Closed-loop Identification Research Articles

High precision identification of dynamic model for accelerometer based on VMD

The dynamic model of accelerometer reflects characteristics of dynamic output changes over time, directly affecting dynamic measurement performance. To solve the problem of low identification accuracy due to pure delay, nonlinearity, and noise, a high-precision closed-loop identification method for dynamic model based on variational mode decomposition (VMD) is proposed. In particular, emphasis is placed on highlighting the issue that equivalent stiffness parameter is more susceptible to noise due to its low parameter sensitivity. Additionally, to address the effects of pure delay and nonlinearity on model identification, a dynamic model of accelerometer containing both is proposed. In response to the impact of noise on model identification, it is proposed to use VMD for noise separation and data reconstruction. Finally, a test platform is established for validation. And experimental results indicate that the model identified using the proposed method shows an increase in model matching degree (MMD) from 90% to 98.8%.

Closed-loop identification of stabilized models using dual input–output parameterization

This paper introduces a dual input–output parameterization (dual IOP) for the identification of linear time-invariant systems from closed-loop data. It draws inspiration from the recent input–output parameterization developed to synthesize a stabilizing controller. The controller is parameterized in terms of closed-loop transfer functions, from the external disturbances to the input and output of the system, constrained to lie in a given subspace. Analogously, the dual IOP method parameterizes the unknown plant with analogous closed-loop transfer functions, also referred to as dual parameters. In this case, these closed-loop transfer functions are constrained to lie in an affine subspace guaranteeing that the identified plant is stabilized by the known controller. Compared with existing closed-loop identification techniques guaranteeing closed-loop stability, such as the dual Youla parameterization, the dual IOP requires neither a doubly-coprime factorization of the controller nor a nominal plant that is stabilized by the controller. The dual IOP does not depend on the order and the state-space realization of the controller either, as in the dual system-level parameterization. Simulation shows that the dual IOP outperforms the existing benchmark methods.

LPV interpolation modeling and modal-based pole placement control for ball screw drive with dynamic variations

This paper presents a linear parameter varying (LPV) interpolation modeling method and modal-based pole placement (PP) control strategy for the ball screw drive (BSD) with varying dynamics. The BSD is modeled as a global LPV model with position-load dependence by selecting position and load as scheduling variables. The global LPV model is obtained from local subspace closed-loop identification and LPV interpolation modeling. A modal-based global LPV model is obtained through the similarity transformation. Based on this model, a modal-based LPV PP control strategy is proposed to achieve various modal control. Specifically, a state feedback control structure with an LPV state observer is designed to realize online state estimation and real-time state feedback control of modal state variables which cannot be measured directly. The steady-state error is minimized by introducing an error state space (SS) model with the integral effects. Moreover, the stability of the closed-loop system is analyzed according to the controllable decomposition and principle of separation. It is experimentally demonstrated that the proposed modal-based LPV PP control strategy can effectively achieve precise tracking and outstanding robustness meantime.

Non-excitation closed-loop identification based on hysteresis bias relay feedback

This paper proposes a closed-loop system identification method based on hysteresis loop bias relay feedback without using excitation. The method utilizes hysteresis loop bias relay instead of a controller to ensure the informativity of data without external excitation and with only noisy feedback. Additionally, this paper proposes a parameter scheme for the hysteresis loop bias relay to guide the selection of parameters more rationally, thus improving the accuracy of the identification model. Compared to recently proposed switching controller methods, the advantage of this method lies in the fact that it requires fewer samples and shortens data collection time. The method's effectiveness is verified through simulation comparisons with typical methods.

Joint input–output identification of unstable systems with kernel regularization

This paper discusses closed-loop identification of unstable systems. In particular, we first apply the joint input–output identification method and then convert the identification problem of unstable systems into that of stable systems, which can be tackled by using kernel-based regularization methods. We propose to identify two transfer functions by kernel regularization, the one from the reference signal to the input, and the one from the reference signal to the output. Since these transfer functions are stable, kernel regularization methods can construct their accurate models. Then the model of unstable system is constructed by ratio of these functions. The effectiveness of the proposed method is demonstrated by a numerical example and a practical experiment with a DC motor.

