Output feedback realization of LQ optimal systems: A general design using data-based synthesis

This paper is an extension of our previous work regarding realization of LQ optimal systems using output feedback in which we showed that the solutions existed when the plant satisfied certain conditions. In this paper, we remove the restrictions set forth in our previous work and present a design which is suitable for any LQ optimal system. This design involves feedback consisting of scalar output, even when a multivariable system is the subject of the design. Moreover, both the discrete-time and the continuous-time formulations of the proposed design are formulated. The present method also combines plant model estimation and control design into a single procedure by using a technique which achieves an output feedback LQ design directly from plant input and output data, thereby eliminating the need for explicit identification of a parametric plant model.     

Application of an iterative identification for control scheme to a neutralization process

In this paper an iterative scheme for identification and control is discussed. During the identification step a plant model which is suitable for the subsequent controller design step is obtained by estimation of the (dual) Youla-parameter from measurements of the input and output of the plant. Using the identified plant model, the frequency response of the ideal controller which perfectly realizes the desired closed-loop response for set-point changes is computed. This controller, in general, may not be realizable or is of high-order. A realizable, low-order controller is then calculated using frequency-weighted approximation. These steps are repeated until the performance of the closed-loop system is satisfactory or cannot be improved further. The proposed scheme is applied successfully to the identification and control of a continuous neutralization reactor.     

Integrating closed-loop identification and control using control energy sensitivity

This paper extracts a plant model from an identified closed-loop system model, and proposes an iterative procedure to find high performance controllers. The algorithm uses control energy sensitivity to connect closed-loop modelling and control design. This sensitivity describes the gradient of the consumed control energy with respect to the achieved output covariance. Hence it captures the relative importance of each output channel in the closed-loop system behaviour. Therefore the identification incorporating control energy sensitivity can characterize models to generate a controller for achieving better closed-loop performance. The procedure is demonstrated in a structural control problem.     

$ell_1$ Optimal Robust Steady-State Tracking for Unknown First-Order Plant

This note considers the problem of the optimal ldquosteady-staterdquo tracking for an unknown first-order plant with an unknown control delay, under the assumption of known upper bounds on model parameters and the control delay. The plant is subjected to perturbations in output and control as well as an exogenous disturbance with unknown upper bounds. The solution of the problem is based on treating the control criterion, which is the worst-case steady-state value of an error signal, as the identification criterion.     

A CLOSED‐LOOP SUBSPACE IDENTIFICATION METHOD FOR CONTINUOUS‐TIME SYSTEMS BASED ON δ‐OPERATOR MODEL

This paper is concerned with a subspace identification of a continuous‐time plant operating in closed‐loop in the framework of the joint input‐output approach. The main procedure consists of two steps. Firstly, the dual‐Youla parametrization of the plant is used for obtaining an equivalent open‐loop problem to the original closed‐loop identification problem. Then, a δ‐operator based IV‐MOESP type subspace identification algorithm is developed to estimate the state space model for the joint input‐output process, whereby a higher‐order state space model of the plant is obtained by an algebraic operation. Subsequently, a model reduction procedure is employed to derive a lower‐order plant model removing irrelevant modes from the higher order model. Simulation results by using numerical and chemical plant models demonstrate the feasibility of the proposed method.     

Persistency of excitation in possible unstable continuous-timesystems, identification, and indirect adaptive control

The author proves persistency of excitation of the output of an output-reachable, possibly unstable linear system under certain input conditions, and applies this result to adaptive identification and indirect adaptive control. In adaptive identification, he proves exponential parameter convergence regardless of stability of the identified plant. In indirect adaptive control he proves exponential parameter convergence along with asymptotic time invariance and global experimental stability of the controlled closed-loop system     

Control oriented system identification: a worst-case/deterministicapproach in H∞

The authors formulate and solve two related control-oriented system identification problems for stable linear shift-invariant distributed parameter plants. In each of these problems the assumed a priori information is minimal, consisting only of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The first of these problems involves identification of a point sample of the plant frequency response from a noisy, finite, output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest. This problem leads naturally to the second problem, which involves identification of the plant transfer function in H_∞ from a finite number of noisy point samples of the plant frequency response. Concrete plans for identification algorithms are provided for each of these two problems     

网络控制系统中在线时延测量及时延补偿

为了克服网络控制系统中随机时延对控制性能产生的影响,提出了基于在线时延测量和一步预测输出(基于在线参数辨识)的随机时延补偿方法。通过对以太网中随机时延的分析,提出一种在以太网中不存在同步时钟的情况下在线测量时延的方法;在在线辨识模型参数基础上,得到对象一步(随机时延小于一个采样周期)预测输出,从而根据测得的时延得到对象由于随机时延而引起的输出量变化;再用变化量加上对象输出量用于控制算法反馈。最后通过基于以太网控制实验平台对液位对象进行控制所得的结果,验证了时延测量方法和随机时延补偿算法的有效性。     

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.     

Comparison of the closed-loop identification methods in terms of the bias distribution

Several schemes for plant model identification in closed-loop operation including classical direct method, two-step identification and closed-loop output error algorithms are considered. These methods are analyzed and compared in terms of the bias distribution of the estimates for the case that the noise model is estimated as well as the case that a fixed model of noise is considered (output error structure). The problems concerning the filtered direct method which is often used in the iterative identification and control scheme are mentioned. It is shown that these problems may be solved by the closed-loop output error identification method.     

