Model predictive control using reduced order models: Guaranteed stability for constrained linear systems

The problem of controlling a high-dimensional linear system subject to hard input and state constraints using model predictive control is considered. Applying model predictive control to high-dimensional systems typically leads to a prohibitive computational complexity. Therefore, reduced order models are employed in many applications. This introduces an approximation error which may deteriorate the closed loop behavior and may even lead to instability. We propose a novel model predictive control scheme using a reduced order model for prediction in combination with an error bounding system. We employ the explicit time and input dependent bound on the model order reduction error to achieve design conditions for constraint fulfillment, recursive feasibility and asymptotic stability for the closed loop of the model predictive controller when applied to the high-dimensional system. Moreover, for a special choice of design parameters, we establish local optimality of the proposed model predictive control scheme. The proposed MPC approach is assessed via examples demonstrating that a good trade-off between computational efficiency and conservatism can be achieved while guaranteeing constraint satisfaction and asymptotic stability.     

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.     

Design of low order estimators using reduced models

A technique is presented for obtaining low order state estimators for time-invariant, linear systems where estimates of a restricted set of state variables are required. The technique is based on reducing the order of the system and then designing a Kalman filter for the reduced order system.     

Computer determination of low order models for high order systems

An investigation directed at finding the best low-order model which approximates a given high-order system is presented. New insight is gained into the cost paid for the simplicity of the model and in the accuracy of the transient response of the model related to the magnitude of a cost function.The problem is solved in the time domain by finding the best pole and zero locations of the model which minimize a defined error criterion. The computer is used to estimate these parameters, via a parameter minimization program. A number of examples are included.     

Viability of methods for generating stable reduced order models

Various methods for generating stable reduced order models are shown to have a serious disadvantage, in that the reduced model may approximate the nondominant poles of the system and hence lead to erroneous approximations. An example is given to compare these methods with the standard Pade approximation method for which this disadvantage does not exist.     

永磁同步直线电机的分数阶超螺旋滑模控制

为了提高永磁同步直线电机的跟踪性能,增强系统的鲁棒性,本文提出了分数阶超螺旋滑模控制策略.首先,针对外部扰动以及系统的未知状态设计广义超螺旋观测器,其能够精确估计永磁同步直线电机的速度和外部扰动.其次,将分数阶理论和终端滑模控制理论相结合,提出有限时间收敛的分数阶超螺旋滑模控制器,以实现永磁同步直线电机的跟踪控制.最后,通过仿真对比验证所提方案的有效性.     

On the class of reduced order models obtainable by projection

The paper investigates the properties of general reduced order models obtained by projection of a higher order system. It answers questions such as, are any two models of different orders related by a projection? Is it possible to obtain the same reduced order model using different projections? How to find, if it exists, a projection that relates the two models?, etc. It is shown that answers to those questions can be obtained by investigating the properties of a certain matrix pencil. The key tool is the Kronecker canonical form, and in some cases of square systems the problem becomes that of generalized eigenvalues.     

The design of optimal reduced order stochastic observers fordiscrete-time linear systems

The minimum variance state estimation of linear discrete-time systems with random white noise input and partially noisy measurements is investigated. An observer of minimal-order that attains the minimum-variance estimation error is found. The structure of this observer is shown to depend strongly on the geometry of the system. This geometry dictates the length of the delays that are applied on the measurements in order to obtain the optimal estimate. The transmission properties of the observer are investigated for systems that are left invertible and free of measurement noise. An explicit expression is found for the transfer function matrix of the observer, from which a simple solution to the linear discrete-time singular optimal filtering problem is obtained     

A generalized constraint reduction method for reduced order MBS models

In this paper we deal with the problem of ill-conditioned reduced order models in the context of redundant formulated nonlinear multibody system dynamics. Proper Orthogonal Decomposition is applied to reduce the physical coordinates, resulting in an overdetermined system. As the original set of algebraic constraint equations becomes, at least partially, redundant, we propose a generalized constraint reduction method, based on the ideas of Principal Component Analysis, to identify a unique and well-conditioned set of reduced constraint equations. Finally, a combination of reduced physical coordinates and reduced constraint coordinates are applied to one purely rigid and one partly flexible large-scale model, pointing out method strengths but also applicability limitations.     

Entropy coefficient of determination for generalized linear models

The objective of the present paper is to propose a predictive power measure for generalized linear models (GLMs). First, basic predictive power measures for GLMs are compared with respect to some desirable properties. We propose a generalized coefficient of determination for GLMs, which is referred to as the entropy coefficient of determination (ECD). The advantage of the measure is discussed in the GLM framework. Second, the asymptotic properties of the maximum likelihood estimator of ECD are discussed. Third, ECD is applied to GLMs with polytomous response variables. Finally, discussions and a conclusion to this study are provided.     

