Closed-loop subspace-based identification algorithm using third-order cumulants

The problem of closed-loop system identification for coloured noise system without any knowledge of feedback controller is considered. We develop a solution to this problem in the framework of subspace identification based on high-order cumulants. The key of the developed algorithm is using the properties that the third-order cumulants are insensitive to any coloured Gaussian noises. By post-multiplying a suitable instrumental variable to the noise terms, the cross third-order cumulants are constructed that become zero when the noises are Gaussian distributed, and meanwhile the column rank of extended observability matrix is maintained. Thus, the standard subspace identification algorithms can be extended to closed-loop system corrupted by arbitrary coloured noises. A numerical simulation is presented to demonstrate the proposed algorithm.     

Non-linear generalised minimum variance control state space design for a second-order Volterra series model

This paper presents a non-linear generalised minimum variance (NGMV) controller for a second-order Volterra series model with a general linear additive disturbance. The Volterra series models provide a natural extension of a linear convolution model with the nonlinearity considered in an additive term. The design procedure is entirely carried out in the state space framework, which facilitates the application of other analysis and design methods in this framework. First, the non-linear minimum variance (NMV) controller is introduced and then by changing the cost function, NGMV controller is defined as an extended version of the linear cases. The cost function is used in the simplest form and can be easily extended to the general case. Simulation results show the effectiveness of the proposed non-linear method.     

Extensions to the design of sampled integrating regulators

The stability properties and design rules for a class of robust integrating regulators are considered. Passivity arguments are employed to define bounds on the parameters of an extended PID regulator and to establish the robustness of the closed-loop stability properties in the presence of sector-bounded non-linear elements in the feedback loop. This approach allows linear and non-linear single-input/single-output and multi-input/multi-oulput systems to be considered in the same framework.     

Identification of delayed system using instrumental variable method

System identification uses system inputs and outputs to raise mathematical models.Various techniques of system identification exist that offer a nominal model and an uncertainty bound.Many practical systems such as thermal processes & chemical processes have inbuilt time delay.If the time delay used in the system model for controller design does not concur with the actual process time delay,a closed-loop system may be unstable or demonstrate unacceptable transient response characteristics so here the time delay is assumed to be time-invariant. This paper proposes on-line identification of delayed complex/uncertain systems using instrumental variable(Ⅳ) method.Parametric uncertainty has been considered which may be represented by variations of certain system parameters over some possible range.This method allows consistent estimation when the system parameters are associated with the noise terms,as the IV methods(IVM’s)usually make no assumption on the noise correlation configuration.The faster convergence of the parameters including noise terms has been proved in this paper.Iterative prefiltering(IP)method has also been used for the identification of the delayed uncertain system and the graphical results given in this paper demonstrate that the convergence results are inferior to the instrumental variable method.     

Projection based MIMO control performance monitoring: I—covariance monitoring in state space

In this paper we propose a new control performance monitoring method based on subspace projections. We begin with a state space model of a generally non-square process and derive the minimum variance control (MVC) law and minimum achievable variance in a state feedback form. We derive a multivariate time delay (MTD) matrix for use with our extended state space formulation, which implicitly is equivalent to the interactor matrix. We show how the minimum variance output space can be considered an optimal subspace of the general closed-loop output space and propose a simple control performance calculation which uses orthogonal projection of filtered output data onto past closed-loop data. Finally, we propose a control performance monitoring technique based on the output covariance and diagnose the cause of suboptimal control performance using generalized eigenvector analysis. The proposed methods are demonstrated on a few simulated examples and an industrial wood waste burning power boiler.     

