Finite-time Mode Research Articles

Quantumness and thermodynamic uncertainty relation of the finite-time Otto cycle.

To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate exactly the mean values and relative error of thermodynamic quantities. In the quasistatic limit, quantumness reduces the productivity and precision of the Otto cycle compared to that in the absence of quantumness, whereas in the finite-time mode, it can increase the cycle's productivity and precision. Interestingly, as the strength (heat conductance) between the system and the bath increases, the precision of the quantum Otto cycle overtakes that of the classical one. Testing the conventional TUR of the Otto cycle, in the region where the entropy production is large enough, we find a tighter bound than that of the conventional TUR. However, in the finite-time mode, both quantum and classical Otto cycles violate the conventional TUR in the region where the entropy production is small. This implies that another modified TUR is required to cover the finite-time Otto cycle. Finally, we discuss the possible origin of this violation in terms of the uncertainty products of the thermodynamic quantities and the relative error near resonance conditions.

Efficiency of a Quantum Otto Heat Engine Operating under a Reservoir at Effective Negative Temperatures.

We perform an experiment in which a quantum heat engine works under two reservoirs, one at a positive spin temperature and the other at an effective negative spin temperature, i.e., when the spin system presents population inversion. We show that the efficiency of this engine can be greater than that when both reservoirs are at positive temperatures. We also demonstrate the counterintuitive result that the Otto efficiency can be beaten only when the quantum engine is operating in the finite-time mode.

Adaptive Fault-Tolerant Spacecraft Pose Tracking With Control Allocation

The concurrent position and attitude (pose) tracking of a rigid spacecraft is addressed in the presence of actuator faults, mass and inertia uncertainties, and unknown external disturbances. The control design relies on a novel hybrid dual-quaternion integral sliding mode that incorporates a hysteretic switching to avoid the quaternion unwinding problem. On the sliding mode, the pose tracking error is globally finite-time convergent. The resultant control law has a simple structure and consists of a nominal control input, which realizes the sliding mode in the fault-free uncertainty-free case, and an adaptive part, which dynamically compensates for the perturbations due to actuator faults and other uncertainties. Moreover, a real-time control allocation algorithm is devised to deliver the control command to position and attitude actuators in proportion to the effectiveness degree of each actuator. Rigorous proof shows that the proposed strategies can stabilize the spacecraft pose trajectory to a small neighborhood of the sliding mode in finite time. Formation flying of earth-orbiting spacecraft and asteroid body-fixed hovering are simulated to demonstrate the efficacy and broad applicability of the proposed method.

Extended state observer-based finite-time guidance laws on account of thruster dynamics

Guidance laws are designed for a near space interceptor with line-of-sight angle as input and on–off type thrust as output. The dynamics of thruster is viewed as a first-order lag with on–off working style and is integrated with the target–interceptor engagement dynamics to design bang-bang type sliding mode guidance laws. An extended state observer is designed to estimate the line-of-sight angular rate and the acceleration of target with the line-of-sight angle as a measurement. It is rigorously proved that the states of guidance system converge to a neighborhood of sliding mode in finite time and the line-of-sight angular rate converges to a neighborhood of the origin along the sliding mode in finite time under the designed guidance laws. Furthermore, in order to reduce the switching frequency of thruster, a sliding mode guidance law with hysteresis-band according to the sufficient condition for finite time convergence is proposed. Then, it is integrated with the bang-bang type sliding mode guidance law to yield a composite guidance law. Simulation results show that the extended state observer can effectively estimate the line-of-sight angular rate and the target acceleration, and the proposed sliding mode guidance laws have better performance than typical proportional guidance law.

Continuous adaptive-gain finite-time control for rigid body attitude dynamics on SO(3)

ABSTRACTIn this paper, the attitude tracking problem for the rigid body with model uncertainties and external disturbances is investigated in a coordinate-free way. A continuous adaptive-gain second-order sliding mode controller is designed to ensure the establishment of a real second-order sliding mode in finite time, and then the predefined nonsingular fast sliding surface further implies finite-time stability of the attitude error vector and the angular velocity error vector. The key feature of the proposed controller is that it does not require the knowledge of the boundary of the disturbance gradient. A rigorous mathematical proof for the stability of the control system is derived by using the Lyapunov function technique. Finally, simulation comparisons illustrate the effectiveness and robustness of the controller.

A novel continuous fractional sliding mode control

ABSTRACTA new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.

Robust finite time control algorithm for satellite attitude control

Finite time controllers robust to inertia matrix uncertainty for satellite attitude stabilization control and attitude tracking control are developed in this paper. A three-stage finite sliding mode is constructed to improve system convergence rate. The singularity issue is solved by using the property of Euler Axis when it's paralleled to angular velocity. Based on this finite time sliding mode, finite time controller is developed to ensure the system state could reach the sliding mode in finite time. System inertia matrix uncertainty and disturbance torque is considered in this paper. The control torque constraint is also considered to ensure the norm of control torque does not exceed system upper bound. Finite time stability of the controller is proved and the controller performance is demonstrated by simulation results.

Impact Time Guidance Law Considering Autopilot Dynamics Based on Variable Coefficients Strategy for Maneuvering Target

This paper investigates the terminal guidance problem for the missile intercepting a maneuvering target with impact time constraint. An impact time guidance law based on finite time convergence control theory is developed regarding the target motion as an unknown disturbance. To further improve the performance of the guidance law, an autopilot dynamics which is considered as a first-order lag is taken into consideration. In the proposed method, the coefficients change with the relative distance between missile and target. This variable coefficient strategy ensures that the missile impacts the target at the desired time with little final miss distance. Then it is proved that states of the guidance system converge to sliding mode in finite time under the proposed guidance law. Numerical simulations are presented to demonstrate the effectiveness of the impact time guidance law with autopilot dynamics (ITGAD).

