Optimal digital controller and observer design for multiple time-delay transfer function matrices with multiple input–output time delays

In this article, we address the optimal digital design methodology for multiple time-delay transfer function matrices with multiple input–output time delays. In our approach, the multiple time-delay analogue transfer function matrix with multiple input–output time delays is minimally realised using a continuous-time state-space model. For deriving an explicit form of the optimal digital controller, the realised continuous-time multiple input–output time-delay system is discretised, and an extended high-order discrete-time state-space model is constructed for discrete-time LQR design. To derive a low-order optimal digital observer for the multiple input–output time-delay system, the multiple time-delay state obtained from the multiple time-delay outputs is discretised. Then, the well-known duality concept is employed to design an optimal digital observer using the low-order discretised multiple input time-delay system together with the newly discretised multiple time-delay state. The proposed approach is restricted to multiple time-delay systems where multiple time delays arise only in the input and output, and not in the state.     

Optimal bilinear observers for bilinear state-space models by interaction matrices

This paper formulates optimal bilinear observers for bilinear state-space models. Observers in bilinear form, as opposed to other nonlinear forms, are required to develop an extension of observer/Kalman filter identification for simultaneous identification of a bilinear state-space model and an associated bilinear observer from noisy input–output measurements. The paper establishes the relationship between the bilinear observer gains and the interaction matrices which are used to convert the original bilinear state-space model to a form that simplifies the identification of such a model. Techniques to find the interaction matrices are developed. In the absence of noises, these matrices produce the gains of the fastest converging observer. In the presence of noises, they minimise the state estimation error in the same manner as a standard steady-state Kalman filter. Numerical examples illustrate both the theoretical and computational aspects of the proposed algorithms.     

Discrete optimal stochastic controller and its forms

An approach to obtain the optimal controller From an optimal criterion is presented. The controller is very general in the sense that it is multivariable, it compensates Tor process delay and it allows a penalty on the input variable variance. The controller can be obtained in two forms: the state-space model form with the steady-state Kalman filter that separates the control algorithm in distinctive steps to provide an insight into the control problem, while the transfer function form is very convenient for implementation.     

An improved state-space model structure and a corresponding predictive functional control design with improved control performance

Conventional state-space model predictive control requires a state estimator/observer to access the state information for feedback controller design. Its drawbacks are the numerical convergence stability of the observer and closed-loop control performance deterioration with activated plant input/output constraints. The recent direct use of measured input and output variables to formulate a non-minimal state-space (NMSS) model overcomes these problems, but the subsequent controller is too sensitive to model mismatch. In this article, an improved structure of NMSS model that incorporates the output-tracking error is first formulated and then a subsequent predictive functional control design is proposed. The proposed controller is tested on both model match and model mismatch cases for comparison with previous controllers. Results show that control performance is improved. In addition, a linear programming method for constraints dealing and a closed form of transfer function representation of the control system are provided for further insight into the proposed method.     

基于微分对策的最优状态观测器和最优状态反馈控制器的设计

研究了线性系统基于二次型指标的最优状态观测器和最优状态反馈控制器的设计问题．将观测状态的状态反馈和状态误差的输出反馈分别作为两个对局方,应用微分对策理论研究了系统的最优控制问题．给出了最优状态观测器和基于状态观测器的最优状态反馈控制的存在性条件．将系统的最优状态观测器和最优控制器的设计问题转化为一对Riccati方程的求解问题．研究表明最优状态观测器在一般情况下不存在．并进一步研究了基于状态观测器的次优控制问题,给出了基于LMI的优化算法．     

自适应鲁棒控制器设计新方法在电液伺服系统中的应用

提出了一种自适应鲁棒控制器设计新方法, 并运用在阀控缸电液位置伺服系统中.首先, 将含有确定、不确定、已知、未知、线性和非线性项的电液伺服系统进行完整地数学建模, 以状态空间的形式表出.然后利用本文所提的新方法设计自适应鲁棒控制器和相应的自适应律来处理所建模型中的各项元素.该控制器通过设计一个带有虚拟控制量的控制状态空间表达式并结合状态观测器来获得.设计合适的虚拟控制量, 可在任意给定条件下, 使所有的系统状态都收敛到所设计的理想状态.接着设计李亚普诺夫函数来证明闭环系统的稳定性.最后建立硬件实验平台与经典自适应鲁棒控制方法进行对比实验验证此自适应鲁棒控制器设计新方法的有效性和优势.     

