Design of saturated controllers for linear singular systems

A designing method is presented to find stabilizing saturated linear controllers for linear continuous time and discrete time singular systems with control constraints. The idea is as follows: The system is first stabilized by a low-gain linear state feedback control. A general Lyapunov function is found, on the basis of which another linear state feedback control is computed. The second step is very similar to a relay control design. The two controls are added and saturated.

Composite disturbance attenuation based saturated control for maintenance of low Earth orbit (LEO) formations

Maintenance of high performance formation control is important for low Earth orbit (LEO) formation missions of small spacecraft.In this paper,a model of nonlinear relative motion dynamics is built,and then nonlinear and important perturbations affecting the formation configuration,such as J 2 and atmospheric drag,are analyzed as disturbances.Global navigation satellite system based relative positioning with nonlinear filtering is adopted to provide state information associated with the perturbations.By combining disturbance observer based control with H ∞ state feedback,a composite disturbance attenuation controller is proposed for maintenance of continuous and accurate formation.With consideration of precise control relying on micro thrusters,a composite disturbance attenuation based saturated controller is designed and its stability is proved.Finally,through numerical simulations,we demonstrate that control accuracy is improved after effectively avoiding perturbations and that stabilization can be satisfied using this method.

Effects of Physical Parameters and Time-Delay Coefficients on the Amplitude and Frequency Bandwidth of Saturation Controller for a Beam Vibration

In this paper, the influence of physical parameters on the width of saturated control frequency band and the influence of time delay parameters on the stability of saturated control system are studied. The analytical solution of the motion equation of the system when the main resonance and the 1:2 internal resonance occur simultaneously is obtained by multiple scale method, experimentally measured natural frequencies of nonlinear beams. The effects of excitation amplitude, delay feedback coefficients and nonlinear coefficients on saturation control are investigated. The results of the study show that the bandwidth of the saturation control can be increased by increasing the value of the external excitation, the nonlinear coefficients enhance the nonlinear phenomena of the system.

H∞ Control for Externally Excited Building Structures with Active Mass Damper under Actuator Saturation

This paper investigates the application of active mass dampers to mitigate the vibrations of building structures subjected to unknown external excitations under controller saturation conditions. By utilizing an H∞ control strategy, the optimal state feedback controller is derived by solving the linear matrix inequality problem for controller saturation. Case studies show that the proposed controller is capable of stabilizing the closed-loop system with good control performance and effectively suppressing vibrations in building structures under unknown external excitation. When compared to controllers that do not consider saturation, the proposed controller requires lower gain and results in reduced energy consumption. The research findings provide valuable insights for addressing real-world building structure control problems, contributing to both theoretical significance and practical applications.

An Improved Fuzzy Predictive Control Algorithm and Its Application to an Industrial CSTR Process

A finite horizon predictive control algorithm, which applies a saturated feedback control law as its local control law, is presented for nonlinear systems with time-delay subject to input constraints. In the algorithm, N free control moves, a saturated local control law and the terminal weighting matrices are solved by a minimization problem based on linear matrix inequality （LMI） constraints online. Compared with the algorithm with a nonsaturated local law, the presented algorithm improves the performances of the closed-loop systems such as feasibility and optimality. This model predictive control （MPC） algorithm is applied to an industrial continuous stirred tank reactor （CSTR） with explicit input constraint. The simulation results demonstrate that the presented algorithm is effective.

Control of switched systems with actuator saturation

This paper is concerned with controller synthesis for linear switched systems with actuator saturation. Based on common Lyapunov function technique and multiple-Lyapunov function technique, two methods for designing state feedback controller are proposed respectively in terms of linear matrix inequalities for the switched systems with saturation. An approach on enlarging the attractive domain is then investigated, The application of the presented approach is illustrated finally by a numerical example.

