parameterization of the controller is independent of the Lyapunov matrices. The main result is the novel parameter-dependent Lyapunov functions that are readily applied to robust static output feedback design of polynomial systems subject to parametric uncertainty. The proposed design conditions are bilinear in the decision variables. Hence, we provide iterative algorithms to solve the design problems. At each iteration, the design condition is cast as parameter-dependent linear matrix inequalities using the sum-of-squares technique and can be efficiently solved. The proposed approach leads to enhanced static output feedback design with computationally tractable formulation. Effectiveness of the proposed approach is demonstrated by numerical examples.

Feedback Linearization Based Robust Control for Linear Permanent Magnet Synchronous Motors

In this study, we designed a feedback linearization control strategy for linear permanent magnet synchronous motors (LPMSMs) as well as a robust control mechanism. First, the highly nonlinear system was transformed into an exact linear system by the feedback linearization technique. Then, we designed a robust controller to mitigate the impact of system parameter disturbances on system performance. This novel robust feedback controller can be applied to electromagnetic force, speed and position control loops in linear motors, correct the errors created by uncertainty factors in the entire system in real time, and set the system’s settling time based on the application environment of the plant. Finally, we performed simulations and experiments using a PC-based motor control system, which demonstrated that the proposed robust feedback controller can achieve good performance in the controlled system with robust anti-disturbance control.

Hammerstein modeling and hybrid control of force and position for a novel integration of actuating and sensing ionic polymer metal composite gripper

An innovative integration of actuating and sensing ionic polymer metal composite (IPMC) gripper is proposed and fabricated in this paper. The IPMC gripper is composed of a stationary copper finger and an IPMC finger attached to a force sensor. In order to make IPMC gripper useful in bio-manipulation application, control strategy is a critical factor to resist nonlinear characteristic of IPMC. Hammerstein model of IPMC output displacement is constructed with static nonlinear portion and dynamic linear portion. We utilize creep operator superposition and auto-regression (ARX) models to represent static nonlinear and dynamic linear portions respectively by modeling methods based on data. Then a novel control scheme is proposed and designed using inverse creep compensator for static nonlinear portion and uncertainty state feedback robust control based on state observer for dynamic linear portion. When IPMC reaches a constant displacement to grasp a miniature object, the grasping force may not be provided enough to complete grasping task. Finally, hybrid control of force and position strategy for IPMC gripper is conducted and realized on physical experimental platform. The experimental results demonstrate the effectiveness of control system to guarantee stable manipulation.

Robust local stabilization of discrete time-varying delayed state systems under saturating actuators

This paper deals with discrete time-varying systems with state-delayed and saturating actuators. A robust state feedback control gain is designed through convex methods ensuring the local stability of the time-varying system with interval time-varying state delay. The estimate of the set of admissible initial conditions is characterized by three convex sets allowing less conservative estimates. Through two numerical examples, we compare our approach with others in the literature and illustrate the better behavior of the proposed methods.

New iterative linear matrix inequality based procedure for H2 and H∞ state feedback control of continuous‐time polytopic systems

SummaryThis article provides new linear matrix inequality (LMI) sufficient conditions for a generalized robust state feedback control synthesis problem for linear continuous‐time polytopic systems. This generalized problem includes the robust stability, H2‐norm, and H∞‐norm problems as special cases. Using a novel general separation result, which separates the state feedback gain from the Lyapunov matrix but with the state feedback gain synthesized from the slack variable, then allows the formulation of LMI sufficient conditions for the generalized problem. Compared to existing parameterized LMI based conditions, where auxiliary scalar parameters are introduced in order to include the quadratic stability conditions (ie, assuming a constant Lyapunov matrix) as a special case, the proposed new conditions are true LMIs and contain as a particular case the optimal quadratic stability solution. Utilizing any initial solution derived by the quadratic or some existing methods as a starting solution, we propose an algorithm based on an iterative procedure, which is recursively feasible in each update, to compute a sequence of nonincreasing upper bounds for the H2‐norm and H∞‐norm. In addition, if no feasible initial solution can be found for some uncertain systems using any existing methods, another algorithm is presented that offers the possibility of obtaining a robust stabilizing gain. Numerical examples from the literature demonstrate that our algorithms can provide less conservative results than existing methods, and they can also find feasible solutions where all other methods fail.

