L^{1}-optimal compensators for continuous-time systems

Previous work has been concerned with minimizing thel^{1}-norm of an error pulse response for discrete-time SISO [1] and MIMO [2] systems. In this paper we study the problem of minimizing the L¹-norm of the error impulse response for SISO continuous-time systems. This problem is quite different from the discrete-time problem in that irrational solutions are obtained even when the problem data are rational. Two methods are suggested for the solution of the continuous-time problem; an exact method which leads to a finite-dimensional nonlinear programming problem, and an approximate method which leads to a linear programming problem.     

Order estimation for linear time-invariant systems using frequencydomain identification methods

A two-step coarse-fine order estimation technique is proposed to determine the order of the numerator and the denominator polynomials of rational transfer function models for single-input/single-output (SISO) linear time-invariant systems. The coarse order estimation is based on rank detection by verification of the stochastic significance of the singular values of a linearized problem. The fine order estimation is based on a statistical analysis of the maximum likelihood cost function. The method is tested on measurements of low-(4 zeros, 6 poles) and high- (58 poles, 58 zeros) order systems     

Design of non-rational MIMO feedback systems with inputs and outputs satisfying certain bounding conditions by using rational approximants

When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out the design with the approximants by means of a method that copes with rational systems. In order to ensure that the design carried out with the approximants still provides satisfactory results for the original system, a criterion of approximation should be explicitly taken into account in the design formulation. This paper derives such a criterion for multi-input multi-output (MIMO) feedback systems whose design objective is to ensure that the absolute values of every error and every controller output components always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. The obtained criterion generalizes a known result which was derived for single-input single-output (SISO) systems; furthermore, for a given rational approximant matrix, it is expressed as a set of inequalities that can be solved in practice. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities. The numerical results clearly demonstrate that the usefulness of the criterion in obtaining a design solution for the original system.     

Frequency-domain stability criteria for SISO and MIMO nonlinear feedback systems with constant and variable time-delays

New frequency-domain criteria are proposed for the $L_2$-stability of both nonlinear single-input-single-output (SISO) and nonlinear multiple-input-multiple-output (MIMO) feedback systems, described by nonlinear integral equations. For SISO systems, the feedback block is a constant scalar gain in product with a linear combination of first-and-third-quadrant scalar nonlinearities (FATQNs) with time-delay argument functions; and, for MIMO systems, it is a constant matrix gain in product with a linear combination of vector FATQNs also with time-delay argument functions. In both the cases, the delay function in the arguments of the nonlinearities may be, in general, i) zero, ii) a constant, iii) variable-time and iv) fixed-history (only for SISO systems). The stability criteria are derived from certain recently introduced algebraic inequalities concerning the scalar and vector nonlinearities, and involve the causal+anticausal O''Shea-Zames-Falb multiplier function (scalar for SISO systems and matrix for MIMO systems). Its time-domain $L_1$-norm is constrained by the coefficients and characteristic parameters (CPs) of the nonlinearities and, in the case of the time-varying delay, by its rate of variation also. The stability criteria, which are independent of Lyapunov-Krasovskii or Lyapunov-Razumikhin functions and do not seem to be derivable by invoking linear matrix inequalities, seem to be the first of their kind. Two numerical examples for each of SISO and MIMO systems illustrate the criteria.     

H @ -Robustness properties preservation in SISO systems when applying SPR substitutions

The preservation of both robust stability and weighted robust performance properties of controlled linear time-invariant single input single output (SISO) systems is studied, when performing substitutions (of the complex Laplace variable s ) by a particular class of rational strictly positive real functions ( SPR functions), the so-called strictly positive real functions of zero relative degree ( SPR0 functions). Concerning weighted robust performance and model-matching, we provide some results on preservation of controller optimality.     

