A hybrid model predictive control strategy for nonlinear plant-wide control

A plant-wide control strategy based on integrating linear model predictive control (LMPC) and nonlinear model predictive control (NMPC) is proposed. The hybrid method is applicable to plants that can be decomposed into approximately linear subsystems and highly nonlinear subsystems that interact via mass and energy flows. LMPC is applied to the linear subsystems and NMPC is applied to the nonlinear subsystems. A simple controller coordination strategy that counteracts interaction effects is proposed for the case of one linear subsystem and one nonlinear subsystem. A reactor/separator process with recycle is used to compare the hybrid method to conventional LMPC and NMPC techniques.     

Model reduction based on regional pole and covariance equivalentrealizations

In this paper a novel model reduction problem is studied for linear continuous-time time-invariant stochastic systems. The purpose of this problem is to design the reduced-order model so that it has the same dominant pole region and steady state output covariance as those of the original full-order model. The resulting reduced-order model can approximate the corresponding original full-order model in two important aspects, i.e., transient and steady state performances. Necessary and sufficient conditions for the existence of desired reduced-order models are established, and an explicit expression for these reduced order model is also presented. An illustrative example is used to demonstrate the effectiveness of the proposed design method     

具有单调性非线性项的非线性系统降维观测器设计

Based on the discussion about the existence and design method of full-order observer for systems with monotone nonlinearities, a reduced-order observer design method is developed under the assumption that a linear matrix inequality (LMI) has positive definite matrix solution and the reduced-order observer gain matrix is computed by the solution of LMI. By a linear transformation, a reduced-order observer which does not contain the information of the derivative of the system output is provided. A model is simulated and some conclusions are drawn based on the comparison of the results of reduced-order observer to that of full-order observer. The simulation shows that the design method developed by this paper has good performance.     

Output feedback control using reduced order models

A method is presented for designing linear output feedback controllers using reduced-order models. These reduced-order models retain only the modes that can be most affected by output feedback. A criterion for determining these modes is also derived. Examples are given to demonstrate the advantage of the proposed method over existing well-known techniques.     

Identification and predictive control of a multistage evaporator

A recurrent neural network-based nonlinear model predictive control (NMPC) scheme in parallel with PI control loops is developed for a simulation model of an industrial-scale five-stage evaporator. Input–output data from system identification experiments are used in training the network using the Levenberg–Marquardt algorithm with automatic differentiation. The same optimization algorithm is used in predictive control of the plant. The scheme is tested with set-point tracking and disturbance rejection problems on the plant while control performance is compared with that of PI controllers, a simplified mechanistic model-based NMPC developed in previous work and a linear model predictive controller (LMPC). Results show significant improvements in control performance by the new parallel NMPC–PI control scheme.     

Semiglobal stabilization and output regulation of singular linear systems with input saturation

The semi-global stabilization problem and output regulation problem of singular linear systems subject to input saturation are addressed. A reduced-order normal system is obtained by a standard coordinate transformation. It is further shown that the controller that solves the stabilization (output regulation) problem of the reduced-order normal systems also solves the stabilization (output regulation) problem of the original singular systems.     

Time-varying feedforward and output feedback controllers for nonlinear time-delay processes

The problem of output regulation of nonlinear time-delay processes with time-varying disturbances is considered. We present a new disturbance-dependent coordinate transformation for the linearization of nonlinear time-varying processes. In our proposed controller configuration, the modified Smith-type predictor plays the central role. Using this approach, the modified Smith-type predictor is composed of a nonlinear process model and a linear internal model. The presented feedforward and dead-time compensation can eliminate the effect of delayed disturbances on the output. With the aid of the incorporating linear internal model it aims to achieve both the asymptotic output regulation and the dead time compensation. A reduced-order controller structure for nonlinear time-delay processes can also asymptotically track the desired trajectory. Finally, the synthesis controllers are successfully implemented for chemical reactor systems.     

Stochastic feedback design for a class of non-linear singularly perturbed systems

A class of non-linear singularly perturbed systems in which the slow and the fast states and the output equations are driven by wide-band noises is considered. A stochastic observer is used in the design of an output feedback controller that stabilizes the corresponding reduced-order Markov model. This controller is, in turn, applied to the full-order system. Our previous results on weak convergence and order reduction and stability are directly applied to justify the use of the reduced-order systems and the stability of the resulting closed-loop systems in some stochastic sense.     

Robust reduced-order sliding mode observer design

In this article, a triple state and output variable transformation-based method combined with linear matrix inequality (LMI) techniques to design a new robust reduced-order sliding mode observer for perturbed linear multiple-input and multiple-output systems is developed. The state and output variables of the original system are triple transformed into suitable canonical form coordinates to facilitate the design of a reduced-order observer. The existing transformations are summarised in this study and presented systematically. A new combined observer configuration is proposed and compared with another type of observers. Global asymptotical stability LMI and sliding mode existence conditions for the coupled observer error system are derived using Lyapunov full quadratic form. Reaching and sliding modes of motion of decoupled observer error system are discussed as well. Two numerical and simulation examples are given to illustrate the usefulness of the proposed design techniques.     

Convergent algorithms for frequency weighted L2 model reduction

This paper is concerned with computing an L₂-optimal reduced-order model for a given stable multivariable linear system in the presence of input and output frequency weightings. By parametrizing a class of reduced-order models in terms of an orthogonal projection and using manifold techniques as tools, both continuous and iterative algorithms are derived and their convergence properties are established. As an application, we show that an L₂ optimal reduced-order filter in the closed-loop sense can be computed using these algorithms.     

