Optimal pole placement design for SISO discrete-time systems

In this paper, we incorporate the placement of one real closed-loop pole into a compensator design framework based upon the Youla parameterization, duality theory, and linear programming. This framework has been used to design discrete-time compensators to solve the l₁ controller design problem as well as other related time-domain optimization problems. Previous work on these problems has focused on deadbeat systems. It is known that these can require high-order controllers. Part of the motivation for this work is to improve the tradeoff between controller order and performance over that, using deadbeat control     

A finite frequency domain approach to fault detection for linear discrete-time systems

This paper deals with the fault detection (FD) problem in the finite frequency domain for linear time-invariant discrete-time systems with bounded disturbances. A fault detection observer is designed by employing two performance indesxes which are used to increase the fault sensitivity in finite frequency domain and attenuate the effects of disturbances in full frequency domain. With the aid of the generalized Kalman–Yakubovich–Popov (GKYP) Lemma, the design methods are presented in terms of solutions to a set of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed method.     

Time optimal design of discrete data systems in the frequency domain

The main objective of any time optimal design is to develop a control law to drive the state variables of the system, from a given set of initial values to a desired set of final values. Sometimes, it is required to drive the systems such that the output for a unit step input is reached in a minimum time, without overshoot [5–7]. Although the problem is normally set in the frequency domain, it is usual to convert it into the time domain for determining the optimal control sequence. It is shown in the paper that the entire time optimal design can be effectively carried out if the transfer function of the plant is given in the Z domain.     

Constrained MIMO dynamic discrete-time modeling exploiting optimal experimental design

This article presents a new multiple input, multiple output (MIMO) constrained discrete-time modeling (DTM) approach for dynamic block-oriented processes that does not require the nonlinear steady state characteristics to be known prior to model development. This approach uses an efficient statistical experimental design to provide design points for sequential step tests. The DTM is developed from this data in two stages. In the first stage, the ultimate response (steady state) model is determined from just the ultimate response data of the sequential step tests. In the second stage, the dynamic parameters are estimated under the constraint of the fitted ultimate response model obtained in the first stage. The constrained formulation is given for MIMO Hammerstein and Wiener block-oriented systems. Comparison of the proposed constrained DTM method is made with unconstrained DTM and constrained continuous-time modeling (CTM). Prediction accuracy of the proposed method is significantly better than unconstrained DTM and comparable to constrained CTM for the process studied.     

Optimal damping of forced oscillations in discrete-time systems

In this paper we consider a linear discrete-time control system affected by an additive sinusoidal disturbance with known frequencies but unknown amplitudes and phases. The problem is to damp this forced oscillation in an optimal fashion. We show that the natural solution from the point of view of optimal control is neither robust with respect to errors in the frequencies, and thus not optimal in practice, nor independent of the unknown amplitudes and phases. The main result of this paper concerns the existence and design of a realizable, robust optimal regulator, which is universal in the sense that it does not depend on the unknown amplitudes and phases and is optimal for all choices of such parameters. The regulator allows for a considerable degree of design freedom to satisfy other design specifications. Finally, it is shown that this regulator is optimal also for a wide class of stochastic control problems     

Optimal control of discrete-time singularly perturbed systems

In this paper, we present a new algorithm for solving the optimal control of discrete-time singularly perturbed systems. The main idea of this algorithm is based on two steps. First, the Hamiltonian difference equation is reduced to the backward recursive form rather than the forward recursive form. Second, the bilinear transformation is applied to transform the derived non-symmetric discrete-time Riccati equations into continuous-time equations. In order to improve the efficiency of this scheme, two matrix permutations are introduced into this algorithm by taking into account the previous work of Gajic and Shen (1991). Therefore, substantial numerical advantages are gained; namely, computation and memory requirements. The F-8 aircraft model is used to illustrate the efficiency of the proposed method.     

线性控制系统窗口频域分析与设计

针对局部频率范围提出了窗口H∞范数的新概念,指出传统H∞范数是窗口H∞.范数的特例.利用GKYP引理证明了广义界实定理,研究了线性控制系统在窗口频域的性能分析问题.基于近似模型匹配原则和广义界实定理,将控制器设计问题转化为窗口H∞范数优化问题.仿真实例表明,窗口H∞范数适于窗口频域的线性控制系统分析和设计.     

Two algorithms for frequency domain design of robust control systems

Two algorithms are described that are useful in the computer-aided design implementation of the robust controller design scheme proposed by Horowitz (1963) and Horowitz and Sidi (1972).     