H∞ optimal and suboptimal controllers for infinitedimensional SISO plants

This paper presents a simple formula for H^∞ optimal and suboptimal controllers for unstable SISO distributed plants, with rational weighting functions. The controller is expressed in terms of i) inner and outer parts of the plant, ii) a finite dimensional spectral factor obtained from the weighting functions, and iii) a rational function satisfying certain interpolation conditions. Under certain genericity assumptions, this rational function is of dimension less than or equal to n₁+l-1 (n₁+l in the suboptimal case), where l is the number of unstable poles of the plant and n₁ is the order of the sensitivity weighting function. There are 2(n₁+l) (2(n₁+l+1) in the suboptimal case) linear equations, which determine this rational function. These linear equations can be written directly from the structure of the controller     

MMSE SQRD based SISO detection for coded MIMO-OFDM systems

In this paper, we propose a minimum mean square error （MMSE） sorted QR decomposition （SQRD） based soft-input soft-output （SISO） detection algorithm for coded multiple-input multiple-output orthogonM frequency division multiplexing （MIMO-OFDM） systems. The proposed detection is derived from the SISO MMSE detection, which is a popular detection strategy for iterative receivers. For each transmitted symbol in the proposed detection, a soft successive interference cancellation （SIC） is performed based on a posteriori probabilities of past detected symbols. Simulation results show that the proposed detection, while needing less computationM efforts, achieves significant performance gain compared with the SISO MMSE detection.     

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output (SISO) and multi-input multi-output (MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii (PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively. In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized. Finally, the effectiveness of the proposed method is confirmed by numerical simulations.      

Comment regarding “On undershoot in SISO systems”

A new model of single-input/single-output (SISO) systems is introduced such that undershoot, overshoot, and s-plane zeros cannot occur and which is a generalization of a model commonly used in the process industry     

Measurement and identification of nonlinear systems consisting oflinear dynamic blocks and one static nonlinearity

This paper considers the measurement and the identification of nonlinear time-invariant single-input/single-output (SISO) systems, consisting of a multivariable linear dynamic system and one static nonlinear SISO system. This includes Wiener-Hammerstein systems in a linear feedback loop. The nonparametric identification of the frequency response functions of the linear parts are obtained without measuring the signals over the static nonlinearity. Measurements on an electronic circuit demonstrate the usability of this identification scheme     

非仿射系统的自学习滑模抗扰控制

针对一类单输入单输出(single-input single-output,SISO)非仿射非线性系统的控制问题,提出了一种自学习滑模抗扰控制方法.该方法用非线性光滑函数设计扩张状态观测器,实现SISO非仿射非线性系统内部不确定性和外部扰动的扩张状态估计,并将扩张状态观测器(extended state observer,ESO)与自学习滑模控制技术融为一体,实现SISO非仿射非线性系统的自学习滑模抗扰控制.该方法不依赖受控对象的数学模型,可以快速跟踪任意给定的参考信号.数值仿真试验表明了该方法响应速度快、控制精度高,具有很强的抗扰动能力,因而是一种鲁棒稳定性很强的控制方法,在SISO非仿射非线性系统控制领域具有重要作用.     

Parameter identification for uncertain linear systems with partialstate measurements under an H∞ criterion

This paper addresses the worst-case parameter identification problem for uncertain single-input/single-output (SISO) and multi-input/multi-output (MIMO) linear systems under partial state measurements and derives worst-case identifiers using the cost-to-come function method. In the SISO case, the worst-case identifier obtained subsumes the Kreisselmeier observer as part of its structure with parameters set at some optimal values. Its structure is different from the common least-squares (LS) identifier, however, in the sense that there is additional dynamics for the state estimate, coupled with the dynamics of the parameter estimate in a nontrivial way. In the MIMO case as well, the worst-case identifier has additional dynamics for the state estimate which do not appear in the conventional LS-based schemes. Also for both SISO and MIMO problems, approximate identifiers are obtained which are numerically much better conditioned when the disturbances in the measurement equations are “small”. The theoretical results are then illustrated on an extensive numerical example to demonstrate the effectiveness of the identification schemes developed     

Loop shaping design related to LQG/LTR for SISO minimum phase plants

One method of model-based compensator design for linear systems consists of two stages: state feedback design and observer design. A key issue in recent work in multivariable synthesis involves selecting the observer (state feedback) gain so that the final loop transfer function is the same as the state feedback (observer) loop transfer function. This is called loop transfer recovery (LTR)(Athans and Stein 1987, Kazerooni and Houpt 1986, Kazerooni et al. 1985, Doyle and Stein 1981). This paper shows how identification of the internal mechanism of the LTR provides simple design rules with little algebra for single-input single-output (SISO) systems. In the SISO case, the LQG/LTR reduces to computation of a compensator that shapes the loop transfer function by (i) cancelling the zeros of the plant with the compensator poles, and (ii) locating a new set of zeros for the compensator to shape the loop transfer function.     

