Time Delay Uncertainties Research Articles

Error-Tracking Iterative Learning Control for Nonlinearly Parametric Time-Delay Systems With Initial State Errors

In this paper, an error-tracking iterative learning control scheme is proposed for a class of nonlinearly parametric time-delay systems with initial state errors. The iterative learning controller is developed by Lyapunov approach. With a desired error trajectory constructed according to the given method, the robust control and learning control are synthetically applied to compensate for nonlinearly parametric time-delay uncertainties. While the closed-loop system operates, as iteration number increases, the controller can make system error perfectly follow its desired error trajectory over the entire time interval, by which, the system state can precisely track its reference signal in the pre-specified part of above-mentioned interval. Numerical results demonstrate the effectiveness of the proposed error-tracking learning control scheme.

On the Model-Free Compensation of Coulomb Friction in the Absence of the Velocity Measurement

This paper demonstrates that the Coulomb friction, the most difficult part of friction to be compensated because of its discontinuity with respect to the velocity, can be precisely compensated without either its mathematical model or a velocity measurement, as commonly required in the literature. Instead, the necessary information needed in the friction compensation is obtained in real time from an implicit extended observer in the context of a common proportional-derivative motion control system, using the proposed linear reference compensation scheme. The robustness of this particular observer design to the time-delay uncertainty resulting from the model reduction is thoroughly investigated, which illustrates the extent to which a high bandwidth can be employed to achieve the favorable dynamic performance such that the limitation on the bandwidth of the original extended state observer (ESO) can be effectively eliminated. Finally, numerical examples are provided to validate the proposed method.

Crash testing difference-smoothing algorithm on a large sample of simulated light curves from TDC1

In this work, we propose refinements to the difference-smoothing algorithm for measurement of time delay from the light curves of the images of a gravitationally lensed quasar. The refinements mainly consist of a more pragmatic approach to choose the smoothing time-scale free parameter, generation of more realistic synthetic light curves for estimation of time delay uncertainty and using a plot of normalized $\chi^2$ computed over a wide range of trial time delay values to assess the reliability of a measured time delay and also for identifying instances of catastrophic failure. We rigorously tested the difference-smoothing algorithm on a large sample of more than thousand pairs of simulated light curves having known true time delays between them from the two most difficult `rungs' -- rung3 and rung4 -- of the first edition of Strong Lens Time Delay Challenge (TDC1) and found an inherent tendency of the algorithm to measure the magnitude of time delay to be higher than the true value of time delay. However, we find that this systematic bias is eliminated by applying a correction to each measured time delay according to the magnitude and sign of the systematic error inferred by applying the time delay estimator on synthetic light curves simulating the measured time delay. Following these refinements, the TDC performance metrics for the difference-smoothing algorithm are found to be competitive with those of the best performing submissions of TDC1 for both the tested `rungs'. The MATLAB codes used in this work and the detailed results are made publicly available at https://github.com/rathnakumars/difference-smoothing

Adaptive Output Feedback Control of Nonlinear Time-Delay Systems With Application to Chemical Reactor Systems

This paper considers the problem of global adaptive stabilization for strict feedback nonlinear systems with time delay and parameter uncertainty. By designing a delay-independent reduced-order observer with two dynamic gains, we propose a universal adaptive control strategy to reduce the conservatism of the growth conditions imposed on nonlinearities. With the help of Lyapunov–Krasovskii functionals, stability analysis is subtly conducted. Finally, the proposed controller is applied to a chemical reactor system to illustrate the usefulness of our results.

Robust multi-objective optimal switching control arising in 1,3-propanediol microbial fed-batch process

This paper considers optimal control of glycerol producing 1,3-propanediol (1,3-PD) via microbial fed-batch fermentation. The fed-batch process is formulated as a nonlinear switched time-delay system. In general, the time-delay in the fed-batch process cannot be exactly estimated. Our goal is to design an optimal switching control scheme to simultaneously maximize 1,3-PD productivity and 1,3-PD yield under time-delay uncertainty. Accordingly, we propose a robust multi-objective optimal switching control model, in which two objectives, i.e., 1,3-PD productivity and 1,3-PD yield, and their sensitivities with respect to uncertain time-delay are considered in the objective vector. The control variables in this problem are the feeding rate of glycerol, the switching instants and the terminal time of the process. By introducing an auxiliary dynamic system to calculate the objective sensitivities and performing a time-scaling transformation, we obtain an equivalent multi-objective optimal switching control problem in standard form. We then convert the equivalent multi-objective optimal control problem into a sequence of single-objective optimal switching control problems by using a modified normal boundary intersection method. A novel gradient-based single-objective solver combining control parameterization with constraint transcription technique is developed to solve these resulting single-objective optimal control problems. Finally, numerical results are provided to verify the effectiveness of the proposed solution approach.

