Unmatched Parametric Uncertainties Research Articles

Backstepping based model reference adaptive control for nuclear reactor with matched and unmatched uncertainties

In this work, a Backstepping Model Reference Adaptive Controller (BMRAC) is designed to control the total power of a Pressurized Water Reactor (PWR). It ensures robustness against matched and unmatched parameter uncertainties and disturbances. Reactor core dynamics based on normalized point kinetics equations with six delayed neutron groups is considered, while parametric variations in thermal feedback coefficients, control rod worth and heat transfer coefficients are considered as uncertainties. Reactivity disturbance is considered as unmatched disturbance and external disturbances that enter from control input are considered as matched disturbance. A stable reference model is designed using linear quadratic regulator (LQR) theory to generate setpoints for reactor power control. The disturbances and uncertainties are estimated by comparing reactor dynamics with a stable predictor model. Matched parameter uncertainties and disturbances are compensated with robust MRAC. To compensate for unmatched disturbance, an integrator backstepping is designed. Projection-based adaptive laws are used to provide robustness to the designed controller. The ultimate boundedness of all signals is verified through Lyapunov analysis. Efficiency of the proposed controller is demonstrated through simulation studies, controller performance is compared with conventional LQR controller and adaptive MRAC controller.

Adaptive control of nonlinear plant with unmatched parametric uncertainties and input saturation

The problem of adaptive control of a parametrically uncertain nonlinear plant presented in a state-feedback form with unmatched uncertainties and input constraint is considered. The solution is based on adaptive backstepping procedure, in which the virtual controls includes the high-order time derivatives of adjustable parameters calculated with the use of an adaptation algorithm with improved parametric convergence. Analytical design of control with compensation for the influence of input constraints is performed using of a special filter. The approach presented in this paper allows one to design an adaptive controller that ensures the boundedness for all signals in the closed-loop system and provides tracking of the reference signal. Simulation results presented in the MATLAB/Simulink environment illustrate the performance of the presented approach and the acceleration of parametric convergence with an increase of the adaptation coefficient. The plant considered in this work describes a wide class of systems, such as various manipulation robots, technological processes, electromagnetic levitation systems, chemical processes, etc. The proposed control algorithm considers natural for practical applications input constraints and significantly reduces the influence of the regulator parameters tuning speed on the control system transient processes.

A new robust discrete-time sliding mode control design for systems with time-varying delays on state and input and unknown unmatched parameter uncertainties

This paper proposes a new robust Discrete-Time Sliding Mode Control (dt-smc) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded (ubb) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller is based on a novel sliding surface. Using a new Lyapunov functional candidate and by introducing slack variables, a less conservative delay-dependent sufficient condition ensuring the asymptotic stability of the closed loop system is derived in terms of Linear Matrix Inequalities (lmis). With respect to that condition a new dt-smc law is synthesized. The proposed control algorithm is applied to an Autonomous Underwater Vehicle (auv). The simulation results demonstrate the effectiveness of the proposed controller.

Adaptive robust bipartite consensus of high-order uncertain multi-agent systems over cooperation-competition networks

This paper investigates the bipartite consensus problem for a class of high-order uncertain multi-agent systems, whose dynamics consist of matched and unmatched parametric uncertainties as well as external disturbances, over cooperation-competition networks. The signed graph theory is introduced to describe collaborative and competitive interactions between agents. A distributed adaptive robust controller is proposed to solve the leaderless bipartite consensus problem first, and it is further shown that the leader-follower bipartite consensus problem can be also addressed by the proposed approach. Stability analysis demonstrates that the closed-loop system can be globally exponentially stable with a prescribed rate of convergence. Finally, simulation examples are provided to verify the theoretical results.

Sliding mode control design for parametric uncertain stochastic systems with state delay using functional observer

This study is concerned with the problem of the functional observer-based sliding mode control (SMC) design for parametric uncertain discrete-time delayed stochastic systems includes mismatched parameter uncertainty in the state matrix and in the delayed state matrix. Stability analysis of sliding function is presented in the time delayed stochastic system with a linear matrix inequality approach. Moreover, it is shown that the state trajectories can be driven onto the specified sliding surface despite the presence of state delay, unmatched parameter uncertainty and stochastic noise in the system. The research is motivated by the fact that the system states are not always accessible for the state feedback. Therefore, SMC is estimated using the functional observer technique. To mitigate the side effect of the parameter uncertainty on the estimation error, a sufficient condition of stability is proposed based on Gershgorin disc theorem. The claims made are validated through numerical simulations.