Linear and nonlinear state-space controllers for magnetic levitation

The problem of precisely controlling (within sensor resolution) the height of a steel ball above the ground by levitating it against the force of gravity using an electromagnet is considered. The state variables used to model the system are the ball's position below the magnet, the ball's speed and the current in the electromagnet. Two state-space controllers are compared in terms of their performance in controlling the ball's position. The first controller is based on feedback linearization where a nonlinear state-space transformation along with nonlinear state feedback is used to linearize the system exactly. A linear controller is then used on the resulting system to control the ball's position. As a direct measurement of ball speed is not available, a nonlinear observer with linear error dynamics is used to estimate the speed. The second controller is a standard linear state feedback controller whose design is based on a linear model found by perturbing the nonlinear system model about an operating point. A linear observer is used to estimate the ball's velocity. Experimental results are presented to compare the effectiveness of the two controllers in terms of their ability to respond to step inputs and to track sinusoidal reference trajectories.     

Discrete-time track following controller design using a state-space disturbance observer

This paper presents a method to design a discrete-time track following controller using a state-space disturbance observer. To improve sensitivity, an add-on state-space disturbance observer is introduced to a LQG/LTR track following controller, which does not affect the observer and state feedback poles thereby preserving the separation principle. Therefore disturbance observer design is possible to shape the sensitivity without affecting the stability of the LQG/LTR track following controller. The proposed disturbance observer is designed in state-space without disturbance model such as plant's inverse dynamics, periodic signal generator, and Q filter. Simulation and experimental results verify the effectiveness of the proposed design method using a disturbance observer.     

New results in state estimation and regulation

An alternative technique to design linear state estimators and regulators is presented. This technique is based on transfer matrix considerations. The optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices.This approach provides further insight, displays the duality of estimation and control nicely, and bridges the state-space and frequency-domain techniques. The resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form.     

Using the filtered CARMA and CARIMA models for state-space self-tuning control

Design procedures of state-space self-tuning controllers are described for both the filtered CARMA and CARIMA models. While closely resembling the generalized approach of Clarke-Kanjilal-Mohtadi (CKM), the proposed methods use the minimum possible dimension for the associated implicit-delay state-space model, and practical issues such us feedforward for linearization, regulation, servo-following, disturbance and offset elminution are considered. The resulting conipart-mental design allows the adjustment of tuning parameters to affecl different control characteristics. For the state-space self-tuners based on the filtered CARIMA model, two different forms can be distinguished: the normal form resembles the controller configuration based on the CARMA model, while the integrating form resembles the CKM self-tuner. Satisfactory results are observed in a simulation study of using the proposed self-tuners to control the steam temperature of a solar central receiver.     

State-space approach to nonlinear predictive generalised minimum variance control

A nonlinear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process, but because of the assumed structure of the system, the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well-known GPC controller.     

一类非线性离散系统模糊控制器的分析和设计

针对一类非线性离散不确定系统,在系统状态不可测的情况下,以T-S模型描述不同状态空间的局部动态区域,并通过中心平均反模糊化、乘积推理、单点模糊化方法得到全局模糊系统模型.基于李亚普诺夫理论和线性矩阵不等式,设计了一种基于观测器的鲁棒控制器,并对离散状态下的此类系统进行了稳定分析.最后通过M ATLAB仿真,证明了该方法的有效性.     

State-space solutions to the ℋ︁∞/LTR design problem

The LTR design problem using an ??∞ optimality criterion is presented for two types of recovery errors, the sensitivity recovery error and the input-output recovery error. For both errors two different approaches are presented. First, following the classical LTR design philosophy, a Luenberger observer based approach is proposed, where the ??∞ part of the controller is appended to a standard full-order observer. Second, allowing for general controllers, an ??∞ state-space problem is formulated directly from the recovery errors. Both approaches lead to controller orders of at most 2n. In the minimum phase case, though, the order of the controllers can be reduced to n in all cases. The control problems corresponding to the various controller types are given as four different singular ??∞ state-space problems, and the solutions are given in terms of the relevant equations and inequalities.     

