Robust Stability Of System Research Articles

Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems

In this study, an adaptive nonsingular terminal sliding mode control technique according to the barrier function is designed for the performance improvement and robust stability of nonlinear systems with outdoor disturbances. For this reason, a novel nonlinear sliding surface is presented based on the states of the system. The nonlinear sliding surface forces the states of the system to converge from initial conditions to zero. Subsequently, a non-singular terminal sliding control scheme is advised for the purpose of finite-time stability of the nonlinear switching surface. Finite-time stabilization of the non-singular terminal sliding surface is verified by the Lyapunov theory. For improvement of the system performance against exterior perturbation, the barrier function adaptive technique is employed to estimate the unknown upper bounds of the exterior disturbance. Finally, the advantage and productivity of the recommended control method is investigated based on the simulation results. In the simulation part, the plasma torch jerk chaotic system is considered as a case study, such that the obtained results are given in different scenarios.

Robust stabilization for affine control systems in Banach spaces

AbstractThis paper is devoted to the investigation of feedback stabilization of affine control systems on real Banach spaces. Under an appropriate decomposition of the state space, we provide sufficient conditions for exponential stabilization of the system at hand. Furthermore, we show that the proposed feedback law remains a stabilizing control under some types of perturbations on the dynamic and the control operator. Finally, two illustrative examples are provided.

High-performance control of fast tool servos with robust disturbance observer and modified [formula omitted] control

Fast tool servo (FTS) is an effective technique for the generation of complicated surfaces in modern precision manufacture industry. In this paper, a novel three-degree-of-freedom (3-DOF) control scheme is proposed for the FTS to achieve good tracking and disturbance rejection performance. Specifically, the 3-DOF control scheme contains a hysteresis compensation term, a modified H∞ feedback control term, a robust disturbance observer (RDOB) term and a feedforward control term. Firstly, a hysteresis compensator is developed based on the modified Prandtl–Ishlinskii (MPI) model to eliminate the intrinsic hysteresis nonlinearity so as to identify the linear dynamic model of the FTS system. A modified mixed-sensitivity-based H∞ feedback control is then proposed to simultaneously provide an excellent damping and tracking performance with a deliberately designed input weighting function. A RDOB is designed for non-minimum phase (NMP) system based on all-pass factorization of the linear dynamics model and the standard H∞ control framework to compensate uncertain external disturbances as well as unmodeled dynamics while guaranteeing the robust stability of closed-loop system. To remove phase delay and enlarge control bandwidth, a closed-loop-inversion feedforward controller is synthesized by integrating a zero-phase error tracking control (ZPETC) with a finite impulse response (FIR) filter. A series of comparative experiments are conducted on a self-developed flux-biased normal-stressed electromagnetic actuated FTS. The experimental results consistently validate the effectiveness and superiority of the proposed scheme in terms of outstanding tracking performance and disturbance rejection.

A P-Q Coordination Based Model Predictive Control for DFIG High-Voltage Ride Through

This paper presents a P-Q coordination based model predictive control (MPC) for doubly fed induction generator (DFIG) to handle high-voltage ride through (HVRT) considering bipolar blocking of high-voltage direct current (HVDC) system. The overvoltage at the point of common coupling (PCC) after DC bipolar blocking and its sensitivity to current injection of DFIG is firstly analyzed based on a typical sending-end AC grid equivalent model. Then, the current feasible region of DFIG operation during overvoltage process is explicitly revealed considering generator and converter constrains. In the proposed HVRT control, a model predictive control (MPC) based method is developed where the minimum voltage tracking error is taken as the main objective function and the constrains are updated every control horizon based on real-time current feasible region. Through the rolling optimization and feedback correction framework, the rotor active and reactive currents of DFIG are coordinated and PCC voltage can be finally controlled to its target value to achieve HVRT. Further, the key MPC parameters are determined by solving an optimal problem to achieve better system robust stability and dynamic performances. Finally, the validity of the proposed control is verified by simulations in MATLAB/Simulink.