Comparison Study between Open-Loop and Closed-Loop Identification for Industrial Hydraulics Actuator System

In control applications involving motion control, precise control of the Industrial Hydraulics Actuator (IHA) is necessary to accurately assess the position of the actuator rod. Non-recursive identification is used to model the system with an open-loop and closed-loop approach for this paper. The grey box approach is used to estimate the continuous model and parameter estimation for the system. The System Identification toolbox in MATLAB is used for the model estimation. The process starts by obtaining the input-output data from the experimental work. The input-output data validation outcome reveals a best-fit percentage for open-loop 88.91% and closed-loop 95.43%, as well as a small Root Mean Square Error (RMSE). This indicates a successful validation between the estimated model and the actual system due to a high degree of agreement. The open-loop and closed-loop identification have proven successful as there is no noteworthy disparity in the outcomes. The closed-loop system can be applied to unstable systems and any potential system.

Closed-loop identification of enzyme kinetics applying model-based design of experiments

This study presents an automated reactor platform for the identification of enzyme kinetic models using model-based design of experiments on the example of the reduction of NAD+ by formate dehydrogenase from Candida boidinii.

Quantitative comparison of reinforcement learning and data-driven model predictive control for chemical and biological processes

As manufacturing processes transition towards digitalization, data-driven process control is emerging as a key area of interest in future artificial intelligence technology. A crucial aspect in implementing data-driven process control is “What should we learn from the data?”. In general, the data-driven control method can be categorized into two main approaches: Learning the model and learning the value. To assist in selecting the more suitable approach, this paper applies six different control methods, with three falling under each approach, to three distinct manufacturing process systems. The simulation results indicate that the model-learning approaches display higher data efficiency and exhibit lower variance in total cost. These methods prove to be particularly advantageous for addressing the regulation problems. Conversely, value-learning approaches show competitive potential in closed-loop identification and in managing economic cost problems. The remaining challenges associated with each technique are discussed, along with practical considerations for their implementation.

Proportional-Integral Control and ARX-based Model Predictive Control for Extractive Dividing Wall Column

Extractive dividing wall column (EDWC) is a typical process intensification technology and possesses significant energy-saving prospects, while the poor dynamic controllability hinders its industrialization goal. In this work, taking the benzene and cyclohexene azeotrope separation as an example, a proportional-integral (PI) control structure based on four-point temperature control loops is proposed for EDWC by considering temperature difference as the discriminant criterion. Subsequently, to improve the control performance of EDWC, two model predictive control (MPC) structures based on auto-regressive with external input (ARX) model obtained from closed-loop identification and linear time-invariant state-space (LTI-SS) model, respectively, are studied for EDWC. The performance of three control structures is tested by ±20 % feed flow rate and composition disturbances, and further quantitatively evaluated by integral absolute error (IAE). The dynamic responses demonstrate that the ARX-based MPC structure achieves the best control performance in the presence of feed flow rate and composition disturbances, which can be attributed to the capability of the identified ARX model to track the dynamic features of EDWC accurately.

Detection and elimination of insignificant interacting subsystems in MIMO closed-loop systems using the least mean square-based partial correlation algorithm

Closed-loop identification of multi-input multi-output (MIMO) systems in large-scale plants has significant difficulties due to subsystem interactions. This complexity is attributed to several input‒output variables, interactions such as recycling to improve or save material and energy, and disturbances such as heating or cooling within the plant. One of the fundamental problems in closed-loop identification is the input perturbation of the interacting subsystems to capture the dynamics of the system for producing an informative dataset and consequently obtaining an accurate model. However, perturbing all the interacting subsystems in the plant increases the applied excitation signals, which makes the identification a nontrivial task. Thus, a precise and quantitative procedure to evaluate the significance and contribution of such interacting subsystems before applying these excitation signals is required to simplify the identification task. Conventional partial correlation analysis is one of the implemented techniques to measure the significance of these interacting subsystems. However, this technique is based on least square estimation. Thus, incorrect estimation of the model errors is produced due to the correlations amongst the process inputs and unmeasured disturbances. Accordingly, this paper describes the implementation of a developed least mean square-based partial correlation algorithm for detecting and eliminating insignificant interacting subsystems of MIMO closed-loop systems. The developed algorithm can discriminate the interacting subsystems that substantially influence the plant interaction from those that do not by minimizing the model regression errors produced due to the process input correlation, unmeasured disturbances, and colored noise. The effectiveness of the proposed method is demonstrated through a case study.