基于扩张状态观测器的车辆横摆稳定模型预测控制器设计

针对车辆横摆稳定性控制问题,本文提出一种基于扩张状态观测器的线性模型预测控制器设计方法.首先,将非线性车辆模型线性化,建立带有模型误差干扰项的线性模型,其中线性化导致的模型误差采用扩张状态观测器估计得到,并证明了观测器的稳定性.然后基于此模型设计线性预测控制器,近似实现了非线性预测控制器的控制效果,同时降低了计算量.最后,通过不同路况下的仿真实验结果,验证了所提方法的计算性能和控制效果.     

Robust observer design for nonlinear uncertain systems with LQ regulators

For a class of uncertain systems with linear nominal dynamics and nonlinear uncertainties, it has been shown (Katayama and Sasaki 1987) that linear quadratic (LQ) state feedback regulators can be used to provide robust asymptotic stability. In this paper, we study the combined observer-controller design problem, based on the linear state feedback regulator proposed by Katayama and Sasaki (1987), so that only output feedback is needed. Both full-order and reduced-order observers are considered. For the full-order observer, we propose an algorithm to synthesize the robust observer gain matrix. It is shown that with the observer it is still possible to achieve robust asymptotic stability. For the reduced-order observer, some conditions are derived to guarantee the robust asymptotic stabilizability of the uncertain systems. The trade-off between the magnitudes of controller and observer gains is clear in our approach. An example is used to illustrate the design process of the robust controller with full-order as well as reduced-order observers.     

A method for reducing the order of multivariable stochastic systems

This correspondence considers the problem of modeling a given linear time-invariant system by a reduced-order model. The method proposed here is based on the minimization of an equation error, which leads to a linear problem. An expression for a reduced-order model is given in the case when a random input is used.     

Fine-tuning an aggregated reduced-order model that approximates a linear,time-invariant system

It is shown that the worst-case error bound, previously developed for linear, time-invariant aggregated reduced-order models, can be used to obtain an output matrix that minimizes the model's worse-case output error while holding fixed the coefficient matrices in the model's differential equation. Two example problems are given to illustrate the fine-tuning improvement in the worst-case output error.     

Global output feedback tracking for nonlinear systems in generalized output-feedback canonical form

A global output feedback dynamic compensator is proposed for stabilization and tracking of a class of systems that are globally diffeomorphic into systems which are in generalized output-feedback canonical form. This form includes as special cases the standard output-feedback canonical form and various other forms considered previously in the literature. Output-dependent nonlinearities are allowed to enter both additively and multiplicatively. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced-order observer and a backstepping controller can be designed to achieve asymptotic tracking. For the special case of linear systems, the designed dynamic controller reduces to the standard reduced-order observer and linear controller. This is the first global output-feedback tracking results for this class of systems.     

A trajectory analysis of near aggregation

The basic idea of aggregation is that there exists a reduced-order model such that, for an appropriate initial condition, the trajectories of the reduced-order model are linear combinations of the trajectories of the full-order model. The authors study systems which do not aggregate exactly, but which `nearly aggregate'. It is shown that for nearly aggregable systems, there exists a reduced-order model such that, for an appropriate initial condition, the trajectories of the reduced-order model are near a linear combination of the trajectories of the full-order model     

Robustness of linear feedback control systems to unmodelled high-frequency dynamics

A basic issue in the control of linear time-invariant plants is the effect of neglected high-frequency dynamics on the performance, in particular on the closed-loop stability, of the control system. In this paper, the robustness of various output feedback control designs, based on a reduced-order model with neglected high-frequency dynamics, is investigated using singular perturbation techniques. A general robust design rule is to avoid static output feedback for systems with unmodelled high-frequency dynamics. From a frequency-domain standpoint, the robust design rule is to avoid closing high-frequency plant loops by using strictly proper controllers or controllers with a low-pass filtering property.     

On reduced-order adaptive output error identification and adaptive IIR filtering

The reduced-order application of Landau's adaptive output error identifier results in a perturbed error system where the perturbation signal is a moving average of the unmodeled portion of the unknown plant output (or desired signal in adaptive filter parlance). It is proven in this paper that if this perturbation signal is sufficiently small and a reduced-order dimension model is sufficiently excited, then the output and parameter estimates of this adaptive identifier/filter remain bounded. The influence of various operating conditions on this quantitatively defined bound are noted. This robustness property is crucial in all real applications, which due to nonlinearities and distributed effects are subject to reduced-order modeling.     

Finite-dimensional control of linear parabolic systems with unbounded output operators

In this paper, we studyH control of linear parabolic systems with unbounded output operators. Our aim is to construct a finite-dimensional stabilizing controller for the linear parabolic system that makes the H norm of the closed-loop transfer function less than a given positive number delta. To this end, we first derive a finite-dimensional reduced-order system for the linear parabolic system. Then, for the reduced-order model, we construct a stabilizing controller that makes theH norm of the closed-loop transfer function less than another positive number. It is proved that the finitedimensional controller together with a residual mode filter plays a role of a finite-dimensional stabilizing controller that makes theH norm of the closed-loop transfer function less than delta for the original linear parabolic system, if the order of residual mode filter is chosen sufficiently large.     

离散随机模型降阶的最小条件信息损失方法

针对随机系统的模型降阶问题,从分析离散线性随机状态方程模型中的条件信息描述机制入手,讨论了模型状态集聚过程中系统的平均条件信息损失.运用在模式识别领域中获得成功应用的最小信息损失准则得出了一种新的模型降阶信息论方法———基于状态集聚的最小条件信息损失方法,并讨论了降阶模型阶次的选择.分析表明,当原系统是渐近稳定时,由该方法得出的降阶模型也是渐近稳定的.该方法运用简单,仿真研究也表明由该方法得出的降阶模型具有良好的近似性能.