State Feedback Sliding Mode Control Research Articles

Ensemble of long short-term memory recurrent neural network for semi-active control of tuned liquid wall damper

A critical challenge in structural control is the design of controllers capable of rapid adaptation to uncertainties, including changes in local dynamics and unknown parameters. A solution is the use of data-based controllers, but these typically require pre-training and may be computationally expensive to utilize. In this paper, the authors proposed a fast neuro-controller capable of pure online learning. The controller is built using an ensemble of recurrent neural networks (ERNNs) based on long short-term memory (LSTM) cells running in parallel. A multi-rate sampler is used to sequentially construct the individual RNN input vectors using local measurements at sampling rates pre-determined from the structure’s natural frequencies. Each RNN performs an individual estimation with the associated sampling rate, and these estimations are assembled into an attention and a dense layer to produce an estimated control force. Critical advantages of the proposed architecture are (1) rapid online adaptation and processing; (2) capability to adapt to local dynamics and non-stationarities; and (3) pure online learning architecture minimizing reliance on pre-training. First, the performance of the ERNNs control algorithm is validated on an actively controlled single-degree-of-freedom system, and stability of the controller is demonstrated. Second, the ERNNs is simulated on a full-scale 20-story building equipped with a semi-active tuned liquid wall damper (TLWD) system that consisted of distributed semi-active tuned liquid multiple column dampers. The ERNNs controller effectively improved the passive performance of the control strategy and performed similarly to that of a full state-feedback sliding mode controller under multi-hazard scenario. The evolution of attention weights under both the wind and seismic hazards demonstrated that the importance of each RNN follows the importance of the structural frequency responses, showing that the controller was capable of capturing and adapting fast-changing dynamics.

Adaptive sliding mode consensus control based on neural network for singular fractional order multi-agent systems

In this paper, a suitable state feedback sliding mode controller is designed for the singular fractional order multi-agent systems (SFOMASs) with uncertainty, in order to realize the consensus problem of multi-agent. First, the sliding mode of the designed SFOMAS is in the form of singular systems. The criterion for the admissible consensus of sliding mode is given by using linear matrix inequality (LMI), and an adaptive law based on radial basis function neural network (RBFNN) is established to ensure the accessibility of SFOMASs. Then, a special method is studied to make the sliding mode of the designed SFOMAS normalization. A sufficient condition for the stability and consensus of sliding mode is given by using LMI, and an adaptive law based on RBFNN is established to ensure the accessibility of SFOMAS. Finally, two numerical examples show the applicability of the proposed method.

Partial state feedback sliding mode control for double-pendulum overhead cranes with unknown disturbances

In this paper, a novel sliding mode controller which requires partial state feedback is proposed for double-pendulum overhead cranes subject to unknown payload parameters and unknown external disturbances. Firstly, it is theoretically proved that the hook and payload tend to their respective equilibrium points concurrently. Secondly, a decoupling transformation is performed on the original nonlinear dynamics of double-pendulum overhead cranes. The novel sliding mode controller that does not require the prior information and motion signals of the payload is designed based on the decoupled nonlinear dynamics. Then, the asymptotic stability of the equilibrium point of double-pendulum overhead cranes is proved by rigorous analysis. Finally, several simulations are conducted to validate the effectiveness and robustness of the proposed controller.

Decentralised state feedback stabilisation for nonlinear interconnected systems using sliding mode control*

In this paper, the stabilisation problem is considered for a class of nonlinear interconnected systems with matched uncertainties and mismatched unknown interconnections. A composite sliding surface is designed firstly, and a set of conditions is developed to guarantee that the corresponding sliding motion is uniformly asymptotically stable. Then, decentralised state feedback sliding mode control is proposed to drive the interconnected systems to the designed sliding surface in finite time, and a sliding motion is maintained thereafter. The bounds on the uncertainties and interconnections have more general nonlinear forms, which are employed in the control design to reject the effects of uncertainties and unknown interconnections to enhance the robustness. It is not required either the isolated nominal subsystems linearisable or the interconnections linearisable. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed control strategy.