A smoothly parameterized family of stabilizable, observable linearsystems containing realizations of all transfer functions of McMillandegree not exceeding n

It is shown that there is a continuously parameterized family F of n-dimensional single-input single-output (SISO) stabilizable detectable linear system Σ(p) which contains at least one realization of each reduced, strictly proper transfer function of McMillan degree not exceeding n. The parameterization map p→Σ(p) is a polynomial function in 2n indeterminates from an open convex polyhedron in R²ⁿ to the linear space of all SISO n-dimensional linear systems     

Neural network controller for a multivariable model of submarine dynamics

Recently, there have been many attempts to use neural networks as a feedback controller. However, most of the reported cases seek to control Single-Input Single-Output (SISO) systems using some sort of adaptive strategy. In this paper, we demonstrate that neural networks can be used for the control of complex multivariable, rather than simply SISO, systems. A modified direct control scheme using a neural network architecture is used with backpropagation as the adaptive algorithm. The proposed algorithm is designed for Multi-Input Multi-Output (MIMO) systems, and is similar to that proposed by Saerens and Soquet [1] and Goldenthal and Farrell [2] for (SISO) systems, and differs only in the form of the gradient approximation. As an example of the application of this approach, we investigate the control of the dynamics of a submarine vehicle with four inputs and four outputs, in which the differential stern, bow and rudder control surfaces are dynamically coordinated to cause the submarine to follow commanded changes in roll, yaw rate, depth rate and pitch attitude. Results obtained using this scheme are compared with those obtained using optimal linear quadratic control.     

Model reduction for state-space symmetric systems

In this paper, the model reduction problem for state-space symmetric systems is investigated. First, it is shown that several model reduction methods, such as balanced truncation, balanced truncation which preserves the DC gain, optimal and suboptimal Hankel norm approximations, inherit the state-space symmetric property. Furthermore, for single input and single output (SISO) state-space symmetric systems, we prove that the H_∞ norm of its transfer functions can be calculated via two simple formulas. Moreover, the SISO state-space symmetric systems are equivalent to systems with zeros interlacing the poles (ZIP) under mild conditions.     

Pinning control and controllability of complex dynamical networks

In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output (SISO) or multi-input multi-output (MIMO) dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant (LTI) systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying (LTV) node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.     

Model reduction for state-space symmetric systems

In this paper, the model reduction problem for state-space symmetric systems is investigated. First, it is shown that several model reduction methods, such as balanced truncation, balanced truncation which preserves the DC gain, optimal and suboptimal Hankel norm approximations, inherit the state-space symmetric property. Furthermore, for single input and single output (SISO) state-space symmetric systems, we prove that the H_∞ norm of its transfer functions can be calculated via two simple formulas. Moreover, the SISO state-space symmetric systems are equivalent to systems with zeros interlacing the poles (ZIP) under mild conditions.     

A simpler formula for the singular values of a certain Hankel operator

This paper deals with the problem of computing the singular values and vectors of a Hankel operator with symbol m^*W where m ε H^∞ is arbitrary inner and W ε H^∞ is rational. A simplified version of the formula given in [6] is obtained for computing the singular values of the Hankel operator. This result is applied to the (one-block) H^∞ optimal control of SISO stable infinite dimensional plants and rational weights. Using this new formula a simple expression is derived for the H^∞ optimal controller whose structure was observed in [9].     

Global almost disturbance decoupling with stability for non minimum-phase single-input single-output nonlinear systems

The so-called problem of almost disturbance decoupling with internal stability (ADDPS) is the following one. Given a system and an (arbitrarily small) number γ > 0, find a feedback law yielding a closed loop system which is stable and in which the gain (in the L₂ sense) between the exogenous input and the regulated output is less than or equal to γ. The complete solution of this problem has been known since a long time in the case of linear systems. In the case of nonlinear systems, the only global results available so far in the literature were about SISO systems having an asymptotically stable zero dynamics. In this paper, a new set of results are presented, dealing with nonlinear SISO systems having a possibly unstable zero dynamics, which include the (general) class of linear SISO systems as a special case.