Robustness Improvement for a Three-Loop Missile Autopilot Using Discontinuous State Feedback

For several decades, the classical three-loop autopilot topologies have been successfully employed as missile longitudinal autopilots. To achieve robustness against matched and unmatched parametric uncertainties, this paper proposes two possible designs from a sliding mode control perspective. This paper first introduces what is termed a variable structure three-loop controller (VS3LC), which requires the same commanded and sensed quantities as the classical three-loop autopilot, but uses discontinuous feedback gains and an additional term for robustness improvement. It is found that the solution of this topology results in continuous equivalent control having the same expression as the classical three-loop autopilot when in sliding mode. Next, another variable structure pitch rate controller (VSPRC) which is insensitive to unmatched model parameter uncertainties as well as matched uncertainties is presented. The VSPRC combined with an additional outer-loop control of acceleration results in another three-loop topology, which is named as a variable structure-combined three-loop controller (VSC3LC). The robust performance and stability of the proposed variable structure controllers are illustrated through numerical simulations.

Robust adaptive sliding sector control and control allocation of a missile with aerodynamic control surfaces and reaction jets

Based on L2 optimal control allocation, an autopilot design approach is proposed for the missile with aerodynamic control surfaces and reaction jets. The control system involves a control allocator and a virtual control law. A robust sliding sector with a parameter update law is proposed to deal with unmatched parameter uncertainties and unknown disturbances in the system. Then a control law is designed to produce virtual control effort signals by using the robust adaptive sliding sector. In order to distribute the virtual signals to the aerodynamic control surfaces and reaction jets on the missile, a control allocator is designed by L2 optimal control allocation strategy. Simulation results show that the missile control system tracks the acceleration command fast and smoothly. In the tracking process, aerodynamic control surfaces cooperate with reaction jets, verifying the effectiveness of the proposed approach.

The sliding mode load frequency control for hybrid power system based on disturbance observer

Abstract Penetration of wind and solar power are increasing in power systems. Intermittent characteristics of renewable sources and random load variation result in system voltage and frequency fluctuation. A load frequency control (LFC) strategy based on sliding mode control (SMC) theory and disturbance observer is proposed for the single area power system. In order to reduce the frequency deviation caused by the unmatched parameter uncertainties such as the renewable source and different load disturbance, the sliding mode load frequency controller is constructed by selecting the appropriate proportional and integral switching surface and the reaching law condition. Furthermore, the sliding mode load frequency controller is reconstructed based on the designed disturbance observer (DOB) to improve the dynamic performance and suppress the chattering. The proposed method is compared with the conventional sliding mode LFC and the robust adaptive LFC (RALFC) by using the matlab software, the simulation results show that the designed LFC has faster response speed and better robust performance.

Robust sliding mode control approach for systems affected by unmatched uncertainties usingH∞with pole clustering constraints

SUMMARY In this paper, the problem of sliding mode control for a class of systems with unmatched parametric uncertainties and external perturbations is considered. LMI technique and polytopic models are used in the design of the switching surface. To achieve some performance requirements and good robustness, in the sliding mode, the H∞ norm and the pole clustering method are investigated. Based on the unit vector control approach, a robust control is developed, then, to direct and maintain the system states onto the sliding manifold in finite time. Finally, the validity of the proposed design strategy is demonstrated through the simulation of the quarter-car suspension system. Copyright © 2014 John Wiley & Sons, Ltd.

Distributed adaptive consensus tracking of a class of networked non‐linear systems with parametric uncertainties

This study investigates a distributed adaptive consensus tracking problem for multiple non-linear strict-feedback systems with parametric uncertainties under a directed communication graph topology. It is assumed that the information of a leader is available for only a limited subset of followers. The distributed adaptive dynamic surface design approach is presented to design the local controller of each follower to guarantee that all networked followers with unmatched parametric uncertainties synchronise to the leader regardless of a lack of the shared information on the communication links. From the Lyapunov stability theorem, it is shown that the consensus tracking errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighbourhood of the origin.