Stability analysis of virtual passive actuator with time delay and parameter uncertainties

The purpose of this paper is to present a virtual passive actuator which enables the manipulator joint to behave as a desired spring-damper system. When the manipulator interacts with an unknown environment or human operator, huge contact force will be generated with a high-stiffness trajectory tracking controller: to avoid violent collisions, the virtual passive actuator is proposed to diminish the interaction force, and adjust the system stiffness to adapt to the environment. With the mathematical model of the virtual passive actuator, the system’s stable region is determined based on the Routh–Hurwitz criterion. The influence of operation time delay, filter and model uncertainty is taken into consideration. Finally, the virtual passive actuator is incorporated into a manipulator, and validity is verified through a set of experiments. Experiment results show that, with the proposed controller, virtual passive actuator joint deformation is proportional to the external torque, and the proportional ratio is close to the stiffness setting: it can perform dynamic behavior just like a spring-damper system when subject to step external torque.

Parameter Identification and Control Scheme for Monitoring Automatic Thickness Control System with Measurement Delay

The thickness of the steel strip is an important indicator of the overall strip quality. Deviations in thickness are primarily controlled using the automatic gauge control (AGC) system of each rolling stand. At the last stand, the monitoring AGC system is usually used, where the deviations in thickness can be directly measured by the X-ray thickness gauge device and used as the input to the AGC system. However, due to the physical distance between the thickness detection device and the rolling stand, time delay is unavoidably present in the thickness control loop, which can affect control performance and lead to system oscillations. Furthermore, the parameters of the system can change due to perturbations from external disturbances. Therefore, this paper proposes an identification and control scheme for monitoring AGC system that can handle time delay and parameter uncertainty. The cross-correlation function is used to estimate the time delay of the system, while the system parameters are identified using a recursive least squares method. The time delay and parameter estimates are then further refined using the Levenberg-Marquardt algorithm, so as to provide the most accurate parameter estimates for the complete system. Simulation results show that, compared with the standard Proportion Integration Differentiation (PID) controller approach, the proposed approach is not affected by changes in the time delay and parameter uncertainties.

Stability analysis for discrete-time switched systems with uncertain time delay and affine parametric uncertainties

This paper studies the stability conditions of a discrete-time switched linear system in the presence of affine parametric uncertainties and an unknown time delay. Based on a discrete Lyapunov functional, sufficient conditions are investigated to determine the upper bound of admissible time delay in the discrete-time switched system. Furthermore, the average dwell time method, which is an effective tool for stability analysis of switched systems, is used to derive the exponential stability conditions. These conditions characterize the switching signal, which does not depend on any uncertainties. Finally, numerical examples are provided to verify and compare the theoretical results.

Adaptive and predictive control of fuel injection with time delay consideration for air–fuel ratio regulation of gasoline direct injection engines

Accurate air–fuel ratio control is a key affecting factor for improving fuel economy and reducing exhaust emissions for internal combustion engines. Challenging issues in air–fuel control are the accurate estimation of cylinder air charge for achieving the stoichiometric in-cylinder air–fuel ratio and the disposition of measurement time delay from the oxygen sensor for removing its limits on the achievable feedback performance. In this article, based on hybrid discrete–continuous-time descriptions for the cylinder air charge dynamics and air–fuel feedback regulation controlled plant, a novel fuel injection controller with adaptive feedback and predictive feedforward is designed to ensure accurate air–fuel control of a gasoline direct injection engine. The feedforward fuel injection is determined based on the cylinder air charge prediction using unscented Kalman filter for the compensation of the injection delay and modelling error and the attenuation of the measurement noise. The feedback fuel compensation is designed as a proportional-integral structure with adaptive gains by means of an adaptive stabilization method of uncertain input delayed systems for the management of the transport delay and parameter uncertainty. The effectiveness of the proposed fuelling control against time delay, modelling error, measurement noise and parameter uncertainty is demonstrated by the simulation utilizing experimental data from a real V6 GDI engine.

Load Frequency Control with Communication Topology Changes in Smart Grid

In this paper, the quality of service of communication infrastructure implemented in multiarea power system for load frequency control application is assessed in smart grid environment. In this study, network induced effects time delay, packet loss, bandwidth, quantization, and change in communication topology (CT) has been addressed to examine the system performance in closed loop. Uncertainty in time delay is approximated using deterministic and stochastic models. The network is modeled considering different network configurations, i.e., change in CT. The modeled communication network guarantees control relevant properties, i.e., stability. The decentralized controller and linear matrix inequality-based linear quadratic regulator is implemented to reduce the dynamic performance (mean square error of states variables) of power system as CT changes. Simulation results suggest that the proposed scheme of networked control is superior with respect to other design methods available in the literature, and thus robust to communication imperfections.