Deep reinforcement learning with reward shaping for tracking control and vibration suppression of flexible link manipulator

This paper puts forward a novel deep reinforcement learning control using deep deterministic policy gradient (DRLC-DDPG) framework to address the reference tracking and vibration suppression problem of rotary flexible link (RFL) manipulator. Specifically, this study attempts to address the continuous action space DRLC problem through DDPG algorithm and presents a Lyapunov function based reward shaping approach for guaranteed deep reinforcement learning (DRL) convergence and enhanced speed of training. The proposed approach synthesizes the hard and soft constraints of the flexible manipulator as a constrained Markov decision problem (MDP) and evaluates the performance of DRLC-DDPG framework through hardware in loop (HIL) testing to realize precise servo tracking and suppressed vibration of the flexible manipulator. For identifying the dynamical model of the RFL, an empirical Auto-Regressive eXogenous (ARX) model using the closed loop identification technique is built. Moreover, to extract the true states (servo angle and deflection angle) from the actual measurements, which typically have the influence of sensor noise, an adaptive Kalman filter (AKF) is augmented with the DRLC scheme. The experimental results of DRLC-DDPG scheme compared with those of the model predictive control (MPC) for several test cases reveal that the proposed scheme is superior to MPC both in terms of trajectory tracking and robustness against the external disturbances and model uncertainty.

A data-driven control methodology applied to throttle valves

Electric throttle valves represent a challenge for control design, as their dynamics involves strong nonlinearities, characterized by an asymmetric hysteresis. Large variability in the characteristics of each valve and erratic steady-state behaviors can also be noticed by carrying out experiments on multiple valves, impairing classical model-based control strategies. Nevertheless, local data-driven linear models can be obtained by system identification, and simple proportional–integral (PI) digital controllers can be tuned individually for each valve, providing good tracking performance. As these controllers cannot be transposed from one valve to another, a robust control design is considered. Taking into account the variability of electric throttle valves, a real-time data-driven strategy is then proposed, using identification in closed-loop and controller re-design. This methodology is necessary if control performance is a key issue, and can be embedded on a low-cost controller board (Arduino® Mega 2560). Experimental results going from frequency analysis and linear design to real-time data-driven control illustrate the methodology presented in the paper.

In-flight estimation of quadrotor mass and inertia using all-accelerometer

In this paper, an on-line closed-loop identification of mainly mass and inertia of an under-actuated aerial vehicle, namely a quadrotor acting as an aerial manipulator, is presented. Being treated as a rigid body, only one set of eighteen- or six tri-axial linear accelerometers is used to facilitate such estimation. Force and torque disturbances acting upon the vehicle during identification are also estimated which will refine the overall estimation quality of the unknown parameters. Namely, recursive linear and nonlinear least squares methods are used to obtain initial and refined estimations, respectively. Random disturbances are introduced to the closed-loop system to ensure enough excitation of the overall system. Issues related to identifiability, stability and performance are discussed. Since the proposed method depends on general kinematical and dynamical analyses of motion, it is claimed that the presented method will be also applicable to a wider range of, mainly, aerial vehicles.

Global Stabilizability Theorems on Discrete-Time Nonlinear Uncertain Systems

This paper focuses on the a basic class of discrete-time nonlinear systems with multiple unknown parameters. We claim that such a system is stabilizable if its nonlinear growth rate is dominated by a polynomial rule. This rule cannot be relaxed in general since it becomes a necessary and sufficient condition when the system has a polynomial form [10]. We further prove that the concerned stabilizable system is possible to grow exponentially fast. Meanwhile, optimality and closed-loop identification are also discussed herein.

