Analysis and Design of Output Feedback PD Controllers for Time-Delay Systems

Direct adaptive control of a single-input single-output linear time-invariant n-dimensional discrete-time system is approached in terms of a 2n-dimensional state representation constructed directly from the input/output difference equation. The central result of the paper de the derivation of a simple procedure for directly determining the controller parameters in adaptive pole placement. The only assumption on the system model is that the minimal order of the system is known a priori; in particular, the given system is not required to be minimum phase. The approach taken in the paper is based on the expression of the system input as a linear function of an expanded (4n-dimensional) regression vector with the coefficient vector of the linear relationship containing the desired controller parameters. In this way the determination of the controller parameters is reduced to a linear-in-the-parameters estimation problem which can be solved using existing parameter estimation schemes. The particular parametrization constructed in this paper is a “state-space” version of the parametrization derived by Elliott [1]. The estimation of controller parameters is based on the standard recursive least squares algorithm. If the expanded regression vector is sufficiently exciting (as opposed to persistently exciting), the closed-loop system is exponentially stable with the closed-loop poles located close to the desired poles for sufficiently large values of the time index.

This paper develops a framework of adaptive compensation of actuator nonlinearities with unknown parameters, for output feedback control of unknown multi-input multi-output linear time-invariant dynamic systems. A new controller parametrization is derived to deal with bilinear parameters from the actuator nonlinearity parameters and the dynamic system parameters, which, based on the LDU decomposition of the system high frequency gain matrix, is capable of overcoming the difficulty caused by a nondiagonal high frequency gain matrix and a special actuator nonlinearity parameter structure. The adaptive actuator nonlinearity compensation control scheme is a model reference adaptive control based design, employing an adaptive output feedback control law combined with an adaptive actuator nonlinearity inverse, to deal with parameter uncertainties in the system dynamics and actuator nonlinearities. Simulation results show the desired adaptive control system performance.

For a single-output linear time-invariant system, output controllability is shown to be a necessary and sufficient condition for the existence of linear state variable feedback that freely assigns the eigenvalues of the closed-loop system that are observable from the output. An application of this result to the single-output linear servomechanism shows that the ability of such a system to track with zero steady-state error and an arbitrary transient response is equivalent to output controllability of the plant, and is independent of the class of command signals and disturbances.

In this paper, a controller called dynamic matrix constrained variable structure controller (DM-CVSC) is proposed. The controller takes advantages of both dynamic matrix (DM) and constrained variable structure controllers. As a result, DM-CVSC is a robust trajectory tracking controller dealing with the constraints on control inputs and also makes decision based on the future behavior of the vehicle. The controller is applied to a linearized model of half-car suspension systems which are subject to different types of road disturbances and measurement noises. In this paper, it is shown that there is a simple formulation for calculating the range of sliding gains for single-input single-output (SISO) linear control systems. As for the multi-input multi-output (MIMO) linear control systems, the calculation of upper sliding gain profile for controller leads to a search problem. To show the efficiency of the proposed controller, it is applied to four different cases involving specific road disturbances and measurement noises. The performance of the proposed controller is compared to various control techniques.

This paper concerns the order reduction of single-input single-output (SISO) linear time-invariant continuous systems based on the impulse response Gramian. From the recursive relationship among the Gramians, a new formula is derived for computing the system matrix in controllability canonical form. The result is applied to the model reduction problem. Reduced models obtained approximate the reduced-order Gramians while preserving some initial time moments and Markov parameters of the original system.

Optimal performance of discrete-time control systems based on network-induced delay

For single-input single-output linear time-invariant discrete-time systems, a simple procedure is given for directly determining the controller parameters in adaptive pole placement. The given system is not required to be minimum phase. The only assumption on the system model is that the minimal order of the system is known a priori. The controller parameters are estimated using a standard recursive least squares algorithm. If an expanded regression vector is sufficiently exciting (as opposed to persistently exciting), the closed-loop system is exponentially stable with the closed-loop poles located close to the desired poles in the limit.

We address the problems of computing operator norms of matrices induced by given norms on the argument and the image space. It is known that aside of a fistful of “solvable cases”, most notably, the case when both given norms are Euclidean, computing operator norm of a matrix is NP-hard. We specify rather general families of norms on the argument and the images space (“ellitopic” and “co-ellitopic”, respectively) allowing for reasonably tight computationally efficient upper-bounding of the associated operator norms. We extend these results to bounding “robust operator norm of uncertain matrix with box uncertainty”, that is, the maximum of operator norms of matrices representable as a linear combination, with coefficients of magnitude <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>, of a collection of given matrices. Finally, we consider some applications of norm bounding, in particular, (1) computationally efficient synthesis of affine non-anticipative finite-horizon control of discrete time linear dynamical systems under bounds on the peak-to-peak gains, (2) signal recovery with uncertainties in sensing matrix, and (3) identification of parameters of time invariant discrete time linear dynamical systems via noisy observations of states and inputs on a given time horizon, in the case of “uncertain-but-bounded” noise varying in a box.

Stabilisation and strong stabilisation (i.e. the problem of stabilising by a stable controller) of linear time-invariant (LTI) multi-input multi-output systems are considered. The considered systems may be finite-dimensional or time-delay systems, which may have multiple discrete time delays. The controllers to be designed may also be either finite-dimensional or time-delay LTI controllers. In the controller design phase, a constrained nonsmooth optimisation-based design method is employed. The effectiveness of the proposed method is illustrated through various benchmark examples which are solved by using the recently developed Matlab-based software called DrStabilization . The examples also show that, in many cases, time-delay controllers may have certain advantages over conventional finite-dimensional controllers.

This paper proposes a new algorithm for achieving discrete-time sliding mode for single input single output systems with bounded matched uncertainty using output feedback. The concept of periodic output feedback is used here. It has been shown that, when the output of the uncertain system with matched uncertainty is sampled slower than the input, there exist a discrete-time quasi sliding mode. The method is very general and is applicable to any controllable and observable linear time invariant single input single output system. The proposed technique is illustrated with numerical examples.

This paper deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals. We propose a new controller parameter optimization approach, which can be carried out experimentally without knowledge of the plant model or the order of the system. The approach has the advantages that controllers can be tuned by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

By connecting information rates (entropy rate and mutual information rate) with classic poles and zeros analysis using Bode's integral formulas, the performance limits and the. conservation law of variety' in scale linear time invariant feedback control systems are discussed from the viewpoint of information theory. A new kind of design constraints is also derived.

The Nyquist stability criterion and the notion of type n systems have been extended from lumped parameter systems to a larger class of linear single-loop single-input single-output time-invariant systems, with constraints presented in the text.

A simple necessary and sufficient LMI condition for the strong delay-independent stability of LTI systems with single delay

This paper investigates the application of associative reinforcement learning techniques to the optimal control of linear discrete-time dynamic systems. Associative reinforcement learning involves the trial and error interaction with a dynamic system to determine the control actions that optimally achieve some desired performance index. The methodology can be applied either online or off-line and in a model based or model free manner. Associative reinforcement learning techniques are applied to the optimal regulator (LQR) control of discrete-time linear systems. Adaptive critic designs are implemented and the convergence speed compared for the different approaches. These methods can determine the optimal state and state/action value function and the optimal policy without requiring system models. (4 pages)