Model predictive control of pressure-swing distillation via closed-loop system identification

In this paper, a laboratory experiment, which was developed to teach undergraduate students at the University of Pretoria, Pretoria, South Africa, some of the main issues regarding closed-loop system identification, is discussed. In this experiment, a plant is identified both from open-loop and closed-loop data. The model obtained from the open-loop data is used as reference to evaluate a closed-loop system identification approach. A motivation for closed-loop system identification and a laboratory experiment in this field is given. The experiment is outlined, each step is discussed, and the experiment is evaluated. This experiment shows that closed-loop system identification can be taught in an uncomplicated manner.

This paper explores the suitability of closed loop system identification (CLID) to construct a model of an uninhabited surface vehicle known as Springer. The process characteristics of Springer are analysed qualitatively. CLID reduces the costs of modelling and increases the safety of operations involved in comparison to open loop identification. There are three basic approaches: direct, indirect and joint input-output. Each of these approaches is briefly outlined and the joint input-output approach can be further classified as two-stage method, co-prime factor identification scheme and projection method. According to the studies in the past decades, it is deemed appropriate to utilise the two-stage method in this study. The CLID model of the Springer, constructed by the two stage method is presented here. (6 pages)

Identification of closed-loop systems with low-order controllers

This paper presents theory and results concerning the analysis of the identification of closed-loop systems using least-squares methods. The least-squares technique is applied in its normal form and in a modified version developed to cope with the bias problem. The analysis has been established following a mathematical investigation of the problem, and by simulation of different identification experiments applied to different structures of closed-loop systems. The results derived from this analysis show the conditions under which the identifiability of the open-loop process can be ensured, considering different situations such as whether or not there is noise present at the system output and whether or not external signals are used to perform the identification experiments. Practical experiments of closed-loop identification on a micromachine system in use in the Department of Electrical Engineering of the University of Manchester are also described. Results for different experimental conditions are prese...

In this paper, a family of discrete-time system models of an Electric Variable Valve Timing (EVVT) actuator for internal combustion engines under different operational conditions were obtained through the closed-loop system identification, where the complicated EVVT actuating system was treated as a black box. Since it is almost impossible to hold the EVVT cam phasing system at the desired operational condition under open-loop control, closed-loop system identification was adopted. Closed-loop EVVT system models were obtained using the PRBS q-Markov Cover system identification, and with the known closed-loop controller the open-loop system models can be obtained under the given system operational condition such as engine speed, oil viscosity, and battery voltage. The LPV (Linear Parameter Varying) system model was formed based on the obtained family of open-loop discrete-time EVVT models, and the resulting LPV model was further validated by the experimental data. The obtained LPV model is intended to be used for designing the gain-scheduling LPV controllers using the LMI (Linear Matrix Inequality) convex optimization.

System identification deals with the problem of building the mathematical models of dynamical systems according to the input and output data. The open-loop system identification (Observer/Kalman Filter SystemIdentification, OKID) for stable systems without requiring feedback control is introduced first. For identifying marginally stable or unstable system, however, feedback control is required to ensure the overall system stability. The algorithm of closed-loop system identification (CLID) with known feedback dynamics is shown next.

In this paper, we propose a simple framework for closed-loop system identification: the stabilized output error method. Traditional closed-loop system identification methods rely on the linearity of the target system, and they require the identification of noise models or prior knowledge or identifiability of the feedback controllers to obtain unbiased estimates. But in many real-world applications, the noise dynamics and feedback controllers are complex and difficult to identify, and the nonlinearity may not be ignored. The proposed framework introduces a virtual controller that stabilizes the error between model prediction and the output of the target system. This enables us to apply the output error method, which gives unbiased estimates without depending on the noise model and is applicable to a wide range of models, including nonlinear systems, to closed-loop system identification problems. The paper describes the framework and gives the theoretical support and design guidelines for virtual controllers. Through numerical examples, we show the effectiveness of the proposed framework in various situations, which include identification of (a) linear gray box models, (b) systems in the presence of disturbances having realistic complexity, and (c) a nonlinear unstable system in a human-in-the-loop environment.

Closed-loop identification of systems with uncertain time delays using ARX–OBF structure

This paper studies the closed-loop system identification (ID) error when a dynamic integral controller is used. Pseudo-random binary sequence (PRBS) q-Markov covariance equivalent realization (Cover) is used to identify the closed-loop model, and the open-loop model is obtained based upon the identified closed-loop model. Accurate open-loop models were obtained using PRBS q-Markov Cover system ID directly. For closed-loop system ID, accurate open-loop identified models were obtained with a proportional controller, but when a dynamic controller was used, low-frequency system ID error was found. This study suggests that extra caution is required when a dynamic integral controller is used for closed-loop system identification. The closed-loop identification framework also has significant effects on closed-loop identification error. Both first- and second-order examples are provided in this paper.