Stable biased reduced order models using the Routh method of reduction

A generalization of the Routh method of reduction is introduced for obtaining stable reduced order models. The reduced models may be ‘ biased ’ in the sense that they may approximate the initial transient response of the high order system more closely than the steady-state response, and vice-versa. Given the desired order of the reduced model, the method of this paper produces a number of stable reduced models which approximate the high order system. The method is easily extended to multi-variable systems. Examples are given to illustrate the method and to make comparisons with other methods of reduction.     

Tangent-phase continued-fraction expansion for stable reduced models of linear discrete-time systems

The tangent-phase continued-fraction expansion for stable reduced models is based on the tangent-phase frequency response to the expansion and the factorization technique to obtain reduced models. In this paper, we propose a new procedure for deriving stable and minimum-phase reduced z-transfer functions by the tangent-phase continued-fraction expansion. The procedure is based on transforming the z-domain tangent-phase function to the p domain, where p = z + z^?1?2, and then expanding the p-domain tangent-phase function into a modified continued fraction. An example is given to illustrate the utility of the procedure.     

A symbolic matrix decomposition algorithm for reduced order linear fractional transformation modelling

In this paper an algorithm that provides an equivalent, but of reduced order, representation for multivariate polynomial matrices is given. It combines ideas from computational symbolic algebra, polynomial/matrix algebraic manipulations and information logic. The algorithm is applied to the problem of finding minimal linear fractional transformation models. Statistical performance analysis of the algorithm reveals that it consistently outperforms currently available algorithms.     

Controllability analysis and optimal control of biomass drying with reduced order models

Complex industrial processes such as the drying of combustible biomass can be modeled with partial differential equations. Due to their complexity, it is not straightforward to use these models for the analysis of system properties or for solving optimal control problems. We show reduced order models can be derived and used for these purposes for industrial drying processes.     

A new set of invariants for linear systems--Application to reduced order compensator design

A new set of invariants for linear systems, weighting the contribution of each state component to the inherent closed-loop LQG behavior of the system is presented, together with applications to model order reduction and reduced order compensator design.     

基于黑洞多目标进化算法的永磁直线同步电机优化设计

应用一种改进的黑洞多目标进化算法(MOBH),实现对圆筒型无槽无铁芯直线永磁同步电机(LPMSM)的多目标优化设计.黑洞进化算法在不同Pareto区域的收敛速度、种群多样性、种群收敛性和亚种群获取等方面具有良好的性能.在分析无槽无铁芯圆筒直线电机的电磁解析模型和MOBH算法基础上,建立电机推力、推力体积比、铜损(效率)...     

Routh approximant state space reduced order models for systems with uncontrollable modes

The problem of deriving time domain reduced order models to systems which are not completely state controllable is considered, and the procedure does not involve the computation of eigenvaiues and eigenvectors of the high-order system. The details are explained and illustrated via a numerical example.     

Dynamical optimization using reduced order models: A method to guarantee performance

Many methods employed for the modeling, analysis, and control of dynamical systems are based on underlying optimization schemes, e.g., parameter estimation and model predictive control. For the popular single and multiple shooting optimization approaches, in each optimization step one or more simulations of the commonly high-dimensional dynamical systems are required. This numerical simulation is frequently the biggest bottleneck concerning the computational effort.In this work, systems described by parameter dependent linear ordinary differential equations (ODEs) are considered. We propose a novel approach employing model order reduction, improved a posteriori bounds for the reduction error, and nonlinear optimization via vertex enumeration. By combining these methods an upper bound for the objective function value of the full order model can be computed efficiently by simulating only the reduced order model. Therefore, the reduced order model can be utilized to minimize an upper bound of the true objective function, ensuring a guaranteed objective function value while reducing the computational effort.The approach is illustrated by studying the parameter estimation problem for a model of an isothermal continuous tube reactor. For this system we derive an asymptotically stable reduction error estimator and analyze the speed-up of the optimization.     

Fault detection in linear discrete dynamic systems by a reduced order generalized-likelihood-ratio method

The detectability by conventional step-hypothesized generalized-likelihood-ratio (SHGLR) method for detection of a parameter change (fault detection) in a linear discrete dynamic system is analysed and it is shown that a weakly-diagnosable-space (WDS) exists for dynamics and sensor faults. Based on the fault detectability, a reduced order SHGLR method is then developed which highly improves the detection rate and speed. In the same framework of the GLR method, another reduced order detection scheme is given, which makes the most use of the information about the input and the state of the system to raise the detectability for faults for the case where the step hypothesis cannot be applied effectively.