Optimal filtering in stochastic discrete-time systems with unknowninputs

In this note we derive a recursive filtering algorithm for the linear discrete-time dynamic system with indeterminate-stochastic inputs. The algorithm is based on the minimax-optimal method of parameter estimation in the linear regression model with parameters of two different types: unknown and stochastic with partially known characteristics     

Optimal finite-precision state-estimate feedback controllerrealizations of discrete-time systems

Investigates the stability issue of a discrete-time control system, where a state-estimate feedback controller (SEFC), digitally implemented with a fixed-point format, is used. A tractable closed-loop stability related measure is derived with finite-word-length implementation consideration of the controller. The optimal realizations of the SEFC are defined as those that maximize this measure and can be shown as the solutions of a nonlinear programming problem. A sophisticated optimization strategy is presented to provide an efficient method for solving this problem, and a numerical example is given to illustrate the design procedure     

Optimal control of discrete-time systems with time-lag controls

Various optimal control problems for discrete-time systems with time-lag controls are discussed. Some of the basic features of this type of system are noted. A simple example is given for illustrative purpose.     

Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems

In this article, we discuss a model order reduction method for multiple-input and multiple-output discrete-time bilinear control systems. Similar to the continuous-time case, we will show that a system can be characterised by a series of generalised transfer functions. This will be achieved by a multivariate Z-transform of kernels corresponding to an explicit solution formula for discrete-time systems. We will further address the problem of generalised tangential interpolation which naturally comes along with this approach. We will introduce a reasonable generalisation of the linear ?₂-norm. Based on this concept, we discuss the choice of interpolation points. Furthermore, an efficient discretisation of continuous-time systems is provided. The performance of the proposed method is evaluated in some numerical examples and compared with the method of balanced truncation for bilinear systems.     

Parametric compensator design in the frequency domain

The parametric approach to the design of observer based compensators has hitherto only been formulated in the time domain. It yields an explicit parametric expression for the state feedback matrix (observer gain) given the closed loop eigenvalues and the corresponding sets of invariant parameter vectors. Using the polynomial approach to the design of observer based compensators this contribution presents an equivalent parameterization in the frequency domain. By introducing the closed loop poles and the set of so-called pole directions as new design parameters, one obtains expressions in parametric form for the polynomial matrix D(s) (D(s)), parameterizing the state feedback (state observer) in the frequency domain. It is shown how the pole directions are related to the invariant parameter vectors used in the time domain approach. Another new result is the parametric design of reduced order observers both in the frequency domain, and derived from those results, in the time domain. The proposed design procedure is also used to provide a parametric solution for the optimal LQG control problem in the presence of partially perfect measurements. Simple examples demonstrate the design procedure.     

Robust design of discrete-time systems via optimization

An optimization approach for the design of robust discrete-time control systems is presented. Using pole clustering, the design specifications for the system time response are recast in the form of inequality constraints governing the free design parameters. Quantitative robustness and disturbance rejection measures are discussed using Lyapunov matrix equations. A performance index combining the robustness and disturbance rejection measures is minimized subject to the parameter inequality constraints to obtain the desired design. A numerical example is given to illustrate the usefulness of the design approach.     

Optimal state reconstruction algorithms for linear discrete-time systems

This paper deals with optimal time-invariant reconstruction of the state of a linear time-invariant discrete-time system from output measurements. The problem is analysed in two settings, depending on whether or not the present output measurement is available for the estimation of the present state. The results prove complete separation of observer and controller design for the optimal dynamic output feedback control with respect to a quadratic cost.     

Robust spectral factor approximation of discrete-time frequency domain power spectras

This paper presents a subspace-based identification algorithm for estimating the state-space quadruple [A,B,C,D] of a minimum-phase spectral factor from matrix-valued power spectrum data. For a given pair [A,C] with A stable, the minimum-phase property is guaranteed via the solution of a conic linear programming (CLP) problem. In comparison with the classical LMI-based solution, this results in a more efficient way to minimize the weighted 2-norm of the error between the estimated and given power spectrum. The conic linear programming problem can be solved in a globally optimal sense. This property is exploited in the derivation of a separable least-squares procedure for the (local) minimization of the above 2-norm with respect to the parameters of the minimal phase spectral factor. The advantages of the derived subspace algorithm and the iterative local minimization procedure are illustrated in a brief simulation study. In this study, the effect of dealing with short length data sets for computing the power spectrum, on the estimated spectral factor, is illustrated.     

On the l_2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the 2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput(MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a matrix of periodic/aperiodic gains A(k), k = 0, 1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities■(■), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions,which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real part(as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of(A(k + 1), A(k)), k = 1, 2,.... iii) They are distinct from and less restrictive than recent results in the literature.     

MIMO离散时间系统混合l1/H2控制

研究了MIMO(多输入多输出)离散时间系统的混合l1/H2优化问题,该问题可描述为最优化一个传递函数矩阵的l1范数同时保证另一个传递函数矩阵的H2范数满足预定的指标.研究了最优目标函数值关于H2范数指标的连续性.证明了MIMO系统混合l1/H2控制问题最优解的存在性.由于基于标定-Q (scaled-Q)方法求解MIMO混合l1/H2问题,避免了进行零点插值运算的困难.通过求解有限维非线性规划问题可得到最优目标值的收敛的上下界.