비정합 불확실성을 갖는 시스템을 위한 적분 슬라이딩 모드 제어기 설계

This paper presents an LMI-based method to design an integral sliding mode controller for a class of uncertain systems with unmatched uncertainties. The uncertain system under consideration may have unmatched parameter uncertainties in the state matrix as well as in the input matrix. Using LMIs an existence condition of a sliding surface is derived. And a switching feedback control law is given. Finally, numerical examples are given to show that the proposed method can be better than the existing results for some cases.

Sliding mode control for uncertain neutral system with time‐delays

PurposeThe purpose of this paper is to find an appropriate sliding mode control strategy for neutral systems with time‐delays in the presence of unmatched parameter uncertainties and external disturbance.Design/methodology/approachOwing to the complexity of uncertain neutral time‐delay systems, some conclusions for system stability and stabilization are complicated non‐linear matrix inequality (NLMI). Through virtual state feedback control, a sliding mode controller is designed to guarantee state trajectories from any initial condition are attracted to the sliding mode plane in a finite time and remain there for all subsequent time, which can avoid the complicated NLMI. Furthermore, a delay‐independent sufficient condition for the design of robust stable sliding mode plane is obtained in term of LMI.FindingsThe sliding mode controller for uncertain neutral time‐delay systems is designed and a delay‐independent sufficient condition for the design of robust stable sliding mode plane is obtained.Research limitations/implicationsThe main limitations are that external disturbance must meet matched condition.Practical implicationsA useful control strategy for uncertain neutral systems with time‐delays.Originality/valueThe virtual state feedback control is designed so to avoid the complicated NLMI.

Robust stabilization of input‐delayed systems with design example for rocket motor control

PurposeThis paper aims to use a new design approach based on a Lagrange mean value theorem for the stabilization of multivariable input‐delayed system by linear controller.Design/methodology/approachThe delay‐dependent asymptotical stability conditions are derived by using augmented Lyapunov‐Krasovskii functionals and formulated in terms of conventional Lyapunov matrix equations and some simple matrix inequalities. Proposed design approach is extended to robust stabilization of multi‐variable input‐delayed systems with unmatched parameter uncertainties. The maximum upper bound of delay size is computed by using a simple optimization algorithm.FindingsA liquid monopropellant rocket motor with a pressure feeding system is considered as a numerical design example. Design example shows the effectiveness of the proposed design approach.Research limitations/implicationsThe proposed approach can be used in the analysis and design of the uncertain multivariable time‐delay systems.Originality/valueThe paper has a great potential in the stability analysis of time‐delay systems and design of time‐delay controllers and may openup a new direction in this area.

ITERATIVE LEARNING CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITH PARAMETRIC UNCERTAINTIES

This paper addresses some issues pertinent to Iterative Learning Control (ILC) of a class of nonlinear systems with time-varying parametric uncertainties. The new control strategy combines the backstepping technique with ILC. The Energy-Function-based (EF-based) approach is employed to derive the control algorithm and analyze learning convergence. Rigorous mathematical proof shows that the proposed learning scheme is able to learn from different control targets and guarantee learning convergence for systems with high relative degree and unmatched parametric uncertainties. A numerical example is given to demonstrate the effectiveness of the proposed approach.

マッチング条件を満たさないパラメータ不確定性をもつあるクラスのプラントに対する適応スライディング面に基づいたモデル追従制御

In this paper, for a class of systems which is linear time invariant and single-input and state accessible with unmatched parametric uncertainties, a new model following control based on an adaptive sliding surface is presented. The tracking error converges to zero asymptotically by the proposed controller in the presence of such uncertainties. In addition, even though there are matching disturbances which have unknown upper bounds, finite time reaching to sliding surface can be achieved and then the performance of the system is invariant to matching disturbances on the sliding mode. Simulation results are also presented to show the strength of the presented method.