Integrated identification and robust control

A framework for integrated identification and control is presented. As part of this framework, frequency domain uncertainty bounds are derived for robust stability tests, a robust stability test for elliptical bounds is developed for SISO systems, a methodology for estimating controller performance is derived, and an optimal experiment design methodology for control-relevant identification is outlined. An example is presented to illustrate how the tools of the framework fit together.     

Improving performance and stability of MPC relevant identification methods

Model Predictive Control (MPC) Relevant Identification (MRI) methods are a good option for identification, if there is model structure mismatch. Herein a new MRI method, named Enhanced Multistep Prediction Error Method (EMPEM), is proposed. EMPEM combines the best characteristics of others MRI methods in a single algorithm. It was developed to identify either closed-loop or open-loop systems; its convergence and stability make it perform better than the other presented methods. To show the advantages of EMPEM, a comparison is made against two other methods (one MRI and one PEM). The statistical analysis indicates that in the cases studied, the performance and the robustness of the new method is equal or better than the other ones.     

Identification and robust control for systems with ellipsoidal parametric uncertainty by convex optimization

In this paper, sufficient conditions for robust output feedback controller design for systems with ellipsoidal parametric uncertainty are given in terms of solutions to a set of linear matrix inequalities (LMIs) Performance specifications are in terms of combined pole placement with sensitivity function shaping in the H₂ or H_∞ norm. Furthermore, an optimal input design technique for parameter estimation that is integrated into the robust control design is employed in this paper. This means that performance specifications on the closed‐loop transfer functions are translated into the requirements on the input signal spectrum. The simulation results show the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Time domain identification for robust control

In this paper, we are concerned with a problem of robust control-oriented system identification in the time domain. Based on the well-known Schur-Takagi-AAK Theorem, we propose a linear algorithm to obtain the nominal model of the plant to be identified and the minimal bound of the uncertainty of the nominal model error which is measured by H^∞-norm. It is also shown that, in the model set defined by the nominal model and the uncertainty bound, there exists at least one model which matches the prescribed input-output data given in the time domain.     

Least costly identification experiment for control

All approaches to optimal experiment design for control have so far focused on deriving an input signal (or input signal spectrum) that minimizes some control-oriented measure of plant/model mismatch between the nominal closed-loop system and the actual closed-loop system, typically under a constraint on the total input power. In practical terms, this amounts to finding the (constrained) input signal that minimizes a measure of a control-oriented model uncertainty set. Here we address the experiment design problem from a “dual” point of view and in a closed-loop setting: given a maximum allowable control-oriented model uncertainty measure compatible with our robust control specifications, what is the cheapest identification experiment that will give us an uncertainty set that is within the required bounds? The identification cost can be measured by either the experiment time, the performance degradation during experimentation due to the added excitation signal, or a combination of both. Our results are presented for the situation where the control objective is disturbance rejection only.     

Relations between uncertainty structures in identification for robust control

Various techniques of system identification exist that provide a nominal model and an uncertainty bound. An important question is what the implications are for the particular choice of the structure in which the uncertainty is described when dealing with robust stability/performance analysis of a given controller and when dealing with robust synthesis. It is shown that an amplitude-bounded (circular) uncertainty set can equivalently be described in terms of an additive, Youla parameter and ν-gap uncertainty. As a result, the choice of structure does not matter provided that the identification methods deliver optimal uncertainty sets rather than an uncertainty bound around a prefixed nominal model. Frequency-dependent closed-loop performance functions based on the uncertainty sets are again bounded by circles in the frequency domain, allowing for analytical expressions for worst-case performance and for the evaluation of the consequences of uncertainty for robust design. The results can be used to tune optimal experimental conditions in view of robust control design and in the further development of experiment-based robust control design methods.     

For model-based control design, closed-loop identification gives better performance

We compare open loop versus closed loop identification when the identified model is used for control design, and when the system itself belongs to the model class, so that only variance errors are relevant. Our measure of controller performance (which is used as our design criterion for identification) is the variance of the error between the output of the ideal closed loop system (with the ideal controller) and that of the actual closed loop system (with the controller computed from the identified model). Under those conditions, we show that, when the controller is a smooth function of the input-output dynamics and the disturbance spectrum, the best controller performance is achieved by performing the identification in closed loop with an operating controller that we characterize. For minimum variance and model reference control design criteria, we show that this ‘optimal operating controller for identification’ is the ideal controller. This then leads to a suboptimal but feasible iterative scheme.     

