Control Of Time-delay Systems Research Articles

Dynamic impact analysis of the time-delay levitation control system on maglev vehicle system after adding smith predictor

The time delay (TD) in the levitation control system significantly affects the dynamic performance of the closed-loop system in electromagnetic suspension (EMS) maglev vehicles. Excessive TD can cause levitation instability, making it essential to explore effective mitigation methods. To address this issue, a Smith Predictor (SP) is integrated into the traditional PID levitation control system. The combination of theoretical analysis and numerical simulation is employed to assess the stability of the time-delay levitation control system after the integration of the Smith Predictor. Theoretical analysis reveals that when TD exceeds a critical threshold, the levitation system becomes unstable. The addition of SP alters the root trajectory of the system characteristic equation from positive to negative, and recovers the levitation system to stable status. Assuming complete knowledge of the dynamic system, the TD compensation value in the SP becomes a key parameter that determines its performance. A minimum effective value (MEV) for TD compensation is identified, correlating with the system's stability region. Under the influence of TD, more complex systems and higher running speeds of the maglev vehicle lead to a narrower stable region and a larger MEV for TD compensation. Given the simulation parameters in this paper, with a system TD of 15 ms and a maximum vehicle speed of 160 km/h, the MEV for TD compensation in the SP should be set at 12 ms.

Disturbance rejection analysis of singular time-delay systems based on state decomposition method

The state decomposition technique (SDT) based on memory state-feedback control (MSFC) is used in this article to provide a new disturbance-rejection (DR) method for singular time-delay systems (STSs). First, under MSFC, a singular time-delay control system with disturbance estimator is constructed. Then, a DR control law, which contains disturbance information and MSFC, is designed. Second, the STS is split into algebraic and differential subsystems based on the SDT. Next, a brand-new enhanced Lyapunov–Krasovskii function (LKF) with fewer state vectors is designed. Additionally, a new delay-dependent admissible criterion with fewer decision variables is obtained based on the LKF by combining a Jensen inequality and two zero equations. Third, the controller is designed according to the decomposition component of the controller gain. Finally, the usefulness and efficiency of the strategy are demonstrated by comparing it to a sliding mode control and a traditional control technique.

Secondary resonance of a cantilever beam with concentrated mass under time delay feedback control

The present work discusses the strongly nonlinear dynamical characteristics of the secondary resonance in a cantilever beam system with concentrated mass regulated through displacement and velocity time delay. Through the homotopy analysis method, the potential superharmonic and subharmonic resonance issues are resolved. A detailed analysis is conducted to investigate the influences of the time delay, feedback gain coefficient, excitation amplitude, and damping coefficient on the nonlinear response. The results show that the system exhibits hardening behavior for superharmonic resonance with one or two peaks and softening behavior for subharmonic resonance. In time delay control systems, increasing the damping coefficient occasionally causes an increase in amplitude. Due to the complexity of the system, it is challenging to definitively determine whether displacement or velocity time delay control is more suitable. Only when specific working conditions are given can it be compared which way is better. Prudently choosing the velocity and displacement time delay factors can restrain the amplitude of the system, adjust the response region, jump frequency and the number of solutions. The findings of this paper are thought to be useful in the design of time delay feedback controllers.

Robust predictive regulation of uncertain time-delay control systems with non-zero references and disturbances

Robust regulation is predictively investigated in time-delay models including uncertainties, non-zero reference, and disturbance. Hence, to handle the complexities induced because of the time-delays, disturbances, and uncertainties, enhancing the transient performance would be a main control goal. To this purpose, the required transient and steady-state specifications are achieved through an integral control structure with adjustable gains. The constraints on the signals and aims of the control algorithm are also described by some linear matrix inequalities. Guaranteeing the stability, a minimisation procedure is found to specify the predictive controller. Several simulations are performed to establish the effectiveness of the introduced plan in comparison with the similar strategy.

Boosted Incremental Nonlinear Dynamic Inversion for Flexible Airplane Gust Load Alleviation

Active gust load alleviation is an important technology for reducing loads on future commercial airplanes so that the structure can be designed to be lighter in order to save fuel. For the intense reduction of gust loads, a highly reactive control system of sensors, control algorithms, and actuators is required, which is not yet available. In this paper, a control algorithm based on incremental nonlinear dynamic inversion is extended so that actuators respond faster. The control algorithm is applied to a future medium-range aircraft with distributed trailing-edge flaps. It is assumed that the vertical acceleration of the center of gravity and the displacement, velocity, and acceleration of the first wing bending mode are available as feedback variables. To allow comparability with other actuator and sensor setups, the authors abstract the actuator dynamics and sensor filter as control system time delay. The feedback gains are adjusted automatically to the control system time delay. In simulation, the authors investigate the influence of the control system time delay on the peak gust loads. They show that gust loads can indeed be intensely reduced with sufficiently small control system time delay in simulation.

Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

Vibration control of an eleven-story structure with MR and TMD dampers using MAC predictive control, considering nonlinear behavior and time delay in the control system

In the last two decades, model predictive control has made significant progress in research and industrial process control. This achievement is through the high ability of model predictive control to solve industrial process control problems in the time domain. It is applicable in many control systems, such as delayed systems, univariate and multivariable systems, non-minimum phase systems, and unstable systems. This strategy is essentially for controlling delayed systems. It is possible to create a time delay in transmitting structure movement data in the systems that use sensors and receivers of sensor-recorded data, which is a factor to reduce the efficiency of the control system and even the instability of the structure. In this study, to investigate and compensate the effect of time delay in the hybrid vibration control system, an 11-story structure with a tuned mass damper and an MR damper was used by model algorithmic control (MAC) and nonlinear behavior of the structure in the control process. The linear and nonlinear structural models are created in OpenSEES, the control system in MATLAB; and the TCP/IP connection method was used to connect two programs. The fuzzy decision system is based on accelerating and decelerating movement. The structure has been subjected to seven earthquakes with maximum accelerations of 0.1 g to 1.0 g with an incremental step of 0.1 g. According to the results of incremental dynamic analysis, the average percentage of the fuzzy control system performance reduction, considering the time delay, is 15.28% and 38.57% for the maximum displacement and base shear in the linear structure, and 8.04% and 5.97% for the nonlinear structure, respectively. The assumed time delays have been effectively overcome using the model algorithmic control system (MAC), determining the prediction horizon of the structural behavior, and optimizing the control force in the control horizon. The performance of the MAC control system has been better than the fuzzy control system and the passive control with TMD. The average improvement percentage of the results of the maximum linear and nonlinear structural displacement response is respectively equal to 10.2 and 11.8 with the MAC control system, compared to the fuzzy control system without time delay. For the maximum base shear, it is equal to 8.32 and 2.49, respectively.

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result.

PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS

This study focuses on designing PI controllers for time-delay systems using various model order reduction techniques to reduce complexity. The stability boundary locus method was used to determine PI parameters that stabilizing reduced order models. After the PI parameters have been determined using the weighted geometric center method, the calculated controller parameters have been implemented in the original system. In this way, the efficiency of the controller design is effectively demonstrated through the reduction techniques. In addition, the study investigated the effectiveness of reduction methods with increasing time delay and adding an integrator to the system. The importance of these results is that they demonstrate the use of model order reduction techniques in the design of controllers for time-delay systems and reveal the advantages of these methods.

Active Disturbance Rejection Fractional-Order Independent Control of Time Delay Systems With Application to Air Floating Motion Platform

Active Disturbance Rejection Fractional-Order Independent Control of Time Delay Systems With Application to Air Floating Motion Platform

Absolute stability of time-delayed Lurie direct control systems with unbounded coefficients

Absolute stability of time-delayed Lurie direct control systems with unbounded coefficients

Mechanism of time-delay feedback control of suspension damping with an annular vibration-absorbing structure

With the aim of enhancing both the ride comfort and the safety of the vehicle, we propose a new type of suspension with an annular vibration-absorbing structure, and establish a 3-DOF 1/4 vehicle model. The structure parameters and time-delay feedback control parameters are determined by particle swarm optimization algorithms, which take the root mean values of body acceleration, suspension dynamic deflection, and tire dynamic displacement as their optimization objectives. We analyze the stability of the suspension control system to ensure the stability of the time-delay control system through the Routh-Hurwitz stability criterion, characteristic root method, and stability switching method. Then, we compare and analyze the response characteristics of conventional suspension, new suspension without time-delay feedback control, and new suspension with time-delay feedback control under simple harmonic excitation and random excitation. The results show that the new suspension with time-delay feedback control has a significant damping effect on the body under the premise of ensuring the stability of the system.

ADRC for a piezoelectric plate with delays and disturbances via frequency response method: Design, analysis and experiments

A large number of uncertainties such as external excitement, model parameter perturbation, complex boundary conditions, time delays, seriously impact the operation of the piezoelectric plate structure. Therefore, an active disturbance rejection controller is designed and implemented based on an extended state observer to address such issues. The controller designed is analyzed in frequency-domain to address the time delays introduced by the sensors, actuators, communicational networks, computational delays, etc. Knowing that the accurate models are difficult to build, the Lissajous graphics and frequency test methods, hence, are implemented to estimate the delay and model parameters of the system. The stability characteristics and performance are verified via two intuitive frequency response methods, the small gain theorem and the Nyquist diagram. Bedsides, the relationship between time delays and control parameters is quantified, which enables controller parameters to be adjusted according to frequency index. This is the first attempt to use the small-gain theorem, which is favored for its numerical precision and computational efficiency, to analyze the active disturbance rejection control of time-delay systems. A case of a disturbed all-clamped piezoelectric plate with delays is, in particular, tested under a hardware-in-the-loop benchmark. Theoretical and experimental results show the effectiveness of the proposed approach to suppress the structure vibration in the presence of delays and disturbances.