Regulator configuration design by means of model predictive control

This paper presents new concepts and methods for regulator configuration design for stable and unstable multivariable systems. Nowadays the self-definitions of dynamic relative gain rarely consider the interaction influences of closed-loop controllers, and the interaction measurement can be also showed from the effects from controlled variables to manipulated variables through closed-loop controllers. Model Predictive Control (MPC) is an important multivariable centralized control strategy; by means of SFPC (State Feedback Predictive Control) and MGPC (Multivariable Generalized Predictive Control), two closed-loop interaction analysis methods are first put forward. Based on the control rate optimized, two inverse normalized gain arrays are obtained from SFPC and MGPC which show the dynamic effects of controlled variables on manipulated variables. With the inverse normalized gain arrays, the regulator configuration design of unstable systems can be carried out due to the effect of multivariable centralized control. Finally the advantages and effectiveness of proposed interaction analysis approaches are highlighted via several examples.     

A general co-ordinate transformation framework for multi-axis motion control with applications in the testing industry

Transforming feedback variables into a different co-ordinate system is a practical and effective way of simplifying controller design for multi-axis motion systems. A general transformation framework is presented in this paper for parallel-actuator systems, including those with overconstraint (i.e. with more actuators than rigid body degrees-of-freedom). Force control for the extra axes is considered, and appropriate transformations from measured actuator positions and forces to position and force variables used for control are given, although solutions are not unique. A number of heuristic techniques which are already used in the structural testing industry can be formalised as part of the new framework; examples are given in the paper. The framework also allows these techniques to be extended to new applications, particularly those with overconstraint.     

基于混沌多项式的指令鲁棒优化及在飞行控制中的应用

本文提出一种新的方法对随机系统进行运动预测和控制指令设计, 该方法可以充分利用已知信息设计控 制指令以提高闭环随机系统的鲁棒性. 首先采用混沌多项式对随机信息进行数学表述, 并利用Galerkin投影法将随 机变量的混沌多项式引入常微分方程中. 然后, 将随机变量的均值和方差考虑至优化问题的成本函数中, 并利用伪 谱法对控制指令进行鲁棒优化. 最后, 将该方法应用于飞行器的动力学预测以及控制指令设计. 仿真结果表明, 该 方法能够预测飞行器飞行过程中不确定性的演化, 其精度与蒙特卡罗方法相当, 并且计算效率更高. 此外, 获得的 控制指令对存在不确定参数或初始条件的随机系统具有强鲁棒性.     

Identification of dynamic models in complex networks with prediction error methods—Basic methods for consistent module estimates

The problem of identifying dynamical models on the basis of measurement data is usually considered in a classical open-loop or closed-loop setting. In this paper, this problem is generalized to dynamical systems that operate in a complex interconnection structure and the objective is to consistently identify the dynamics of a particular module in the network. For a known interconnection structure it is shown that the classical prediction error methods for closed-loop identification can be generalized to provide consistent model estimates, under specified experimental circumstances. Two classes of methods considered in this paper are the direct method and the joint-IO method that rely on consistent noise models, and indirect methods that rely on external excitation signals like two-stage and IV methods. Graph theoretical tools are presented to verify the topological conditions under which the several methods lead to consistent module estimates.     

An improved model predictive control approach based on extended non-minimal state space formulation

This paper presents a new design method of model predictive control (MPC) based on extended non-minimal state space models, in which the measured input and output variables, their past values together with the defined output errors are chosen as the state variables. It shows that this approach does not need the design of an observer to access the state information any more and by augmenting the process model and its objective function to include the changes of the system state variables, the control performances are superior to those of the controller that does not bear this feature. Furthermore, closed-loop transfer function representation of the model predictive control system facilitates the use of frequency response analysis methods for the nominal control performances of the system.     

Comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models

The estimation of the parameters of a transfer function model is considered. Relationships between the total least squares (TLS) and instrumental variable (IV) approaches are outlined. Both methods are able to compute strongly consistent parameter estimates. TLS can be considered as a variation on the IV method where the IV are functions of the time instant and the estimated model parameters. TLS computes strongly consistent estimates of the true model parameters if the outputs and possibly the inputs are independently disturbed by discrete, stationary white noise with zero mean and equal variance. The IV need not be generated. Hence TLS is much simpler to use but more restrictive (IV allows arbitrary noise models) and computationally not so attractive. Next, simulation results are presented comparing the short sample accuracy properties of both methods. When the outputs and possibly the inputs are disturbed by stationary zero mean while noise, TLS outperforms the ordinary IV methods. The accuracy becomes comparable by extending the IV sufficiently. The superiority of TLS is particularly clear in cases where the zeros of the polynomial operating on the outputs are close to the unit circle or where both the inputs and outputs are noisy.     