Development of fractures in soft rock surrounding a roadway and their control

As the excavation of roadway, new fractures will be formed and the pre-existing fractures extend with the redistribution of stress in surrounding rocks. Eventually, fracture zone and bed separation are formed in rocks because of the developed fractures. Therefore, mastering the fracture evolution of surrounding rocks is very important to maintain the stability of roadway. The surrounding rocks of main haulage road- way in a certain coal mine is so broken and loose that the supporting is very difficult. Based on compre- hensive anal[ysis of the engineering geological conditions, a sight instrument was used to observe the fractures of internal surrounding rocks, Four indices, i.e., the width of fracture zone W, the number of fractures n, the width of fractures d and rock fracture designation RFD, are put forward to evaluate the fracture dewelopment. According to the evolution rules of the soft rock roadway from this paper, control principles by stages and by regions are presented through the research. At the same time, the best time of grouting reinforcement is determined on the basis of fracture saturation. Field practice shows that the roadway can satisfy normal production during service periods by suitable first support and grouting reinforcement.

A Suitable Active Control for Suppression the Vibrations of a Cantilever Beam

In our consideration,a comparison between four different types of controllers for suppression the vibrations of the cantilever beam excited by an external force is carried out.Those four types are the linear velocity feedback control,the cubic velocity feedback control,the non-linear saturation controller(NSC)and the positive position feedback(PPF)controller.The suitable type is the PPF controller for suppression the vibrations of the cantilever beam.The approximate solution obtained up to the first approximation by using the multiple scale method.The PPF controller effectiveness is studied on the system.We used frequency-response equations to investigate the stability of a cantilever beam.We notified that,there is a good agreement between the analytical solution and the numerical solution.

Photo-Doped Active Electrically Controlled Terahertz Modulator

We demonstrate an electric-controlled terahertz（THz） modulator which can be used to realize amplitude modulation of terahertz waves with slight photo-doping. The THz pulse transmission was efficiently modulated by electrically controlling the monolayer silicon-based device. The modulation depth reached 100% almost when the applied voltage was 7V at an external laser intensity of 0.6W/cm2. The saturation voltage reduced with the increase of the photo-excited intensity. In a THz continuous wave（CW）system, a significant fall in both THz transmission and reflection was also observed with the increase of applied voltage. This reduction in the THz transmission and reflection was induced by the absorption for electron injection. The results show that a high-efficiency and high modulation depth broadband electric-controlled terahertz modulator in a pure Si structure has been realized.

Anti-saturation fault-tolerant adaptive torsional vibration control with fixed-time prescribed performance for rolling mill main drive system

An anti-saturation fault-tolerant adaptive torsional vibration control method with fixed-time prescribed performance for the rolling mill main drive system(RMMDS)was investigated,which is affected by control input saturation,actuator faults,sensor measurement errors,and parameter perturbations.First,we gave a continuously differentiable saturation function to approximate the control input saturation characteristic of the RMMDS,translating the saturation characteristic into the matched uncertainty and unknown time-varying gain in the system.Then,an RMMDS mathematical model with unmatched uncertainty and unknown time-varying gain was developed,taking into account the presence of control input saturation,actuator faults,sensor measurement errors,and parameter perturbations.Based on the established mathematical model,an error transformation model of the roll speed tracking was constructed by the equivalent error transformation method.According to the error transformation model,a barrier Lyapunov function and a novel adaptive controller were studied to ensure that the roll speed tracking error always evolves inside a fixed-time asymmetric constraint.Finally,numerical simulations were performed in Matlab/Simulink to verify the effectiveness and superiority of the proposed control method in suppressing the RMMDS torsional vibration.

Global stabilizer of a general class of feedback nonlinear systems and its exponential convergence

We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent, Our stabilizer consists of a nested saturation function, which is a nonlinear combination of saturation functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above,

Improving existing"reaching law"for better discrete control of seismically-excited building structures

In this paper,a novel"composite reaching law"was explained in details:1)the equation of discrete motion for a control system;2)the design of discrete-time variable structure control.In addition,the model of a three-storey shear-type building structure was used to verify the effectiveness of the discrete variable structure control method.The results of numerical example analysis of the model show that the control law can effectively reduce the peak value of seismic response of the building structure and the chattering effect of the control system.