A Novel Hybrid Robust Control Design Method for F-16 Aircraft Longitudinal Dynamics

This paper presents a hybrid robust control design method for a third-order lower-triangular model of nonlinear dynamic systems in the presence of disturbance. In this paper, a novel control design is presented systematically to synthesize a robust nonlinear feedback controller, called backstepping sliding mode control (BSMC), for the proposed system by a combined approach of backstepping design and sliding mode control. In this approach, a family of the “sliding surface” is introduced in state transformations. Then, a smooth switching function of the sliding surface is introduced and enforced to include in virtual feedbacks and a real control law from the control selection phrases of the backstepping design loop. The achieved control method proves a well-tracking command with asymptotic stability, provides a robustness in the presence of uncertainties, and eliminates completely a chattering phenomenon. The application of flight-path angle control corresponding to the longitudinal dynamics of a high-performance F-16 aircraft simulation model is implemented. Under some assumptions, full nonlinear longitudinal dynamics is reformed into a lower-triangular system for a direct application to formulate a control law. A closed-loop system is achieved for in-flight simulation with different flight profiles for a comparison of the existing methods. Also, an external disturbance on different loading/unloading conditions in flight is applied to verify and validate robustness of the proposed control method.

Randomized probabilistic approach for parametric uncertainties in unmanned helicopters

SummaryParametric uncertainties and the problems associated with the design of robust state feedback control tends to be a major concern for achieving stable operation of nonlinear systems. To overcome these drawbacks, this article provides a perspective on a randomized algorithm based probabilistic control for nonlinear systems. The control approach aims at development of randomized algorithms for control of unmanned helicopters which are subjected to uncertainties. A controller gain is synthesized by developing a robust probabilistic approach using sequential randomized algorithm with the two degree of freedom helicopter system. Subsequently, the stability and reachability for the action of developed controller is validated with the help of Lyapunov asymptotic stability and reach tube analysis, and the corresponding results were analyzed. A comparative assessment of simulation and real‐time control results of projected approaches on helicopter model are presented for validation of the controller response.

Functional observer–controller method for unmeasured premise variables Takagi-Sugeno systems with external disturbance

A functional observer–controller design problem of Takagi-Sugeno fuzzy systems with unmeasured premise variables and external disturbance is investigated in this paper. First, robust state feedback controller is designed based on a relaxed fuzzy Lyapunov approach. With an estimation membership functions of transformation technique, a fuzzy functional observer is introduced to estimate the unmeasured premise variables and system control input. By using a robust separation principle, the observer and controller errors system is proved to be stable and robust to external disturbance. Finally, the estimation and control effects of the proposed method are verified through several engineering examples.

On LMI conditions to design robust static output feedback controller for continuous-time linear systems subject to norm-bounded uncertainties

This paper addresses the problem of Static Output Feedback (SOF) stabilisation for continuous-time linear systems subject to norm-bounded parameter uncertainties using the Linear Matrix Inequality (LMI) approach. Usually, this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearise to get non-conservative LMI conditions. We present first, in this paper, some background results on the SOF controller design and that are found to be extended to the case of norm-bounded uncertainties. We show that some restrictions on the feasibility of these results should be guaranteed. Moreover, by means of some technical Lemmas, we transform the BMI into a new LMI with a line search over a scalar variable. An enhanced and less conservative LMI condition with a line search over two scalar variables is also developed. Furthermore, a simplified version of each LMI condition without a priori fixed parameters is also presented. An extensive portfolio of numerical examples is presented in order to evaluate the conservativeness and to show the superiority of the proposed design method to the background results.

Low-conservative robust composite nonlinear feedback control for singular time-delay systems

A low-conservative composite nonlinear feedback controller is proposed for singular time-delay systems with time-varying delay. The proposed composite nonlinear feedback controller not only improves the transient responses of the closed-loop system but it also has less conservatism than other composite nonlinear feedback controllers. The gain of the linear part of the composite nonlinear feedback controller is obtained by precise mathematical calculation to depend not only on the upper bound of the delay but also on the delay range and rate of its changes. More advantages of the proposed composite nonlinear feedback controller are its accurate operation in the presence of actuator saturation, model uncertainties, and system singularities. The linear and nonlinear parts of the proposed controller are designed by solving a linear matrix inequality problem confirmed through a theorem using Lyapunov stability analysis. The theoretical achievements are endorsed by computer simulation through numerical and practical examples.