Profoundly Robust Controlling Strategy for Uncertain Nonlinear Mimo System Using T–S Fuzzy System

In this paper, we addressed the problem of developing a robust control scheme for the MIMO nonlinear system; to achieve this, we adopt nonlinear systems with plant uncertainties, time-delayed uncertainties, and external disturbances. A fuzzy logic system is used to approximate the unknown nonlinear functions, and a Takagi–Sugeno (T–S) fuzzy observer is presented for state estimations. The designed control law works on basis of indirect T–S fuzzy control and utilizes two online approximations which allowed instantaneous insertion of finding gains of delayed state uncertainties. The benefit of employing a T–S fuzzy system is utilize of analytical results which are linear instead of approximating functions of nonlinear system with online update laws. The T–S fuzzy tracking control utilizes variable structure control method to resolve the system uncertainties, time-delayed uncertainty, and the external disturbances such that H ∞ tracking performance is achieved. The control rules are derived based on a Lyapunov criterion and the Riccati inequality such that all states of the system are uniformly ultimately limited. Therefore, the effect can be reduced to any prescribed level to achieve H ∞ tracking performance. A two-connected inverted pendulums system on carts used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

Disturbance rejection in DOC-out temperature control for DPF regeneration

Control of diesel oxidation catalyst (DOC) outlet temperature is critical for downstream diesel particulate filter regeneration, but is challenging to control due to the non-minimum phase behavior and varying time delay. To effectively address this issue, a novel and time-efficient composite controller based on modified active disturbance rejection control (mADRC) is proposed for DOC-out temperature control in this paper. The proposed mADRC-based composite controller is a new combination of a model-based feedforward controller and a mADRC with time delay compensation through the mass flow rate of exhaust gas. The model-based feedforward controller is designed to partially compensate the variations of DOC inlet temperature and mass flow rate, while the mADRC is proposed to address the remain disturbances and model uncertainties including time delay uncertainties. Simulation and test results through a high-fidelity Gamma Technologies-Power model demonstrate the effectiveness and robustness of the proposed composite controller in the DOC-out temperature control under steady state and a highly transient new European dynamic cycle (NEDC).

Design of a wide area damping controller based on partial right eigenstructure assignment

The paper demonstrates the application of partial right eigenstructure assignment for designing an output-feedback based wide area damping controller in a power system. The unique feature of the controller is that it utilizes the additional design freedom provided by right eigenvectors along with eigenvalue placement to improve the dynamic behaviour of the system. The fact that multi-input–multi-output (MIMO) systems provide more design freedom than just manipulating the eigenvalues of the system has been exploited for controller design. Supplementary loops on two static VAR compensators (SVC) have been used utilized to achieve the damping of oscillations. The first part of the paper uses a quadratic optimization based formulation to design a controller for a nominal operating point of the system. The second part demonstrates the incorporation of time delay of feedback signals in controller design. This methodology makes the designed controller robust to uncertainty in communication latency of feedback signals. The feedback signal selection for the controller is based on an input/output controllability metric specific to output feedback. An algorithm explaining the framework and the results of its implementation on the IEEE 68 bus test system has been provided. The results show the effectiveness of the controller to damp oscillations and robustification of the damping of these oscillations to time delay uncertainties.

Mean square consensus of multi-agent systems with multiplicative noises and time delays under directed fixed topologies

This paper investigates the mean square consensus problem of multi-agent systems impacted by the combined uncertainty of multiplicative noises and time delays. Considering general network under directed fixed topologies, we propose consensus protocol that take into account both the multiplicative noises and time delays. Using tools from stochastic differential delay equation (SDDE), martingale theory and stochastic inequality, we establish sufficient conditions and obtain the explicit consensus gain and delay upper bounds under which the proposed protocol leads to mean square consensus. In addition, we compare the impact of multiplicative and additive noise and reach the conclusion that multiplicative noises have the property of stabilizing effect. Simulations demonstrate the theoretical results.

Discrete-time repetitive optimal control: Robotic manipulators

This paper proposes a discrete-time repetitive optimal control of electrically driven robotic manipulators using an uncertainty estimator. The proposed control method can be used for performing repetitive motion, which covers many industrial applications of robotic manipulators. This kind of control law is in the class of torque-based control in which the joint torques are generated by permanent magnet dc motors in the current mode. The motor current is regulated using a proportional-integral controller. The novelty of this paper is a modification in using the discrete-time linear quadratic control for the robot manipulator, which is a nonlinear uncertain system. For this purpose, a novel discrete linear time-variant model is introduced for the robotic system. Then, a time-delay uncertainty estimator is added to the discrete-time linear quadratic control to compensate the nonlinearity and uncertainty associated with the model. The proposed control approach is verified by stability analysis. Simulation results show the superiority of the proposed discrete-time repetitive optimal control over the discrete-time linear quadratic control.