To what extent and in what ways can two closed-loop dynamic systems be said to be similar? This question arises in a wide range of dynamic systems modeling and control system applications. For example, bounds on error models are fundamental to the controller optimization with modern control methods. Metrics such as the structured singular value are direct measures of the degree to which properties such as stability or performance are maintained in the presence of specified uncertainties or variations in the plant model. Similarly, controls-related areas such as system identification, model reduction, and experimental model validation employ measures of similarity between multiple realizations of a dynamic system. Each area has its tools and approaches, with each tool more or less suited for one application or the other. Similarity in the context of closed-loop model validation via flight test is subtly different from error measures in the typical controls oriented application. Whereas similarity in a robust control context relates to plant variation and the attendant affect on stability and performance, in this context similarity metrics are sought that assess the relevance of a dynamic system test for the purpose of validating the stability and performance of a similar dynamic system. Similarity in the context of system identification is much more relevant than are robust control analogies in that errors between one dynamic system (the test article) and another (the nominal design model) are sought for the purpose of bounding the validity of a model for control and analysis. Yet system identification typically involves open-loop plant models which are independent of the control system (with the exception of limited developments in closed-loop system identification which is nonetheless focused on obtaining open-loop plant models from closed-loop data). Moreover the objectives of system identification are not the same as a flight test and hence system identification error metrics are not directly relevant. In applications such as launch vehicles where the open loop plant is unstable it is similarity of the closed-loop system dynamics of a flight test that are relevant.

Parametric identification of noisy closed-loop linear systems

A feedback connection of a Hammerstein system and a linear controller provides a good approach to modeling systems with static actuator nonlinearity or input saturation during closed-loop experiments. This paper discusses the Output Error (OE) identification of such closed-loop Hammerstein systems that requires a nonlinear optimization due to the non-convexity of the output error. An iterative IV (Instrumental Variables) identification algorithm is proposed for the nonlinear optimization. The basic idea is to express the nonlinear parameter estimation as an iterative IV estimation using gradient based updates. The proposed iterative IV identification method is applied to the simulation data from a Hammerstein system with input static nonlinearity. The simulation study shows the effectiveness of the proposed identification algorithms.

PurposeThe purpose of this paper extends the authors’ previous contributions on aircraft system identification, such as open loop identification or closed loop identification, to cascade system identification. Because the cascade system is one special network system, existing in lots of practical engineers, more unknown systems are needed to identify simultaneously within the statistical environment with the probabilistic noises. Consider this problem of cascade system identification, prediction error method is proposed to identify three unknown systems, which are parameterized by three unknown parameter vectors. Then the cascade system identification is transferred as one parameter identification problem, being solved by the online subgradient descent algorithm. Furthermore, the nonparametric estimation is proposed to consider the general case without any parameterized process. To make up the identification mission, model validation process is given to show the asymptotic interval of the identified parameter. Finally, simulation example confirms the proposed theoretical results.Design/methodology/approachFirstly, aircraft system identification is reviewed through the understanding about system identification and advances in control theory, then cascade system identification is introduced to be one special network system. Secondly, for the problem of cascade system identification, prediction error method and online subgradient decent algorithm are combined together to identify the cascade system with the parameterized systems. Thirdly from the point of more general completeness, another way is proposed to identify the nonparametric estimation, then model validation process is added to complete the whole identification mission.FindingsThis cascade system corresponds to one network system, existing in lots of practice, such as aircraft, ship and robot, so it is necessary to identify this cascade system, paving a way for latter network system identification. Parametric and nonparametric estimations are all studied within the statistical environment. Then research on bounded noise is an ongoing work.Originality/valueTo the best of the authors’ knowledge, research on aircraft system identification only concern on open loop and closed loop system identification, no any identification results about network system identification. This paper considers cascade system identification, being one special case on network system identification, so this paper paves a basic way for latter more advanced system identification and control theory.

Good mathematical models are vital for design of model based controllers and accurate system response predictions. Such mathematical models can be derived by employing either first principle method or empirical method. Empirical method involves model identification based on input and output data. This method is also known as system identification. Many real-time systems are inherently closed loop systems. Moreover, it is not possible to get data from an open loop system in process industry. In such cases, closed loop system identification is useful. In system identification, selection of model structure is critical. In this paper, a first order integer model and four different fractional models were identified for a DC motor in closed loop. Fractional order model parameters were optimized by minimization of sum of squared errors (SSE), using Genetic Algorithm (GA). Results show that fractional order models fit better than first order integer model. Among the four fractional models identified, the fractional model with least parameters yielded best result.

Multivariable closed-loop system identification of plants under model predictive control