Development of a new linearizing controller using Lyapunov stability theory and model reference control

<p><span>One of the most challenging aspects in the nonlinear control of a magnetic levitation (Maglev) system is to find an efficient control algorithm to achieve the stability and accuracy of the closed-loop system. The challenge is then to develop a linearizing control algorithm to maintain a steel ball at a desired position. In this paper, a novel linearizing control algorithm is proposed, which consists of the Lyapunov direct method (LDM) and the model reference control (MRC). The Lyapunov function is developed using the nonlinear equations of the magnetic levitation system, and the reference model is a linear second order system. Two control methods are developed to guarantee system robustness and output stability. Firstly, a new integral linear quadratic regulator (ILQR) is designed for the reference model. Then, an additional innovative proportional gain is combined with the linearizing controller to make the nonlinear control signal stronger. The simulation results indicate that the proposed linearizing controller has excellent set-point tracking, no time delay, fast rising and settling times, and achieves states stability.</span></p>

Barrier function-based adaptive nonsingular sliding mode control of disturbed nonlinear systems: A linear matrix inequality approach

In this study, a novel barrier function-based adaptive non-singular terminal sliding mode control methodology is suggested for robust stability of disturbed nonlinear systems. It is proved that the barrier function-based control method can force the state trajectories to converge to a region near origin in the finite time. A sufficient criterion is derived using Lyapunov stability theorem and linear matrix inequalities (LMIs) to satisfy the asymptotic stability of state trajectories. In addition, the design eliminates the necessity to have any knowledge about the upper bounds of external disturbances; a common requirement in sliding mode control implementation. The stability analysis verifies that the system states, under the designed control scheme, can asymptotically converge to a pre-defined region. Lastly, simulation studies are presented to confirm the efficacy and robustness of proposed approach.

Nonfragile H∞ tracking control strategies for classes of linear and bilinear uncertain Takagi-Sugeno fuzzy systems

This paper presents fuzzy tracking control strategies for classes of linear and bilinear Takagi-Sugeno Fuzzy System with Uncertainties and Disturbances (T-S FSUD). For both classes, the Lyapunov direct approach and the parallel distributed compensation concept are used to design nonfragile H∞ tracking controllers, which ensure the robust asymptotic stability of augmented systems despite the presence of parameter uncertainties, external disturbances, and controllers fragility. Besides that, based on the Schur complement, the separation lemma, and through some variable transformations, sufficient stability conditions of each augmented T-S FSUD are established and formulated in terms of linear matrix inequalities. Finally, numerical simulations are carried out to demonstrate the validity and the applicability of designed control schemes on tracking control of an inverted pendulum and a nonlinear mechanical system.

Study of robust stability of indoor temperature control system

The stages of design and study of the indoor temperature control system have been considered. An assessment of the possibilities of the indoor temperature control of a discrete model of the control system has been carried out. The transfer function of the control object with interval coefficients of the numerator and denominator polynomials taking into account possible ranges of change of the greatest time constant responsible for the enclosing structures has been obtained. The applied graphical method of studying the obtained system has provided an output of the family of root trajectories on a complex plane and visually demonstrated absolute and robust absolute stability of the automatic temperature control system. The simulation carried out in the MATLAB system has confirmed the correctness of the results obtained.

Improved robust stability and stabilisation conditions for discrete-time linear systems with time-varying delay

Improved robust stability and stabilisation conditions for discrete-time linear systems with time-varying delay

Asymptotic Tracking Control on Profiling Posture of Sprayer Boom Systems With Position Uncertainties

An adaptive and robust backstepping method based on wavelet network approximation was proposed to solve the problems of load variation, unmodeled uncertainties, physical parameter perturbation and external disturbance in the sprayer boom profiling system. Firstly, a complete mathematical model for the boom system with uncertainties, unknowns and nonlinear terms was established and transformed into a state space form with strict feedback. Secondly, the designed wavelet primitive was used to construct the neural network, to approximate the virtual equivalent control part of the backstepping method under the condition that the optimal error is bounded. The adaptive update law was selected to estimate the unknown parameters. The robust compensation term was introduced to reduce the adverse effect of the composite interference on the system. The input command signal order requirement was reduced. Finally, suitable functions were constructed by means of the Lyapunov stability theory, to prove that the position tracking error of the closed-loop system asymptotically converges to the origin. The simulation results show that, the proposed control method can realize the rapid maneuver adjustment of the sprayer boom position and posture, and effectively enhance the robust stability and control accuracy of the boom system.

Robust Feedback Stability of Networked Multi-agent Negative Imaginary Systems on Undirected Graph

Robust Feedback Stability of Networked Multi-agent Negative Imaginary Systems on Undirected Graph

Robust stabilization for uncertain saturated systems with multiple time delays

<abstract><p>This paper is concerned with the robust stabilization problem for uncertain saturated linear systems with multiple discrete delays. First of all, a new distributed-delay-dependent polytopic approach is proposed, and a new type of Lyapunov-Krasovskii functional is constructed. Then, by further incorporating some integral inequalities, both stabilization and robust stabilization conditions are proposed in terms of linear matrix inequalities under which the closed-loop systems are asymptotically stable for admissible initial conditions. Finally, a simulation example is given to illustrate the feasibility and advantages of the obtained results.</p></abstract>

Robust Stability Analysis of Time-Varying Delay Systems

The generalized Myshkis problem consists in analysis of robust stability of time-delay system under variation of its parameters within a set in an infinite-dimensional space. In our paper, we consider a linear system, where the delay is a bounded function under an additional restriction on its growth rate. Some sufficient conditions of solvability of the generalized Myshkis problem are expressed in the form of quadratic convex optimization task. The new approach is based on a modification of the Lyapunov-Razumikhin method.

Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control.

This paper is concerned with the robust finite-time stability and stabilization of impulsive systems subject to hybrid disturbances that consists of external disturbances and hybrid impulses with time-varying jump maps. First, the global finite-time stability and local finite-time stability of a scalar impulsive system are ensured by the analysis of cumulative effect of hybrid impulses. Then, asymptotic stabilization and finite-time stabilization of second-order system subject to hybrid disturbances are achieved by linear sliding-mode control and non-singular terminal sliding-mode control. It shows that the stable systems under control are robust to external disturbances and hybrid impulses with non-destabilizing cumulative effect. If the hybrid impulses have destabilizing cumulative effect, the systems are also capable of absorbing the hybrid impulsive disturbances by the designed sliding-mode control strategies. Finally, the effectiveness of theoretical results is verified by numerical simulation and the tracking control of linear motor.

Improved robust stability and stabilisation conditions for discrete-time linear systems with time-varying delay

Improved robust stability and stabilisation conditions for discrete-time linear systems with time-varying delay

LMI conditions for evaluating and increasing stability margins of uncertain continuous-time linear systems

This article investigates the robust stability of uncertain continuous-time linear systems with parameters belonging to intervals. Differently from the techniques available in the literature, the proposed method, formulated in terms of an iterative algorithm based on LMIs, treats the interval bounds as optimization variables and can be used, for instance, to search for the maximum variation around nominal values. Experiments involving the fragility analysis of controllers and volume maximization of the polyhedral region centered on nominal parameters are presented to illustrate possible applications of the proposed technique.

Characterization of PI feedback controller gains for interconnected ODE - hyperbolic PDE systems

In this paper, we give explicit criteria to guarantee the robust stabilization of simple first-order transport systems coupled with finite-dimensional dynamics, using Proportional or Proportional Integral boundary output feedback controllers. Using a frequency-sweeping approach developed for Time-Delay Systems, we characterize the closed-loop stability intervals in the parameter space for several interconnected partial differential equations and ordinary differential equations configurations. The performances of the proposed boundary feedback controllers are compared with other classical approaches in simulation. The proposed methodology is a necessary step before a detailed comparison between proportional integral controllers with low computational complexity and other control approaches for infinite-dimensional systems.

구동기 동역학이 존재하는 잡음감쇠-외란관측기의 안정성

In this paper, we study the robust stability of closed-loop system with noise reduction-disturbance observer (NR-DOB) when the relative degree of plant is greater than that of nominal model. Compared with the case where the relative degree of plant is the same as that of nominal model, it is shown that the nominal model for NR-DOB controller should be carefully chosen in order to achieve the robust stability. Computer simulation results to confirm the proposed condition are also included.

Robust normalization and stabilization of descriptor fractional-order systems with uncertainties in all matrices

This paper focuses on the robust normalization and stabilization problems for descriptor fractional-order systems with norm-bounded uncertainties in all system coefficient matrices, including the state derivative coefficient matrix. The proportional and derivative state feedback control is introduced simultaneously to normalize and stabilize such systems. Novel sufficient conditions for the robust normalization and stabilization of such closed-loop systems are presented. Then, both the proportional feedback gain and the derivative feedback gain are obtained simultaneously by solving linear matrix inequalities. Finally, numerical examples are provided to show that the proposed approach is applicable and less conservative than the existing results.

Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for nth-Order Perturbed Nonlinear Systems

In this study, an adaptive nonsingular finite time control technique based on a barrier function terminal sliding mode controller is proposed for the robust stability of nth-order nonlinear dynamic systems with external disturbances. The barrier function adaptive terminal sliding mode control makes the convergence of tracking errors to a region near zero in the finite time. Moreover, the suggested method does not need the information of upper bounds of perturbations which are commonly applied to the sliding mode control procedure. The Lyapunov stability analysis proves that the errors converge to the determined region. Last of all, simulations and experimental results on a complex new chaotic system with a high Kaplan–Yorke dimension are provided to confirm the efficacy of the planned method. The results demonstrate that the suggested controller has a stronger tracking than the adaptive controller and the results are satisfactory with the application of the controller based on chaotic synchronization on the chaotic system.