Model validation for control and controller validation in a prediction error identification framework—Part II: illustrations

In this paper, we illustrate our new results on model validation for control and controller validation in a prediction error identification framework, developed in a companion paper (Gevers et al., Automatica (2003) 39(3) pii: S005-1098(02)00234-0), through two realistic simulation examples, covering widely different control design applications. The first is the control of a flexible mechanical system (the Landau benchmark example) with a tracking objective, the second is the control of a ferrosilicon production process with a disturbance rejection objective.     

Dynamic input signal design for the identification of constrained systems

In current model predictive control (MPC) practise, the accuracy of the model from system identification is often the crucial factor for the final success. This makes the input signal design a very important step in MPC applications. Because the identification task should move the outputs within some constraints, a constrained design method is needed. Previous constrained signal design methods are usually based on the steady-state gain matrix of a process. Ignoring the system dynamics makes these designs either too conservative when the dynamics are overdamped or allows them to violate the output constraints in the case of underdamped dynamics. In order to address these problems, a new design method making use of the prior approximate estimate of the system dynamics is proposed in this paper. Furthermore, an iterative method of signal design for identification experiments is proposed, and a criterion is defined to compare the accuracy of two successive dynamic models. An example on a subsystem of the challenging Tennessee Eastman process is used to prove the effectiveness of the proposed method.     

SM identification of approximating models for H∞ robust control

Set Membership (SM) H_∞ identification of mixed parametric and non-parametric models is investigated, aimed to estimate a low-order approximating model and an identification error, giving a measure of the unmodelled dynamics in a form well suited for H_∞ control methodologies. In particular, the problem of estimating the parameters of the parametric part and the H_∞ bound on the modelling error is solved using frequency domain data, supposing l_∞ bounded measurement errors and that the system to be identified is exponentially stable. The effectiveness of the proposed procedure is tested on some numerical examples, showing the advantages of the proposed methods over the existing non-parametric H_∞ identification approaches, in terms of lower model order and of tightness in the modelling error bounds. Copyright © 1999 John Wiley & Sons, Ltd.     

Dimensional analysis for robust control of planar vehicle dynamics

Most engineered systems with similar functions, which are designed under strict external constraints, share similar dynamics. Using a dimensionless model as system representation, a dimensionless robust controller can be designed and implemented for a class of dynamically similar systems that are different in physical dimension. Dimensionless transformations of timescale, inputs and outputs determine a nominal plant model and plant‐to‐plant uncertainties in a dimensionless form. Using parameter‐dependent normalization, a normalized dimensionless model can be derived that has lower levels of plant‐to‐plant uncertainty than previous formulations (IEEE Trans. Contr. Syst. Technol. 2005; 13 (4):624–630). The benefit of this dimensional analysis is demonstrated by the dynamic analysis of different types of planar vehicle systems. Numerical results show that, by using dimensional analysis, it is possible to obtain a controller that is robust to plant‐to‐plant parametric uncertainties among specific classes of systems designed with widely varying physical dimensions. Copyright © 2007 John Wiley & Sons, Ltd.     

不确定时滞系统的全局鲁棒最优滑模控制

针对一类不确定性时滞系统, 研究线性二次型最优调节器的鲁棒性设计问题. 首先基于级数近似方法, 将原标称时滞系统的最优调节器问题转化为迭代求解一族不含时滞的两点边值问题, 从而获得标称时滞系统最优控制的近似解. 然后将滑模控制理论应用于最优调节器的设计, 使得系统对于不确定性具有全局的鲁棒性, 并且其理想滑动模态与标称系统的最优闭环控制系统相一致, 从而实现了全局鲁棒最优滑模控制. 仿真示例将所提出的方法与相应的二次型最优控制进行比较, 验证了该方法的有效性和优越性.     