Robust attitude coordinated control for spacecraft formation with communication delays

In this paper,attitude coordinated tracking control algorithms for multiple spacecraft formation are investigated with consideration of parametric uncertainties,external disturbances,communication delays and actuator saturation.Initially,a sliding mode delay-dependent attitude coordinated controller is proposed under bounded external disturbances.However,neither inertia uncertainty nor actuator constraint has been taken into account.Then,a robust saturated delaydependent attitude coordinated control law is further derived,where uncertainties and external disturbances are handled by Chebyshev neural networks（CNN）.In addition,command filter technique is introduced to facilitate the backstepping design procedure,through which actuator saturation problem is solved.Thus the spacecraft in the formation are able to track the reference attitude trajectory even in the presence of time-varying communication delays.Rigorous analysis is presented by using Lyapunov-Krasovskii approach to demonstrate the stability of the closed-loop system under both control algorithms.Finally,the numerical examples are carried out to illustrate the efficiency of the theoretical results.

Transient Performance Improvement in Tracking Control for a Class of Nonlinear Systems with Input Saturation

This paper addresses the composite nonlinear feedback（CNF） control for a class of singleinput single-output nonlinear systems with input saturation to track a time varying reference target with good transient performance. The CNF control law consists of a tracking control law and a performance compensator. The tracking control law is designed to drive the output of the system to track the time varying reference target rapidly, while the performance compensator is used to reduce the overshoot caused by the tracking control law. The stability of the closed-loop system is established. The design procedure and the improvement of transient performance of the closed-loop system are illustrated with a numerical example and the controlled Van del Pol oscillator.

H_∞ Inverse Optimal Adaptive Fault-Tolerant Attitude Control for Flexible Spacecraft with Input Saturation

An adaptive inverse optimal attitude controller for flexible spacecraft with fault-free actuator is designed based on adaptive control Lyapunov function and inverse optimal methodology subjected to unknown parameter uncertainties,external disturbances and input saturation.The partial loss of actuator effectiveness and the additive faults are considered simultaneously to deal with actuator faults,and the prior knowledge of bounds on the effectiveness factors of the actuators is assumed to be unknown.A fault-tolerant control version is designed to handle the system with actuator fault by introducing a parameter update law to estimate the lower bound of the partial loss of actuator effectiveness faults.The proposed fault-tolerant attitude controller ensures robustness and stabilization,and it achieves H_∞ optimality with respect to a family of cost functionals.The usefulness of the proposed algorithms is assessed and compared with the conventional approaches through numerical simulations.

Robust Semi-Global Leaderless Consensus and Containment Control of Identical Linear Systems with Imperfect Actuators

This paper investigates both the robust semi-global leaderless consensus problem and the robust semi-global containment control problem for a group of identical linear systems with imperfect actuators. The imperfect actuators are characterized by nonlinearities such as saturation and dead zone and there input output relationships are not precisely known. The dynamics of follower agents are also affected by the input additive disturbances. Low-and-high gain feedback consensus protocols are constructed to solve these problems. More specifically, it is shown that robust semi-global leaderless consensus can be achieved over a connected undirected graph and robust semi-global containment control can be achieved when each follower agent has access to the information of at least one leader agent. Numerical simulation illustrates the theoretical results.

New stabilization design for planar vertical take-off and landing aircrafts

This paper presents a new stabilizing control law for a planar vertical take-off and landing aircraft.The model is first transformed into an equivalent form,and then a control law consisting of a linear term and a saturated term is given for a related subsystem,with the saturation levels being assigned as large as possible.Compared to the existing saturation scheme in which all states are restricted by saturations,the design brings about a relatively fast convergence.The effectiveness and advantage of the design are validated by numerical simulations.