Repetitive control of servo systems with time delays

In many industrial robotic servo applications there is a need to track periodic reference signals and/or reject periodic disturbances. Moreover, time-delays are usually unavoidable in control systems due to the sensoring and communication delays. This paper presents an alternative repetitive control design for systems with constant time-delays in both forward and feedback control channels, which are dedicated to track/reject periodic signals. An additional delay is introduced together with the plant delays to construct an internal model for periodic signals, and a simple compensator based on the plant model inverse is utilized to stabilize the closed-loop system. Sufficient stability conditions of the closed-loop system and the robustness analysis against modeling uncertainties are studied. The proposed idea is further extended for general time-delay systems with only a delay term in the forward control channel. The “plug-in” structure used in conventional repetitive control designs is avoided, so that it leads to a simpler control configuration, i.e. only a proportional parameter and the cutoff frequency of a low-pass filter are required to be selected. Simulations based on a hard disk drive system and practical experiments on a rotary robotic servo system are provided to evaluate the effectiveness of the proposed method.     

Optimal control of multivariable systems with pure time delays

A brief review of the development of the theory and computational approaches for the optimal control of multivariable systems having pure time delays is given. Following this is a detailed discussion of the optimal feedback control of both linear and non-linear systems having pure time delays. A neighboring optimal feedback control scheme is developed for non-linear problems, and a chemical reactor control problem is worked to illustrate the performance of the controller.     

Optimum control of distributed parameter systems with time delays

This paper discusses the optimum control of distributed parameter systems with time delays which are governed by a set of partial differential-difference equations. The technique of dynamic programming is used to derive the functional equations associated with optimization. Specific results are derived for linear systems with quadratic performance index. Also, an explicit condition for the complete null controllability of linear systems is given. The paper concludes with a discussion on the approximate solutions for the minimum energy control of a simple linear parabolic system with a time delay.     

Robust control of flexible structures with stable bandpass controllers

In this paper, a control law for the active vibration control of mechanical flexible systems is considered. The proposed strategy minimizes an index and results in a stable stabilizing controller with bandpass frequency shape, due to the presence of zeros at the origin. The control authority is thus effective in a chosen band of frequency, resulting in a selective broadband control action, as opposed to narrow-band (tonal) vibration reduction. Moreover, the explicit closed-form solution of the controller is also obtained, thus avoiding numerical calculation of the solution of the Riccati equations, which can be ill-conditioned in the case of very high-order, poorly damped flexible systems. The parametrization of all the controllers is also given and a family of controllers with the above properties is deduced. The case is also obtained as a byproduct. The controller is based on a colocated actuators/sensors pair strategy and numerical simulations are presented, showing the robustness of the proposed approach even for systems with zero damping. Finally, experimental results on a skin panel of a Boeing 717 aircraft also prove the effectiveness of the proposed approach in practical complex applications, with global vibration reduction performances.     

Stable sampled-data feedback control of dynamic systems with time delays

Conditions for asymptotic stability of linear systems with time varying delays are obtained by specific application of a comparison method. The conditions are used to design stable sampled-data feedback controllers for linear systems governed by time invariant differential-difference equations.     

Design of networked control systems with bounded arbitrary time delays

This paper is mainly concerned with the model predictive control (MPC) of networked control systems (NCSs) with uncertain time delay and data packets disorder. The network-induced time delay is described as bounded and arbitrary process. For the usual state feedback controller, by considering all the possibilities of delays, an augmented state space model of the closed-loop system, which characterizes all the delay cases, is obtained. The stability conditions are given according to the Lyapunov method based on this augmented model. The stability property is inherited in MPC which explicitly considers the physical constraints. A numerical example is given to demonstrate the effectiveness of the proposed MPC.     

On controllability of linear systems with time delays in control

The problems of controllability of linear processes with time delays described by the differential equationdot{x}(t) = A(t)x(t) + summin{i=0}max{k} B_{i}(t)u(t-h_{i}and satisfied in Euclidean space Rⁿare considered. The necessary and sufficient conditions for controllability, using the transition matrix of the process, are given. By the additional assumption that the matricesA,B_{i}are analytic int, another criterion of controllability, using the matricesAand Bionly, is proved.     

Robust adaptive control of nonlinear systems with unknown time delays

In this paper, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

Controllability of Boolean control networks with time delays in states

This paper investigates the controllability of Boolean networks with time-invariant delays in states. After a brief introduction on converting the logic dynamics to discrete time delay systems, the controllability via two kinds of controls is studied. One kind of control is generated by Boolean control networks, another kind of control is free Boolean sequences. In both cases, necessary and sufficient conditions of the controllability of Boolean control networks are proved. Finally, examples are given to illustrate the efficiency of the obtained results.     