Projection based MIMO control performance monitoring: II––measured disturbances and setpoint changes

In this paper the performance monitoring method based on subspace projections from Part I [J. Proc. Cont. 13 (2003) 739] is extended to include measured disturbances and setpoint changes. It was shown in [J. Proc. Cont. 13 (2003) 739] that the minimum variance output space is an optimal subspace of the general closed-loop output space and that orthogonal projections of filtered output data onto past closed-loop output data can be used to assess the performance of feedback controllers. This paper demonstrates that the same framework is directly applicable to systems with measured disturbances by augmenting the data matrix with those measured disturbances. Furthermore, it provides a means of separating suboptimal control performance between that arising from unmeasured disturbances and that due to measured disturbances. The effect of setpoint changes on control performance can be calculated as special feedforward variables. The controller is generally time-varying to include the case of model predictive control. A simulation example and an industrial boiler process are used to demonstrate the effectiveness of the proposed method.     

Nonlinear robust control of a small-scale helicopter on a test bench

A nonlinear robust controller design procedure is presented, which is designed to simultaneously satisfy multiple conflicting closed-loop performance specifications. Significantly, a robust performance specification for the experimental system, developed for studying the attitude control of a small-scale helicopter in our previous work, is discussed quantitatively. The robust performance specifications and nominal multiple closed-loop performance specifications are conflicting. Use of the Convex Integrated Design (CID) method can provide, where feasible, a single closed-loop controller which satisfies a set of multiple conflicting performance specifications. However, the resultant controller has a complex form. Here, the standard CID method is extended to a more general control system framework to solve the conflicting simultaneous performance design problem. When compared with the standard CID design, the extended CID design procedure generates a relatively simple closed-loop controller. Finally, the synthesised controller is tested in simulation and is validated with an experimental small-scale test helicopter, demonstrating the performance of the proposed controller.     

Solution of the discrete-time stochastic optimal control problem in the 2-domain

The design of discrete-time optimal multivariate systems is considered in the z-domain. The constant plant can be non-square, unstable and/or non-minimum phase and feedback system dynamics can be modelled. The stationary coloured noise processes are assumed to be represented by discrete rational spectral densities. The system can contain transport delay elements and the effects of plant saturation can be limited by the choice of performance criterion. The system inputs are assumed to contain both stochastic and deterministic components.

The two-stage design procedure is original and it enables the stochastic and deterministic control functions to be separated, A performance criterion is first defined which is insensitive to the deterministic signals and this defines the closed-loop optimal controller. The resulting closed-loop system acts as an optimum regulator to minimize the effects of stochastic disturbances. A second tracking error performance criterion is then specified which determines the optimal reference input to the closed-loop system. This reference signal is generated by two further discrete-time controllers. The first controller ensures that the plant is following a desired trajectory and the second acts as a feedforward controller to counteract measurable disturbances. The minimum variance regulators of Astrom (1970) and Peterka (1972) are also derived from these results.     

Stability of two-dimensional feedback systems

Stability conditions for discrete-time linear dynamical systems in two independent variables are considered. A new proof of a known condition is given, enabling a more transparent interpretation. It is shown that closed-loop stability of a feedback system can be determined from open-loop information by using an infinite family of Nyquist plots. On the basis of these results, the extension of classical design methods, using root loci and frequency response, is advocated.     

A survey of multidisciplinary design optimization methods in launch vehicle design

Optimal design of launch vehicles is a complex problem which requires the use of specific techniques called Multidisciplinary Design Optimization (MDO) methods. MDO methodologies are applied in various domains and are an interesting strategy to solve such an optimization problem. This paper surveys the different MDO methods and their applications to launch vehicle design. The paper is focused on the analysis of the launch vehicle design problem and brings out the advantages and the drawbacks of the main MDO methods in this specific problem. Some characteristics such as the robustness, the calculation costs, the flexibility, the convergence speed or the implementation difficulty are considered in order to determine the methods which are the most appropriate in the launch vehicle design framework. From this analysis, several ways of improvement of the MDO methods are proposed to take into account the specificities of the launch vehicle design problem in order to improve the efficiency of the optimization process.     