Quadratic robust tracking control — A Polynomial Matrix Approach

A quadratic robust tracking problem is solved using a polynomial matrix approach. Because of the possibly unstable mode of the control sequence we propose a new quadratic cost function of error and control sequences to facilitate the optimization. The optimal controller makes the plant output track the reference sequence robustly and minimizes the proposed quadratic cost function. We also present the parametrized set of suboptimal controllers which yield finite costs so that there exists the central optimal controller in the set when the parameter is set to zero. The usefulness of our proposed cost function is demonstrated by simulation examples. Our design procedure has advantages over two other possible approaches: the LQ state-space approach and the Wiener–Hopf approach which may be tried to tackle the same problem. Our approach obviates the need to construct a dynamic observer compared to the state-space approach and it is computationally attractive compared to the Wiener–Hopf approach.     

Controller design for parabolic distributed parameter systems using finite integral transform techniques

A procedure is presented for designing a control system for distributed parameter systems of parabolic type based on the reduced-order decoupled state-space model obtained by a finite integral-transform technique. A Kalman filter is used as an observer to estimate the state variables, and state feedback control is performed. The method was applied to a one-dimensional heat conduction process and a moving bed adsorber. Both state estimation and control performances were satisfactory in spite of the model and parameter uncertainties. Following this controller design approach, the searching algorithms for the optimal sensors' and the optimal actuators' allocation problems were solved. These algorithms were applied to a one-dimensional heat conduction process in order to confirm the state estimator and controller performance. The fastest state estimation could be achieved by assigning the sensors at the optimal locations and the desired state distribution was realized with a few actuators located at the optimal positions.     

Wiener-Hopf design of the optimal decoupling control system with state-space formulas

The optimal decoupling controller minimizing a given quadratic cost function is derived for the generalized plant model with two-degree-of-freedom controller configuration. A minimal set of assumptions for the existence of the optimal controller is presented in both the frequency and the state-space domains. The optimal controller formula is described in the frequency domain and the corresponding state-space formula is derived for computational efficiency.     

Uniquely identifiable state-space and ARMA parametrizations for multivariable linear systems

Multivariable systems can be represented, in a uniquely identifiable way, either by canonical forms or by so-called overlapping forms. The advantage of the latter is that they do not require the a priori estimation of a set of structural invariants (e.g. Kronecker invariants). We show here how to define uniquely identifiable overlapping parametrizations for state-space and ARMA models. We show that these parametrizations are all related to a set of intrinsic invariants, which are obtained from the Markov parameters of the system. Different forms of overlapping ARMA parametrizations are derived and their properties discussed.     

基于数据的网络化系统最优控制

针对网络介入导致的系统动态复杂性增加及建模困难等问题,提出了基于数据驱动控制的思想,独立于系统模型设计控制器。利用在线获取的系统输入/输出当前数据和历史数据,分别构造系统的输入数据矩阵和输出数据矩阵,建立两者之间的线性关系,获得当前采样时刻系统的Markov参数,将该参数代入到Markov参数形式表示的Riccati方程解中,获取最优控制增益。同时利用输入与输出之间的线性关系,构造一个控制器状态观测器,利用估计的控制器状态参与计算最优控制律。最后,在Truetime1.5和Matlab仿真平台上验证了提出的控制器是有效的。     

Time-domain approaches to multichannel optimal deconvolution

Using the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, two time-domain approaches to multichannel optimal deconvolution are presented. In the first approach, the multichannel optimal deconvolution estimators are given in the ARMA innovation filters form, where the solution of the Diophantine equations is required. Their global and local asymptotic stability is proved. In the second approach, the multichannel ARMA recursive Wiener deconvolution filters without the Diophantine equations are presented, which have asymptotic stability. The relationship between the ARMA innovation filters and ARMA Wiener deconvolution filters is discussed. Each approach can handle the deconvolution filtering, smoothing and prediction problems in a unified framework. An illustrative example and two simulation examples show their effectiveness.     

具有执行器饱和特性的不确定系统预测控制器设计

针对具有执行器饱和特征的不确定系统,提出了一种带有状态观测器的新型预测控制器设计方法.该方法在滚动优化的每一步,采用带有饱和特性的反馈控制结构得到一个最优控制律.使无穷时域性能指标最小.考虑在状态不完全已知的情况下,设计了带有状态观测器的预测控制器,并通过观测器参数调整使闭环系统渐近稳定.通过仿真实验验证了所设计控制器的有效性.