Retracted: Application Research of Time Delay System Control in Mobile Sensor Networks Based on Deep Reinforcement Learning

Retracted: Application Research of Time Delay System Control in Mobile Sensor Networks Based on Deep Reinforcement Learning

Event-triggered [formula omitted]-gain control for networked systems with time-varying delays and round-robin communication protocol

This paper studies the event-triggered (ET) L2-gain control issues for time-delay networked control systems (NCSs) subject to round-robin protocol. The considered NCS consists of n sensor nodes, where the communication from the sensors to the controller is scheduled by round-robin protocol. This protocol requires that, at every sampling instant, only one sensor is chosen to use the sensor/controller network and transmits its measurement information toward the controller. On the other hand, the ET strategy is adopted in the controller/actuator network, which means that the actuator will receive the updated control input signal in the situation that the predefined ET conditions are satisfied. The utilization of round-robin protocol and ET strategy will help to relieve the burden of network transmission. The network resources and bandwidth will be saved. By developing appropriate Lyapunov functional, sufficient conditions in matrix inequalities are established in order to achieve the stability and L2-gain of the studied systems. Then, a novel iterative algorithm is presented to solve the derived stability conditions so as to design the controllers and obtain the minimal L2-gain simultaneously. Two examples are executed at last to demonstrate the validness and benefits of our results.

Lyapunov-based robust optimal control for time-delay systems with application in milling process

In this paper, we propose an optimal delay-independent robust controller based on the Lyapunov–Krakovskii theorem for the milling process as a time-delay system in the presence of varying axial depth of cut and different parametric uncertainty, such as stiffness, damping, etc. Milling is widely used in the manufacturing processes for the production of complex-shaped workpieces with high accuracy. However, chatter is a self-excited vibration that may cause adverse effects, such as tool damage, poor surface quality, excessive noise, etc. The dynamic model of the milling process is considered a two-dimensional time-delay system. A nonlinear programming with linear matrix inequality constraints is solved in order to obtain the controller gain where the objective function is corresponding to the norm-2 of controller gain, and the constraints guarantee robust stability. Using the semi-discretization method, stability lobes are shown in both uncontrolled and controlled plants to illustrate the improvement of the stable region via the proposed controller. Bifurcation phenomena have been improved with this controller by postponing the adverse effects to the higher values of the axial depth of cut, reducing the amplitude of limit cycles, and changing the type of bifurcation. Finally, we will compare the proposed controller with an intelligent controller in order to show the efficiency of the proposed method. It is shown that the proposed controller has improved the integral absolute error index by about 3.65 times compared with the intelligent controller.

Control of time-delay systems through modified Smith predictor using sliding mode controller

Smith-Predictor (SP) is used as a dead-time compensating tool for chemical processes as they are Integrating-Plus-Dead-Time (IPDT), pure integrating-type process, and higher-order-integrating-process. The performances of these processes can be improved by modifying SP. The present work deals with the control of dead-time by integrating the first-order-plus-dead-time (IFOPDT) or first-order-plus-dead-time process (FOPDT), and a modified sliding-mode-controller (SMC) in the proposed modified-Smith-predictor (MSP) structure. Here, a modified novel SMC discontinuous tuning-parameter is derived analytically to satisfy performance criteria such as speed adjustment, reducing overshoot and chattering effects. Furthermore, the MSP-SMC structure is implemented in six different processes. This is done to counteract time-delay and constant load-disturbance for integrating processes and a nonlinear system separately. Also, the proposed work is implemented in the real-time lab setup of a neutralisation process. Furthermore, the robustness and invariance properties of the SMC have been analysed against parametric uncertainty. The optimality of the proposed controller parameters is tested by giving uncertainty in the dead time of the process parameters. The proposed design is also implemented in the non-linear and Multi-Input-Multi-Output processes. The performance metrics, IAEs, of 6 case studies have been obtained using MATLAB and the peak overshoots are compared with similar kinds of works.

Delay Compensation of Neutral-Type Time-Delay Control Systems by Cascaded-Observers

Delay Compensation of Neutral-Type Time-Delay Control Systems by Cascaded-Observers

Control barrier functionals: Safety‐critical control for time delay systems

AbstarctThis work presents a theoretical framework for the safety‐critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay‐free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.

Design and analysis of active disturbance rejection control for time-delay systems using frequency-sweeping

For the typical first-order systems with time-delay, this paper explors the control capability of linear active disturbance rejection control (LADRC). Firstly, the critical time-delay of LADRC is analyzed using the frequency-sweeping method and the Routh criterion, and the stable time-delay interval starting from zero is accurately obtained, which reveals the limitations of general LADRC on large time-delay. Then in view of the large time-delay, an LADRC controller is developed and verified to be effective, along with the robustness analysis. Finally, numerical simulations show the accuracy of critical time-delay, and demonstrate the effectiveness and robustness of the proposed controller compared with other modified LADRCs.