Identification of time delays in linear stochastic systems

This paper presents a new approach to the explicit identification of an input time delay in continuous-time linear systems. The system model is converted to a discrete-time version, assuming that a digital computer is to be used for time delay estimation and control. A recursive identification algorithm based on parallel Kalman filtering and Bayes' estimation is developed. The sampling rate is adapted during the time delay estimation process using the most recent estimate of the time delay. This method assures that the estimate of the time delay approaches the true value with each successive iteration. The proposed method also has the advantage of a fast convergence rate because prior knowledge of the delay, if available, can be effectively utilized.     

Model reference control of uncertain systems with time delays in plant state and control

We consider a linear model reference control system in which the plant system and input matrices are uncertain and the plant state and control have retarded arguments. We present a control system consisting of a non-linear control law to handle the uncertainties. Under certain assumptions, this controller guarantees that all solutions are uniformly ultimately bounded. We also demonstrate the attractiveness of the switching hypersurface and show that along the hypersurface the trajectories are insensitive to system parameter variations.     

Optimal control for linear systems with multiple time delays in control input

This note presents the optimal linear-quadratic (LQ) regulator for a linear system with multiple time delays in the control input. Optimality of the solution is proved in two steps. First, a necessary optimality condition is derived from the maximum principle. Then, the sufficiency of this condition is established by verifying that it satisfies the Hamilton-Jacobi-Bellman equation. Using an illustrative example, the performance of the obtained optimal regulator is compared against the performance of the optimal LQ regulator for linear systems without delays and some other feasible feedback regulators that are linear in the state variables. Finally, the note establishes a duality between the solutions of the optimal filtering problem for linear systems with multiple time delays in the observations and the optimal LQ control problem for linear systems with multiple time delays in the control input.     

Input shaping and time-optimal control of flexible structures

We consider the problem of minimum time input shaping and its relation to the classical time-optimal control problem. We demonstrate that some typical minimum time input shapers are equivalent to the time-optimal control of different, although related, systems. The analytical proofs are based on the optimality criteria stipulated by the Karush-Kuhn-Tucker conditions.     

A sufficient condition for optimal control problems with time delays

This paper considers a class of systems modeled by ordinary differential equations which contain a delay in both the state and control variables. A sufficient condition for the optimal control of such systems is presented. The condition is a modification of a sufficient condition for optimal control problems without time delays. The application of the result is illustrated by examples.     

Adaptive neural network control of nonlinear systems with unknown time delays

In this note, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for such that iterative backstepping design can be carried out. In addition, controller singularity problems are solved by using the integral Lyapunov function and employing practical robust neural network control. The feasibility of neural network approximation of unknown system functions is guaranteed over practical compact sets. It is proved that the proposed systematic backstepping design method is able to guarantee semiglobally uniformly ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.     

Adaptive neural control of nonlinear MIMO systems with unknown time delays

In this paper, a novel adaptive NN control scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear time-delay systems. RBF NNs are used to tackle unknown nonlinear functions, then the adaptive NN tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The proposed controller guarantees uniform ultimate boundedness (UUB) of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters for each subsystem is reduced to one, triple problems of “explosion of complexity”, “curse of dimension” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.     

Self-learning fuzzy neural networks for control of uncertainsystems with time delays

We address the problem of control of uncertain systems with time delays. Using the fuzzy logic control and artificial neural network methodologies, we present a self-learning fuzzy neural control scheme for general uncertain processes. In this scheme, a neural network compensator is designed instead of the classical Smith predictor for attenuating the adverse effects of time delays of the uncertain systems. The scheme has been used in control of welding pool dynamics of the arc welding process, and the experiment results show the control scheme available.     

Exploitation of time delays for improved process control

A methodology for the identification of multivariable processes is developed that can achieve a higher level of controllability by increasing one or more time delays between the inputs and outputs. By examining the delays in the numerator and denominator of the inverse of the process transfer function matrix, a procedure is given for the identification of the delays which should be increased, and by how much these delays should be increased, in order to yield the best performance. A simple heat recovery network provides a practical example of the application of this technique. An enhanced multidelay compensator, designed on the basis of the process model with increased delays, yields a consistently better closed loop response than existing compensators.     

Identification of time delays using a polynomial identification method

An algorithm for the exact least-squares identification of an approximate continuous-time time-delay system is derived and its operation verified by simulation.     

Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays

This study introduces a guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy models with time-delays. The state feedback and generalized dynamic output feedback approaches are considered. The generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base. It considers both the dynamic part and the output part of T-S fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems. Based on delay-dependent Lyapunov functional approach, some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation (PDC) first. Second, the corresponding conditions are extended into the generalized dynamic output feedback closed-loop system via so-called generalized PDC technique. The upper bound of time-delay can be obtained using convex optimization such that the system can be stabilized for all time-delays whose sizes are not larger than the bound. The minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function. The effectiveness of the proposed method can be shown by the simulation examples.