Decentralised Sliding Mode Control for Nonlinear Interconnected Systems with Unknown Interconnections

Abstract In this paper, a novel decentralised robust state feedback sliding mode control is presented to stabilise a class of nonlinear interconnected systems with matched uncertainty and unknown interconnections. A composite sliding surface is designed, and a set of conditions are developed to guarantee that the corresponding sliding motion is uniformly asymptotically stable. Then, a decentralised state feedback sliding mode control is proposed to drive interconnected systems to the designed sliding surface in finite time, and sliding motion occurs thereafter. The bounds on the uncertainties and interconnections are known nonlinear functions, which are employed in the control design to reject the effects of uncertainties and unknown interconnections to enhance the robustness. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed control strategy.

Event-Triggered Sliding Mode Control of Discrete-Time Markov Jump Systems

This paper studies the problem of event-triggered sliding mode control of discrete-time Markov jump systems (MJSs). Two kinds of classical control schemes, which are observer-based control and state-feedback control schemes, are employed to handle the proposed synthesis problem. The event-triggered observer-based sliding mode controller and event-triggered state-feedback sliding mode controller are established by plunge of discrete-time event detectors into the studied control system, respectively. Moreover, the proposed event-triggered sliding mode controllers can guarantee the MJSs to be stochastically stable with ${H}_{\infty}$ performance, and ensure the finite-time reachability of the specified sliding manifold. Simulation results are provided to illustrate the effectiveness of the proposed theoretical results.

TLBO optimized sliding mode controller for multi-area multi-source nonlinear interconnected AGC system

Abstract This paper represents design of output feedback sliding mode controller (SMC) for multi area multi-source interconnected power system. After designing output feedback SMC, teaching and learning based optimization (TLBO) technique is utilized to optimize feedback gain and switching vector of the controller. The superiority of the proposed approach is shown by comparing the result with output feedback tuned SMC with differential evolution and particle swarm optimization and state feedback SMC tuned with genetic algorithm for a two area thermal interconnected power system. Further, the proposed approach is extended to multi-area multi-source non linear automatic generation control (AGC) system with/without HVDC link. First area consists up thermal, hydro and gas; second area consists up thermal, hydro and nuclear as generating unit. Additionally, the superiority of proposed approach is shown by sensitivity analysis, which is carried out with wide changes in system parameters.

Robust guaranteed-cost sliding control for brushless DC motors by LMI

Two state feedback sliding mode control schemes are developed for position control for brushless DC motor drives. The first controller design achieves the desired swiftness of response. In addition to swiftness, the second controller drastically reduces system’s chattering by adding the guaranteed cost constraint. The proposed controller consists of two parts, linear and non-linear. Linear matrix inequalities (LMIs) optimisation is used to design the linear part that achieves the desired dynamic performance: it is robust against system uncertainties, and is based on a new sufficient condition for the existence problem; the non-linear part is created to guarantee that the sliding surface is attained. System uncertainty due to changes in drive’s load inertia is represented with norm- bounded structure. The main advantages of this technique are that: the LMI algorithm includes an optimal part to preclude high control efforts, and the control burden is heavily placed on the linear part to improve the chattering problem of the conventional sliding mode control.

State feedback sliding mode control without chattering by constructing Hurwitz matrix for AUV movement

This paper presents a new method to eliminate the chattering of state feedback sliding mode control (SMC) law for the mobile control of an autonomous underwater vehicle (AUV) which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.

Robust adaptive sliding mode attitude control and vibration damping of flexible spacecraft subject to unknown disturbance and uncertainty

This paper is concerned with the development of a control system for rotational manoeuvre and vibration suppression of a flexible spacecraft. The design approach presented here treats the problem of spacecraft attitude control separately from the elastic vibration suppression problem. As a stepping stone, a state feedback sliding mode control command is designed to achieve the reference trajectory tracking control of attitude angle. This is followed by the design of an adaptive sliding mode control law using only output for robust stabilization of spacecraft in the presence of parametric uncertainty and external disturbances. Even if this controller has the ability to reject the disturbance and deal with uncertainty, it excites the elastic modes of flexible appendages. The undesirable vibration is then actively suppressed by applying feedback control voltages to the piezoceramic actuators, in which the modal velocity feedback control method is adopted here for determining the control voltages. The effectiveness of the control schemes in handling external disturbance and uncertainty in the system parameters is also studied. Both analytical and numerical results are presented to show the theoretical and practical merit of this hybrid approach.