Observer-based robust optimal control for helicopter with uncertainties and disturbances

Unknown model uncertainties and external disturbances widely exist in helicopter dynamics and bring adverse effects on control performance. Optimal control techniques have been extensively studied for helicopters, but these methods cannot effectively handle flight control problems since they are sensitive to uncertainties and disturbances. This paper proposes an observer-based robust optimal control scheme that enables a helicopter to fly optimally and reduce the influence of unknown model uncertainties and external disturbances. A control Lyapunov function (CLF) is firstly constructed using the backstepping method, then Sontag's formula is utilized to design an inverse optimal controller to stabilize the nominal system. Furthermore, it is stressed that the radial basis function (RBF) neural network is introduced to establish an observer with adaptive laws, approximating and compensating for the unknown model uncertainties and external disturbances to enhance the robustness of the closed-loop system. The uniform ultimate boundedness of the closed-loop system is ensured using the presented control approach via Lyapunov stability analysis. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control strategy.     

MPC relevant identification––tuning the noise model

The philosophy of identification by minimizing an objective function that is commensurate with the control objective function is called control relevant identification. The control relevant method studied in this paper minimizes a multistep ahead prediction error objective function, suitable for model predictive controllers, to obtain an optimal multistep ahead predictor. It is shown that the method described in this paper provides better designed performance of the controller. A number of properties of this method in the context of FIR models are presented in this paper. The noise model plays a pivotal role in determining the performance of multistep ahead prediction errors. A method for tuning the noise model using the proposed control relevant method is presented in this paper.     

System identification for generic model control

System identification methods build mathematical models of dynamical systems based on observed data. The intended use of the model should always be reflected in the methods and techniques used for identification. In this paper an identification scheme is derived for the case where the model is going to be used for GMC controller design. The aim of GMC control is to make the output approach a setpoint along a given desired trajectory. This is reflected in the identification scheme which is non-standard in two ways. Firstly, the emphasis is on the output trajectories of the models, and secondly we try to make the prediction errors follow an error trajectory determined by the controller parameters. Simulation studies are included which show that the derived identification scheme performs well.     

组合航天器的姿态控制与结构鲁棒控制分配

针对空间臂捕获未知目标航天器后的控制问题, 本文提出了一种新方案. 基于动量的估计方法和递推最小二乘 算法在线估计组合式航天器的惯性参数, 并通过一种基于比例微分反馈的直接参数方法处理组合姿态控制系统, 此方法 给出了完整的参数化双反馈增益. 考虑到推力器的配置和配置矩阵的测量误差, 提出了具有多面体和多胞体形式摄动的 鲁棒控制分配方法. 最后, 数值仿真结果验证了所提方法的有效性.     

Input signal design for identification of max-plus-linear systems

Max-plus-linear systems efficiently describe the dynamics of event time sequences of a class of discrete event systems. The present contribution addresses the problem of designing adequate input signals for state space identification of max-plus-linear systems. It is shown that the input signal design problem can be rewritten as a set of upper bound constraints and therefore solved using an existing algorithm. This input signal design method allows to incorporate additional objectives and constraints, e.g. minimum or maximum input event separation, time order constraints, etc., which are desirable or even required for the input signals and the resulting process behavior.     

An optimal control approach to robust tracking of linear systems

In our early work, we show that one way to solve a robust control problem of an uncertain system is to translate the robust control problem into an optimal control problem. If the system is linear, then the optimal control problem becomes a linear quadratic regulator (LQR) problem, which can be solved by solving an algebraic Riccati equation. In this article, we extend the optimal control approach to robust tracking of linear systems. We assume that the control objective is not simply to drive the state to zero but rather to track a non-zero reference signal. We assume that the reference signal to be tracked is a polynomial function of time. We first investigated the tracking problem under the conditions that all state variables are available for feedback and show that the robust tracking problem can be solved by solving an algebraic Riccati equation. Because the state feedback is not always available in practice, we also investigated the output feedback. We show that if we place the poles of the observer sufficiently left of the imaginary axis, the robust tracking problem can be solved. As in the case of the state feedback, the observer and feedback can be obtained by solving two algebraic Riccati equations.