Application-Oriented Input Spectrum Design in Closed-Loop Identification

In the paper, a problem of real-time input design, where the spectral characteristic of the external excitation signal is optimized considering the fixed bound on the ellipsoidal constraint applied to the quality measure of the estimated model, has been presented. We designed a compensator close to the complementary sensitivity function such that the resulting closed-loop system is stable and guarantees robust performance. The contribution of this work comprises a comparison of the KYP and frequency grid methods for the worst-case minimization between the identified plant and all models in the uncertainty region. It has been noted that the input design problem considering the frequency grid is far more numerically robust than the KYP method and guarantees that more than 90% of the estimated model parameters are clustered inside the assumed confidence region. The proposed approach is verified by numerical examples, and the sensitivity of the input spectrum design to the estimates of model parameters is discussed.

Multi-task sparse identification for closed-loop systems with general observation sequences

To achieve the simultaneous and accurate identification of sparse parameters for multiple systems, a multi-task sparse identification algorithm is proposed for systems with general sequences, including stationary time series and feedback control. By minimizing the sum of L2-norm and weighted multi-task L2,1 regularization terms, the sparse pattern of parameters are shared between different tasks, which leads to a reduction in workload while improving the sparsity and accuracy of the estimates. To cope with online identification, an online multi-task sparse identification algorithm is presented, together with proof of convergence of the estimates. Finally, two closed-loop identification are given to support the theoretical analysis and to demonstrate the advantages of the proposed algorithm.

Closed Loop Identification and Control for Input Time Delay Systems

In this research, the identification results for open-loop time delay systems are extended to closed-loop systems. It is shown that a subspace identification method used in open-loop systems can be applied to closed-loop systems. When the subspace identification method was used directly, problems such as increasing poles and unstable zeros caused by numerical errors were encountered; however, these problems can be prevented by a shift operation. Finally, the simulated identification results for the time delay system and the improved control performance using the estimated time delay are shown.

Closed-Loop System Identification Approach of the Inertial Models

The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained according to the identification procedures in the open-loop, or in the closed-loop. In the open-loop, the identification methods are well known and offer good process approximation, which is not valid for the closed-loop identification, when the system provides the feedback output and doesn’t permit it to be identified in the open-loop. This paper offers an approach for experimental identification in the closed-loop, which supposes the approximation of the process with inertial models, with or without time delay and astatism. The coefficients are calculated based on the values of the critical transfer coefficient and period of the underdamped response of the closed-loop system with P controller, when system achieves the limit of stability. Finally, the closed-loop identification was verified by the computer simulation and the obtained results demonstrated, that the identification procedure in the closed-loop offers good results in process of estimation of the model of the process.

State Estimation for Closed-Loop LPV System Identification via Kernel Methods⋆

This paper proposes a state-estimation method for closed-loop identification of linear-parameter-varying (LPV) systems by extending an approach for linear-time-invariant (LTI) systems and applying kernel canonical correlation analysis (KCCA). The proposed method estimates the state term from the one-step-ahead prediction via a kernel approach. The incomplete Cholesky decomposition (ICD) is introduced to reduce the complexity of the KCCA. A simple numerical simulation shows the effectiveness of the proposed approach.

Closed-loop identification of multi-axis active magnetic bearing systems based on decentralized and decoupling control

In response to the open-loop instability of magnetic bearing systems, this paper develops a closed-loop identification method to obtain an accurate plant model for controller design. The identification method is based on a decentralized and decoupling control architecture, which allows the decoupling of the multi-input-multi-output (MIMO) system into two single-input-single-output (SISO) systems for simplifying the identification process. The identification uses a pseudo-random binary sequence as the excitation signal. A parameterized model is obtained through a parameter estimation algorithm based on the output error model. To ensure that the model prediction error can converge during the computation process, a filter is incorporated into the estimation algorithm. The filter can be synthesized systematically by solving a set of linear matrix inequalities. The performance of the proposed closed-loop identification method is firstly verified by simulations. Then it is implemented on a five-axis magnetic bearing platform and the parameterized model obtained from the identification is compared to the experimental frequency response.