SISO Continuous-System Reduction via Impulse Response Gramian by Iterative Formulae

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

In this paper, we analyse some fundamental structural properties of linear time-invariant multivariable systems in the controller canonical form and present a direct method for the computation of bases and associated friends for output-nulling, input-containing and reachability subspaces in terms of the parameters of the system and the invariant zero structure, both in the nondefective and in the defective case. Using this analysis, it is possible to express the solvability conditions of important control and estimation problems in terms of easily checkable conditions on the system matrices.

It is shown in this paper that any state space realization (A, b, c) of a given transfer function T(s) = β(s/α(s with α(s) monic and dim(A) = deg(α(s)), satisfies the identity β(A) = Qc(A, b)SαQo(A, c) where Qc(A, b) and Qo(A, c) are the controllability matrix and observability matrix of the matrix triple (A, b, c), respectively, and Sα is a nonsingular symmetric matrix. Such an identity gives a deep relationship between the state space description and the transfer function description of single-input single-output (SISO) linear systems. As a direct conclusion, we arrive at the well-known result that a realization of any transfer function is minimal if and only if the numerator and the denominator of the transfer function is coprime. Such a result is also extended to the SISO descriptor linear system case. As an applications, a complete solution to the commuting matrix equation AX = XA is proposed and the minimal realization of multi-input multi-output (MIMO) linear system is considered.

A method for model reduction of linear discrete systems is proposed. It is based on the impulse-response Gramian proposed by the authors (1989) for discrete systems. This Gramian is an extension of the one proposed for linear continuous systems and contains information on the input-output behavior of the system. The rth-order reduced-order models are made to retain the first r Markov parameters and the first r*r elements of the impulse-response Gramian of the original system. The relation between this method and the q-Markov cover method is also discussed. The method is illustrated by a numerical example. >

: This report considers a feedback control law for linear time-varying and time invariant discrete systems based on a receding horizon concept applied to a minimum energy problem with fixed terminal constraints. The control law is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems as well as extending some well known methods for stabilizing time invariant systems. In particular, the stabilizing gains of the feedback control law are obtained from the solution to a discrete Riccati equation over an arbitrary finite time interval, which is relatively easy to compute. The gain matrix reduces to a constant matrix for linear time invariant systems. Some stability results will turn out to be special cases of these results. The results parallel those for linear continuous time systems, although the technical details are tedious and more involved.

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.

A Single-Input Single-Output (SISO) linear system can represent various physical systems. One of the challenges in controlling practical systems is that the settling point and settling time cannot be prescribed together. In this paper, a novel Self-Tuning Control (STC) algorithm is presented, which ensures system stability while allowing the simultaneous determination of the settling time and settling point. Four possible scenarios will be defined to investigate the effectiveness of the proposed control method. Three different practices will be described in the simulation section for each scenario. Linear Quadratic Regulation (LQR) will be employed for comparison purposes. MATLAB software will be used to test and simulate these practices. The simulations will demonstrate that the STC is an optimal solution for SISO linear systems, comparable to LQR, with the significant advantage of guaranteeing the attainment of the settling point at the predefined settling time.

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.