Impact of discontinuous harvesting on fishery dynamics in a stock-effort fishing model

We consider a stock-effort fishing model with discontinuous harvesting strategies. Under some reasonable assumptions on the discontinuous harvesting function, we are able to confirm the well-posedness of the model, describe the structure of possible equilibria as well as establish the stability/instability of the equilibria. Most interestingly, we find that the solutions of the fishing model can arrive at a sliding mode in finite time. A qualitative analysis shows that the goal of maintaining the system at a sustainable equilibrium and optimizing the harvesting can be achieved by introducing the discontinuous harvesting strategies. From the viewpoint of optimal harvesting, we can obtain that discontinuous harvesting strategies are superior to continuous harvesting strategies, which are usually adopted in previous literature. The main difficulty resides in the discontinuity of the model, and is conquered by exploiting the theory of differential equations with discontinuous righthand sides and variable structure system theory.

Adaptive terminal sliding mode control for nonlinear differential inclusion systems with disturbance

This paper deals with the adaptive terminal sliding mode control for nonlinear differential inclusion systems subjected to disturbance. The upper bound of the disturbance is unknown. First, the fast terminal sliding mode surface is established and sufficient condition for fast convergence is given. Then the adaptive sliding mode controller is designed to make the state of system arrive at the sliding mode in finite time. A numerical example is provided to show the effectiveness of the proposed method.

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchronization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master's and the slave's system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

Adaptive Variable Structure Control for Uncertain Linear Time-Invariant Delay Singular Systems

This paper discusses the control problems of singular linear time-invariant delay systems with uncertainties. A new adaptive variable structure control strategy is given by Lyapunov stability theory. The invariance of sliding mode is proved in the circumstances of the external disturbance and parameter perturbation with matching conditions. Through memory and memoryless of the linear state feedback, the control strategy ensure that system reaches sliding mode in finite time and the closed-loop system is global asymptotic stable. Simulation results further show that the strategy is feasible and effective.

New methodologies for adaptive sliding mode control

This article proposes new methodologies for the design of adaptive sliding mode control. The goal is to obtain a robust sliding mode adaptive-gain control law with respect to uncertainties and perturbations without the knowledge of uncertainties/perturbations bound (only the boundness feature is known). The proposed approaches consist in having a dynamical adaptive control gain that establishes a sliding mode in finite time. Gain dynamics also ensures that there is no overestimation of the gain with respect to the real a priori unknown value of uncertainties. The efficacy of both proposed algorithms is confirmed on a tutorial example and while controlling an electropneumatic actuator.

Robust synchronization of drive–response chaotic systems via adaptive sliding mode control

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.

Design of sliding mode controllers with bounded L 2 gain performance: an LMI approach

This paper is devoted to the design of robust controllers for sliding mode control systems. A linear fractional transformation (LFT) framework is adopted to describe the systems subject to model uncertainties and external disturbances. A linear matrix inequality (LMI) technique is then developed into the design of both sliding mode and reaching phase control laws. It is shown that by solving a set of LMIs, the switching surface can be designed such that the dynamics in the sliding mode achieve robust stability and bounded L 2 gain performance with respect to matched and unmatched uncertainties in the presence of disturbances. Furthermore, a reaching phase control law is presented to eliminate the undesirable chattering effect and maintain the robustness property all the time whether the system evolves into its sliding mode in finite time or not. Finally, an observer based control law is also developed to achieve the robust performance during the reaching phase. The results are illustrated by an example.

Robust control for nonlinear time-varying systems with application to a robotic manipulator

Sliding mode control methods have been used widely because they provide robustness against parameter variations and disturbances. This paper focuses on the problem of a robust output-sliding control design for a class of nonlinear time-varying systems. Output signals are used for the switching function definition. The control law formulation is emphasized. Input and output linearization is used. Output tracking can be achieved against a class of time-varying parameter variations and external disturbances. An application to a two-degree-of-freedom manipulator indicates that the proposed switching control law drives the system state trajectories onto the chosen sliding mode in finite time and the output tracking is guaranteed.

Variable Structure Control of Robot Manipulators with Perturbation Estimator

The idea of perturbation compensation is incorporated in variable structure control (VSC) of robot manipulators to cancel the effects of system parametric uncertainties and external disturbances and hence alleviate control chattering. By using the dynamic response of the robot as characterized by the sliding function, a technique is proposed to deduce the system perturbation signal. For practical implementation, a perturbation estimator is introduced to approximate the system uncertainties. Estimates of the bounds on modelling errors and external disturbances are not required while signal measurement uncertainties can be accommodated. The suggested VSC law ensures that the robot control system reaches the sliding mode in finite time and with prescribed transient behaviour. Detailed computer simulation results are presented to demonstrate the effectiveness of this new approach.

Robust Control of a Manufacturing Facility with Uncertain Processing Rates

A procedure is presented for designing a real-time controller that, despite imprecise knowledge of the processing rates of a multi-part-type manufacturing facility, will achieve a desired cyclical operation mode and will return the facility to this operating mode in finite time when isolated disturbances occur. To achieve finite-time disturbance correction, while compensating for the uncertainty in processing rates, the controller uses a switching strategy to specify the processing times and idling intervals for each part-type, and to dynamically allocate the raw material input rate.