On nonlinearity in neural encoding models applied to the primary visual cortex

Within the regression framework, we show how different levels of nonlinearity influence the instantaneous firing rate prediction of single neurons. Nonlinearity can be achieved in several ways. In particular, we can enrich the predictor set with basis expansions of the input variables (enlarging the number of inputs) or train a simple but different model for each area of the data domain. Spline-based models are popular within the first category. Kernel smoothing methods fall into the second category. Whereas the first choice is useful for globally characterizing complex functions, the second is very handy for temporal data and is able to include inner-state subject variations. Also, interactions among stimuli are considered. We compare state-of-the-art firing rate prediction methods with some more sophisticated spline-based nonlinear methods: multivariate adaptive regression splines and sparse additive models. We also study the impact of kernel smoothing. Finally, we explore the combination of various local models in an incremental learning procedure. Our goal is to demonstrate that appropriate nonlinearity treatment can greatly improve the results. We test our hypothesis on both synthetic data and real neuronal recordings in cat primary visual cortex, giving a plausible explanation of the results from a biological perspective.     

Realizations of BELS as WIV method in both direct and indirect closed-loop system identification

The bias eliminated least squares (BELS) method, which is known as efficient for unknown parameter estimation of transfer function in the correlated noise case, has been developed and applied effectively to the closed-loop system identification. In this paper, under the general settings, the realizations of the BELS method as a weighted instrumental variables (WIV) method in both direct and indirect closed-loop system identification are established through constructing an appropriate weighting matrix in the WIV method. The constructed structures are similar in both cases, which reveals that all the proof procedures of the two realizations are the same. Thus, the unified realizations of the BELS as the WIV method for the closed-loop system identification can be built. A simulation example is given to validate our theoretical analysis. Supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104), the Ministerial Foundation of China (Grant No. A2220060039), and the Fundamental Research Foundation of BIT (Grant No. 1010050320810)     

Optimised configuration of sensors for fault tolerant control of an electro-magnetic suspension system

For any given system the number and location of sensors can affect the closed-loop performance as well as the reliability of the system. Hence, one problem in control system design is the selection of the sensors in some optimum sense that considers both the system performance and reliability. Although some methods have been proposed that deal with some of the aforementioned aspects, in this work, a design framework dealing with both control and reliability aspects is presented. The proposed framework is able to identify the best sensor set for which optimum performance is achieved even under single or multiple sensor failures with minimum sensor redundancy. The proposed systematic framework combines linear quadratic Gaussian control, fault tolerant control and multiobjective optimisation. The efficacy of the proposed framework is shown via appropriate simulations on an electro-magnetic suspension system.     

Self-tuning control application to a nuclear power plant

The aim of this paper is to investigate the application possibilities of a self-tuning control method to a pressurized-water reactor (PWR) nuclear power plant. A self-tuning control algorithm which incorporates pole assignment into the generalized minimum variance strategy with a particular form of cost function is employed. This algorithm enables closed-loop system stability characteristics to be readily specified and facilitates reference following. The control system design is based on a second-order linear model with unknown, time-varying parameters. To ensure that this low-order model describes the complex real dynamics well enough for control purposes, control parameters are updated on-line with a recursive estimation sequences of the extended least-squares method. Weighting polynomials are also adjusted on-line to keep closed-loop poles at the desired location and to satisfy the zero steady-state condition and disturbance rejection. The purpose of this control system is to hold the average coolant temperature in the reactor as near as possible to a desired but changing reference value in the load-following mode of the nuclear power plant. The position of the control rods is an appropriate control variable. Simulation results are very successful and show the possibilities of the adaptive control application to actual plants.