Rejecting the effects of both input disturbance and measurement noise: A second‐order control system example

SummaryThis article originates from the well‐accepted observations in practice: rejection of both input disturbance and measurement noise is practically important for high‐precision tracking control, and the classic estimators, such as the uncertainty and disturbance estimator (UDE) and disturbance observer, are proven to be inherently sensitive to measurement noises. Motivated by these observations, we develop a robust control solution and demonstrate the possibility of unifying the design of noise estimator (NE) and UDE for a class of second‐order systems. Interestingly, the NE and UDE have three important features in common: (i) the designs are based on system model and reliable state measurement; (ii) a first‐order filter is used to ensure that the design is physical realizable, rather than to filter out undesired signals; (iii) the filter parameters are readily determined by an introduced singular perturbation parameter. The performance of UDE is improved when augmented with NE to reject measurement noises. Then, a simple mapping for parameter tuning is presented, by which the estimation performance can be explicitly analyzed using the singular perturbation theory. Comparative simulation and experimental studies show that the proposed NE+UDE‐based solution is not only less sensitive to measurement noise than the classic UDE‐based control, but also able to deliver superior trajectory‐tracking performance over other robust output feedback control approaches.

A finite time adaptive back‐stepping sliding mode control for instantaneous active‐reactive power dynamics based DFIG‐wind generation towards improved grid stability

AbstractIn this paper, a low computational, robust nonlinear feedback control is proposed as independent distributed generation controller (IDGC) for doubly fed induction generator (DFIG) based wind power generation system (WPGS). WPGS integration as distributed generation (DG) to grid point of common coupling (PCC) is reflecting high power loss profile in terms of low frequency oscillations under grid operational contingencies and have high instability hazard under unbounded uncertainties like unintentional islanding operation. Thus, to improve the stability margin of DFIG‐WPGS integration fast DG dynamic relations are obtained, where instantaneous active‐reactive power (P‐Q) formulation is proposed to avoid unnecessary phase locked loop (PLL) angle (ω) estimation. The feedback path is designed with proposed finite time adaptive backstepping sliding mode control (FTABSMC) for IDGC operation according to ISA‐95 standards. The FTABSMC is ensured with bounded/unbounded uncertainty handling capability by incorporating backstepping based dynamic error profile depletion and with enhanced stability margin by finite time sliding surface based error trajectory to equilibrium. Further, the adaptive sliding surface estimation is proposed in terms of dynamic uncertainty (energy fluctuation) for robust unbounded uncertainty handling. The stability improvement is established with small‐signal (SS) based closed loop analysis of considered DFIG‐WPGS. The uncertainty handling capability is presented thought rigorous case studies in MATLAB based simulation environment and TMS 320 digital signal processor (DSP) based processor‐in‐loop (PIL) validation.

Adaptive Super-Twisting Sliding Mode Control for Mobile Robots Based on High-Gain Observers

In this paper, a robust adaptive output feedback control strategy based on a sliding mode super-twisting algorithm is designed for the trajectory tracking control of a wheeled mobile robot. First, a robust adaptive law is designed to eliminate the influence of parameter uncertainties. Second, a double-power sliding mode surface is designed to improve the response speed of the robot system. Finally, a high-gain observer is employed to estimate the speed information. The stability of the closed-loop system is proved using the Lyapunov stability theorem. The effectiveness of the proposed control strategy is verified by simulation.

Optimal robust model predictive reset control design for performance improvement of uncertain linear system

This study aims to design a robust reset dynamic output feedback control (DOFC) for a class of uncertain linear systems. This procedure is performed as following. First, the elements of the robust DOFC are designed via the linear matrix inequality (LMI) technique such that closed-loop exponential stability is achieved. Second, reset law which contains value of after reset and a constraint for the reset action is determined. Genetic algorithm (GA) is applied to minimize the proposed objective function to find the reset times by using the specified after reset value for individual reset instances. To do this, a model-predictive-based optimization is adopted by using output information. The proposed robust controller is applied to two uncertain systems; distillation column, and B747-100/200 aircraft model. The merits of the proposed robust reset controller in improving transient performance are demonstrated by comparing its results with state-of-the-art methods.

Robust output feedback control of fixed-wing aircraft

PurposeThis paper aims to devise a robust controller for the non-linear aircraft model using output feedback control topology in the presence of uncertain aerodynamic parameters.Design/methodology/approachFeedback linearization-based state feedback (SFB) controller is considered along with a robust outer loop control which is designed using Lyapunov’s second method. A high-gain observer (HGO) in accordance with the separation principle is used to implement the output feedback (OFB) control scheme. The robustness of the controller and observer is assessed by introducing uncertain aerodynamics coefficients in the dynamic model. The proposed scheme is validated using MATLAB/SIMULINK.FindingsThe efficacy of the proposed scheme is authenticated with the simulation results which show that HGO-based OFB control achieves the SFB control performance for a small value of the high-gain parameter in the presence of uncertain aerodynamic parameters.Originality/valueA HGO for the non-linear model of aircraft with uncertain parameters is a novel contribution which could be further used for the unmanned aerial vehicles autopilot, flight trajectory tracking and path following.