Sliding Mode State Feedback Control for Uncertain Discrete-Time Markov Jump Systems

AbstractThis paper considers the development of a state feedback sliding mode controller for a class of uncertain discrete-time Markov jump systems. A sufficient condition is provided to guarantee the existence of the discrete-time sliding modes in an LMI form. And a sliding mode controller is designed to make the system states convergent to the designed stochastically stable sliding mode and keep a sliding motion. The controller is designed to tolerate the matched uncertainty, which is considered to be a function of the system states and the control inputs. A numerical example is given to illustrate the proposed method.

Adaptive Sliding Mode Attitude and Vibration Control of Flexible Spacecraft Under Unknown Disturbance and Uncertainty

This paper is concerned with the development of a control system for rotational maneuver and vibration suppression of a flexible spacecraft. It is assumed that the system parameters are unknown. The design approach presented here treats the problem of spacecraft attitude control separately from the elastic vibration suppression problem. As a stepping stone, a state feedback sliding mode control command is designed for the reaction wheel to achieve the reference trajectory tracking control of attitude angle. This is followed by the design of an adaptive sliding mode control (ASMC) law using only the output for robust stabilization of spacecraft in the presence of parametric uncertainty and external disturbances. Although this controller has the ability to reject the disturbance, deal with uncertainty and to ensure that the system output errors asymptotically converge to the sliding mode during the commanded motion, it excites the elastic modes of flexible appendages. The undesirable vibration is actively suppressed by applying feedback control voltages to the piezoceramic actuators, in which the control voltages are determined using the modal velocity feedback control method. Both analytical and numerical results are presented to show the theoretical and practical merits of this hybrid approach

Sliding-mode control design for a complex valued sliding manifold

This paper gives precise conditions for the existence of a state feedback sliding-mode controller to achieve a complex, closed-loop eigenstructure. This structure can be advantageous in providing maximum flexibility in specifying closed-loop dynamics. It is found that the controller is inherently dynamic in general, and recovers standard sliding-mode control results when all real elements are chosen for the switching surface matrix. A control design algorithm is presented, and robustness of the resulting closed-loop system is demonstrated. An illustrative example is provided.

A new algorithm for discrete-time sliding-mode control using fast output sampling feedback

This paper presents a new approach for sliding-mode control (SMC) of discrete-time systems using the reaching law approach together with the fast output sampling (FOS) feedback technique. This method does not need the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement. A numerical example demonstrates the design technique. Simulation results show that the proposed FOS SMC technique produces the same results as obtained by state feedback SMC technique.

State Feedback Sliding Mode Control for SISO Systems with Time-Delay: Controllable single input variable structure systems with and without time-delay are considered

In this paper controllable variable structure systems (VSS) without time delay in canonical form and with time-delay in phase variables and in control law are considered. Synthesis of stable sliding modes is studied by Lyapunov function method and by Lyapunov-Krasovskii functional method. Theorems of asymptotical stability in large motion of systems with and without-time delay are given.

State feedback sliding mode control of a class of uncertain time delay systems

The robust stability of a class of uncertain systems involving internal delays while being regulated by a sliding mode controller (SMC) is studied. The method for designing a SMC is proposed for the generation of a sliding motion in the system. The robustness property and asymptotic stability of the system are discussed and conditions for the design of the switching hyperplane are given. Further generalisation results, which lead to a simple design and implementation, are made for the case when the system is in companion form. A method is proposed for the elimination of limit cycles in systems being regulated by a relay SMC while allowing the generation of sliding motion and thus ensuring the closed-loop asymptotic stability.