An advanced reconfigurable controller enhanced by a multiple model architecture is proposed as a tool to achieve fault tolerance in complex nonlinear systems. The most complete adaptive critic design, globalized dual heuristic programming (GDHP), constitutes a highly flexible nonlinear adaptive controller responsible for the generation of new control solutions for novel plant dynamics introduced by unknown faults. The main contribution of the presented work focuses on a novel fault tolerant control supervisor. Working on a higher hierarchical level, the proposed supervisor makes use of two quality indices to perform fault detection, identification and isolation based on the knowledge stored in a dynamic model bank (DMB). In the event of abrupt known faults, such knowledge is then used to greatly reduce the reconfiguration time of the GDHP controller. The synergy of the proposed supervisor and GDHP goes beyond, as solutions designed by the controller to previously unknown faults are autonomously added to the model bank. The fine interrelations between the algorithm's subsystems and its advanced capabilities are illustrated through extensive numerical simulations of a single-input single-output (SISO) linear system and of a multiple-input multiple-output (MIMO) nonlinear system, both subject to a series of fault scenarios involving expected and unexpected, abrupt and incipient faults. Note to Practitioners-The raising complexity of physical plants and control missions inevitably leads to increasing occurrence, diversity and severity of faults. Take automated production process as an example, the extent of time a plant is capable of maintaining acceptable performance levels is now considered to be the single factor with the highest impact on profitability. For a growing number of plants, it has become impractical to list all possible fault scenarios in order to take the necessary steps to assure continuous healthy operation. Therefore, it is now essential to have a control algorithm dedicated to the provision of tailored control solutions capable of maintaining stability and as much performance as possible during the occurrence of faults. This is the goal of fault tolerant control. In the presented paper, the most complete adaptive critic design, globalized dual heuristic programming (GDHP), is responsible for the generation of new control solutions for novel plant dynamics introduced by faults unknown at design time. A highly flexible nonlinear adaptive controller, GDHP is capable of dealing with both abrupt and incipient (gradually changing dynamics) faults. Working on a higher hierarchical level, a novel fault supervisor is introduced which makes use of two quality indices to perform fault detection, identification and isolation based on the knowledge stored in a dynamic model bank (DMB). In the event of abrupt known faults, such knowledge is then used to greatly reduce the convergence time of the GDHP controller. The synergy of the proposed supervisor and GDHP goes further, as solutions designed by the controller to previously unknown faults are autonomously added to the model bank in fact allowing the supervisor to learn new fault scenarios and their solutions as they occur. The fine interrelations between the algorithm's subsystems and its advanced capabilities are illustrated through extensive numerical simulations.

In this paper we analyze proportional-derivative output feedback control for single-input single-output linear time-invariant dynamical systems with discrete state delays. The main focus of the presented work is the analysis of the effect of arbitrarily small implementation errors, such as a feedback delay or a finite-difference approximation of the derivative, on the stability of the closed loop. More specifically, it will be shown that the classical notion of stability does not suffice to adequately describe the asymptotic behavior of the closed loop system in the presence of these implementation errors, as stability might be lost even when these errors are made arbitrarily small. This paper therefore considers strong stability, which eliminates this well-posedness problem by not only requiring stability but by also enforcing that stability is preserved for sufficiently small perturbations. To conclude this paper, a controller design methodology for proportional-derivative output feedback controllers that strongly stabilize the system, is proposed.

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.

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.

In this paper, we consider the problem of identification of discrete-time, single-input single-output linear time-invariant systems. The prior information about the unknown plant is that it belongs to a certain set of LTI systems. The plant can be identified using input-output experiments, where the input can be chosen freely and the observed output is corrupted by an additive disturbance which is assumed to be bounded and has low-correlation. This set of disturbance includes uniformly bounded sequences that satisfy a time averages correlation condition. The motivation for using such a disturbance set is that the disturbances resemble stochastic white noise processes. In particular, a white noise signal belongs to this set with high probability if the bound on the correlations approaches zero at a certain rate. This paper analyzes the problem of worst-case identification in the presence of the above set of disturbances.

The main idea of the theory of discrete-time single-input single-output linear time-invariant systems (LTI-system) is that every such system has an input-output map that can be represented by the familiar convolution. Such a system is called system of convolution type. It was recently discovered by Boyd and Sandberg, that not all LTI-systems are systems of convolution type. Since not all LTI-systems are of convolution type it would be interesting to characterize the systems of convolution type. In this paper such a characterization is given with the help of the approximation behaviour of the system with respect to FIR-systems. A necessary and sufficient condition is given, such that the system is a system of convolution type. Some applications for the filter design are also described.

Nature has the key to solve every single problem that exists. This paper strives to propose a method which is based on flower pollination algorithm to acquire a stable reduced order model (ROM) of a higher order linear time-invariant (LTI) system. The suggested method utilizes Pade-based moment matching technique to deduce denominator approximants for the reduced order system, whereas the reduced order approximants of numerator polynomial are obtained using flower pollination (FP) algorithm. To prove the viability of the suggested method, numerical examples are solved considering single-input single-output (SISO) systems. A comparison has been drawn between suggested method and existing methods which are available in the current literature and is presented in this paper. This comparison is founded on a performance index which is known as integral square error (ISE).