Online global learning in direct fuzzy controllers

A novel approach to achieve real-time global learning in fuzzy controllers is proposed. Both the rule consequents and the membership functions defined in the premises of the fuzzy rules are tuned using a one-step algorithm, which is capable of controlling nonlinear plants with no prior offline training. Direct control is achieved by means of two auxiliary systems: The first one is responsible for adapting the consequents of the main controller's rules to minimize the error arising at the plant output, while the second auxiliary system compiles real input-output data obtained from the plant. The system then learns in real time from these data taking into account, not the current state of the plant but rather the global identification performed. Simulation results show that this approach leads to an enhanced control policy thanks to the global learning performed, avoiding overfitting.     

Closed-loop data-driven simulation

Closed-loop data-driven simulation refers to the problem of finding the set of all responses of a closed-loop system to a given reference signal directly from an input/output trajectory of the plant and a representation of the controller. Conditions under which the problem has a solution are given and an algorithm for computing the solution is presented. The problem formulation and its solution are in the spirit of the deterministic subspace identification algorithms, i.e. in the theoretical analysis of the method, the data is assumed exact (noise free). The results have applications in data-driven control, e.g. testing controller's performance directly from closed-loop data of the plant in feedback with possibly different controller.     

Indirect adaptive structure for multivariable neural identification and control of a pilot distillation plant

This paper describes the design and implementation of an indirect adaptive controller that uses neural networks both for identification and control of an experimental pilot distillation column containing a mixture of ethanol and water. The MATLAB platform is applied both for the neural identification and control of the distillation plant using the Levenberg–Marquardt approach, enabling also optimal input/output net configuration. The neural controller performance has been analyzed and illustrated via experimental tests on the pilot distillation column monitored under the LabVIEW platform. Both platforms have been linked together by constituting an integrated process control interface. The obtained experimental results demonstrate the effectiveness of the neural indirect adaptive control scheme as compared to proportional–integrative–derivative, when real-time multivariable control is demanded, even in presence of disturbances.     

Estimation of modelling errors of a closed-loop system and application to identification

A method for estimating the modelling errors of a process using closed-loop data is proposed. The theoretical analysis and implementation of the method are illustrated. A new algorithm of system identification which identifies the plant as an impulse response sequence or a transfer function model using the output of a feedback control system is derived. An illustrative example which shows the use of the proposed method for the estimation of modelling errors and its application to closed-loop identification is also included.     

A Method of Dispersion Statistical Linearization of Nonlinear Stochastic Systems of the Hammerstein Class

Consideration was given to the method of statistical linearization of nonlinear stochastic plants on the basis of the dispersion identification theory for the Hammerstein class of models. The problem is notable for taking into account the dynamic nonlinearities of the plant. Models of statistical linearization were constructed with regard for the plant output noise of the kind of white noise and martingale sequence. Solution was obtained in the class of gradient recurrent identification algorithms. The necessary and sufficient conditions for strong consistency of the parameter estimates provided by these algorithms were presented. The results obtained were used for adaptive following of the plant output. Fitness of this method was substantiated by the example of a particular plant.     

Adaptive receding horizon control for constrained MIMO systems

An adaptive control algorithm for open-loop stable, constrained, linear, multiple input multiple output systems is presented. The proposed approach can deal with both input and output constraints, as well as measurement noise and output disturbances. The adaptive controller consists of an iterative set membership identification algorithm, that provides a set of candidate plant models at each time step, and a model predictive controller, that enforces input and output constraints for all the plants inside the model set. The algorithm relies only on the solution of standard convex optimization problems that are guaranteed to be recursively feasible. The experimental results obtained by applying the proposed controller to a quad-tank testbed are presented.     

Robust control of multidimensional nonstationary linear plants

Solved was the problem was of constructing a robust control system with linear nonstationary multidimensional control plant compensating the parametric and external bounded perturbations to within δ if the derivatives of the output vector are not measured and fully if the derivatives are measured.     

Accurate identification for control: the necessity of an iterativescheme

If approximate identification and model-based control design are used to accomplish a high-performance control system, then the two procedures must be treated as a joint problem. Solving this joint problem by means of separate identification and control design procedures practically entails an iterative scheme. A frequency-response identification technique and a robust control design method are used to set up such an iterative scheme. Each identification step uses the previously designed controller to obtain new data from the plant. The associated identification problem has been solved by means of a coprime factorization of the unknown plant. The technique's utility is illustrated by an example     

Tracking in linear MIMO systems under external perturbations

Consideration was given to tracking the given trajectories of the output variables of the linear multiple-input multiple-output dynamic systems under uncontrollable external perturbations. A procedure to rearrange the mathematical model of a control plant in a consistent block form of controllability and observability of the output (measurable) variables with regard for the external perturbations was developed within the framework of the block approach. This form underlies the decomposition procedures of feedback design enabling one to track the given trajectories invariantly to the external perturbations.     

An approach to multivariable system identification

Two prototype identifiable structures are presented which make possible the identification via an equation-error model reference adaptive system of linear plants with rational transfer function matrices. The structures include as specialisations many of the particular structures presented hitherto in the literature. Convergence properties are also discussed, and several modes of convergence are distinguished: model output to plant output, model transfer function matrix to plant transfer function matrix, and model parameters to plant parameters. Conditions are presented for exponentially fast convergence in the absence of noise.