Time-delay and estimation uncertainty impact on the heuristic-based power control of optical networks

In this work, the performance of distributed power control algorithm based on heuristic optimization and considering the time-delay and estimation uncertainty is investigated in the scenario of optical networks. Time-delay allied to signal-to-noise-plus-interference ratio estimation uncertainty at the receiver side can affect decisively the network stability and the quality solution of the transmitted power optimization. In this work we have deployed a heuristic method based on particle swarm optimization (PSO) approach to allocate suitable transmitted power for the optical network nodes. Our numerical finding has demonstrated a suitable convergence of the PSO algorithm, as well as its limits, when the delay and uncertainty caused by estimation errors arise. Indeed, the rate-of-converge of the PSO algorithm has degraded substantially when delay and uncertainty become superior to 20 %, indicating that a tolerable uncertainty is about 10–15 %.

Interval-model-based global optimization framework for robust stability and performance of PID controllers

PID controller structure is regarded as a standard in the control-engineering community and is supported by a vast range of automation hardware. Therefore, PID controllers are widely used in industrial practice. However, the problem of tuning the controller parameters has to be tackled by the control engineer and this is often not dealt with in an optimal way, resulting in poor control performance and even compromised safety. The paper proposes a framework, which involves using an interval model for describing the uncertain or variable dynamics of the process. The framework employs a particle swarm optimization algorithm for obtaining the best performing PID controller with regard to several possible criteria, but at the same time taking into account the complementary sensitivity function constraints, which ensure robustness within the bounds of the uncertain parameters’ intervals. Hence, the presented approach enables a simple, computationally tractable and efficient constrained optimization solution for tuning the parameters of the controller, while considering the eventual gain, pole, zero and time-delay uncertainties defined using an interval model of the controlled process. The results provide good control performance while assuring stability within the prescribed uncertainty constraints. Furthermore, the controller performance is adequate only if the relative system perturbations are considered, as proposed in the paper. The proposed approach has been tested on various examples. The results suggest that it is a useful framework for obtaining adequate controller parameters, which ensure robust stability and favorable control performance of the closed-loop, even when considerable process uncertainties are expected.

Decentralized discrete sliding mode controller for TITO processes with time delay with experimental application

Multiple input multiple output systems posses interaction among the variables and hence are difficult to control. In addition, if these systems have slow and non-linear dynamics with time delays; it becomes more difficult to control them under the effect of parametric uncertainty. This paper presents the decentralized discrete time sliding mode controller (DSMC) for the robust tracking of two input two output (TITO) chemical processes with time delay. The ideal decoupler is used to reduce interaction among the system variables by forming decentralized structure consisting decoupled subsystems. Then for each subsystem, DSMC is independently designed and the control signal is applied to the TITO system after passing it through the decoupler. In the design procedure, an optimal sliding surface is chosen as a linear function of the system’s state error and the coefficients of sliding surface are computed by minimizing the quadratic performance index. A delay ahead predictor–corrector is used to handle system’s time delay and plant-model uncertainties. The control law is derived from the discrete time state model and sliding surface. A variable gain switching control law is proposed which results into power rate reaching law with power equal to 1. The methodology integrates ideal decoupler, optimal sliding surface and delay ahead prediction–correction; and therefore results optimal performance of the systems with less interaction. The stability condition is derived using Lyapunov approach. The stability condition results into chatter free convergent quasi sliding mode. Two benchmark simulation examples are used to demonstrate effectiveness of the proposed controller and an experimentation is performed on interacting coupled tank level control system to show its applicability to real life non-linear TITO systems.

English

English

Bilateral Teleoperation Systems Using Backtracking Search optimization Algorithm Based Iterative Learning Control

A B S T R A C T This paper deals with the application of iterative learning control (ILC) to further improve performance of bilateral telerobotic systems based on Smith predictor. The aim is to achieve robust stability and optimal transparency for these systems simultaneously. The proposed control structure makes the slave manipulator follow the master in spite of uncertainties in time delays appeared in communication channel and model parameters of master-slave robots, called model mismatch. The time delays are considered to be large, unknown and asymmetric, but the upper bound of the delay is assumed to be known. The main aspect of the proposed controller is that a designer can use the classical controller like proportional-integrator-derivative (PID). However, one of its main difficulties is how to assign proper parameter values for the controller. In other words, the parameters of the controller are not unique and are chosen only to satisfy the stability condition. To solve this problem, in this paper, the local controller is also optimized by backtracking search optimization algorithm (BSA), which is a novel heuristic algorithm with a simple construction. Simulation results illustrate the appropriate performance of the proposed controller.