Step Response Data Research Articles

Fractional-Order Modeling and Identification for an SCR Denitrification Process

This paper presents an application of a fractional-order system on modeling an industrial process system with large inertia and time delay. The traditional integer-order model of the process system is extended to a fractional-order one in this work. To identify the parameters of the proposed fractional-order model, an output-error identification algorithm is presented. Based on the experimental step response data of the selective catalytic reduction (SCR) denitrification process in a power plant, this proposed fractional-order model shows a better fitting result compared with the typical integer-order models. An integer-order proportional–integral (PI) controller is designed for the process plant using a simple scheme according to the identified fractional-order and integer-order models, respectively. Validation tests are performed based on the obtained fractional-order and integer-order models, demonstrating the advantages of the proposed fractional-order model with the corresponding system identification approach for industrial processes with large inertia and time delay.

Temperature control research for laser-induction hybrid strengthening process

Temperature control research for laser-induction hybrid strengthening process

Research on automation control technology of electrical and electronic equipment combined with integrated wireless module

Abstract This paper discusses the critical impact of informatization automation on plant automation, and takes a water plant’s coagulation dosing automation control system as an example to explore the value of integrated wireless modules in the automation of electrical equipment. Algorithms for directly identifying the parameters of the second-order continuous model by regression model and based on the step response data are investigated, as well as the selection of the DMC algorithm for mathematical modeling of the coagulation dosing automation control. Finally, the effectiveness of the automated dosing system was verified by comparing its effectiveness in improving the qualified rate of precipitation water quality, reducing drug consumption and effluent turbidity, and improving stability. The study’s results showed that after using the coagulation dosing automation system, the water plant’s sedimentation water quality pass rate was increased from the original 85%~95% to 95%~100%. The drug consumption and effluent turbidity were reduced by 20.3% and 33.09% respectively, while the stability was also improved to different degrees. The coagulation dosing automated control system can dosage chemicals more accurately, safely and stably, which has specific reference value for developing the water purification industry.

A Novel Toolbox for Automatic Design of Fractional Order PI Controllers Based on Automatic System Identification from Step Response Data

This paper describes a novel automatic control toolbox, designed for non-experienced practitioners. Fractional order (FO) controllers are easily tuned with the main purpose of easy practical implementation. Experimental step data are required for the automatic FO controller tuning. An embedded system identification algorithm uses the step data to obtain a process model as a second order plus dead-time (SOPDT) system. Finally, the FO controller is computed based on the previously estimated SOPDT model in order to fulfil a set of user-imposed frequency domain performance specifications: phase margin, gain crossover frequency and gain margin maximization. Experimental step response data from a strongly nonlinear vertical take-off and landing unit have been used to design an FO controller using the toolbox. The experimental closed loop results validate the proposed toolbox. The end result is a user-friendly automatic fractional order controller tuning with endless possibilities of real-world applicability.

Novel Parameter Identification Method for Basis Weight Control Loop of Papermaking Process

The basis weight control loop of the papermaking process is a non-linear system with time-delay and time-varying. It is impractical to identify a model that can restore the model of real papermaking process. Determining a more accurate identification model is very important for designing the controller of the control system and maintaining the stable operation of the papermaking process. In this study, a strange nonchaotic particle swarm optimization (SNPSO) algorithm is proposed to identify the models of real papermaking processes, and this identification ability is significantly enhanced compared with particle swarm optimization (PSO). First, random particles are initialized by strange nonchaotic sequences to obtain high-quality solutions. Furthermore, the weight of linear attenuation is replaced by strange nonchaotic sequence and the time-varying acceleration coefficients and a mutation rule with strange nonchaotic characteristics are utilized in SNPSO. The above strategies effectively improve the global and local search ability of particles and the ability to escape from local optimization. To illustrate the effectiveness of SNPSO, step response data are used to identify the models of real industrial processes. Compared with classical PSO, PSO with time-varying acceleration coefficients (PSO-TVAC) and modified particle swarm optimization (MPSO), the simulation results demonstrate that SNPSO has stronger identification ability, faster convergence speed, and better robustness.

Estimation of First Order Plus Dead Time and Second Order Plus Dead Time models from noisy step response data

SummaryThis paper proposes the estimation of first‐order‐plus‐dead‐time (FOPDT) and second‐order‐plus‐dead‐time (SOPDT) models from noisy step response data. The model parameters are estimated by computation of areas, which makes it robust in the presence of stochastic disturbances in the step response data. The efficiency of the methodology is extensively tested in various numerical examples as well as in real‐life experimental tests. The results—comparing our proposed estimation method with some other methods—suggest that the novel algorithm can be used with noisy step response data and adequately approximates high‐order systems. Moreover, it does not require any system identification expertise, making it readily accessible for the nonexperienced user in industrial practice. The method is successfully validated for overdamped, reasonably underdamped, as well as highly oscillatory processes, hence offering a comprehensive estimation method.

Research on Identification Algorithm of Cascade Control System

Aiming at the problem of object model identification of modern industrial process control systems, a new closed-loop moment parameter identification online method based on the data of normal operation of the running system is proposed. In this method, only one step response data of the system is required, and appropriate convergence factors are introduced into the Laplace formula, the trapezoidal integral method is used to calculate the values of two derivatives of the transfer function, then the four unknown parameters of the second-order model can be solved by fitting the data with the least square method, and the target model can be identified. Finally, the simulation results of building different objects through Matlab show that the identification method has general applicability and good robustness with high recognition, and it is not sensitive to noise signals.

Application of Dynamic Input Shaping for a Dual-Mirror System

Abstract The task of trajectory planning for a dual-mirror optical pointing system greatly benefits from carefully designed dynamic input signals. This paper summarizes the application of multivariable input shaping (IS) for a dual-mirror system, starting from initial open-loop step-response data. The optical pointing system presented consists of two fast steering mirrors (FSM) for which dynamically coupled input signals are designed, while adhering to mechanical and input signal constraints. For the solution, the planned trajectories for the dual-mirrors are determined via (inverse) kinematic analysis. A linear program (LP) problem is used to compute the dynamic input signal for each of the FSMs, with one of the mirrors acting as an image motion compensation device that guarantees tracking of a planned trajectory within a specified accuracy and the operating constraints of the FSMs.

Convolution and Volterra Series Approach to Reduced-Order Modeling of Unsteady Aerodynamic Loads

A combined approach of linear convolution and higher-order Volterra series (VS) to reduced-order modeling of unsteady transonic aerodynamic loads is presented. Our framework offers a simple method to determine the memory depth of the system, clearly separates the linear and the nonlinear (NL) contributions, and significantly reduces the effort required to generate a model for a wide range of reduced frequencies. The generated models use step-response data in the linear and the NL ranges, thus separating the model generation from any specific input signal or a particular reduced frequency. The models were compared against and validated using the computational fluid dynamics results of an oscillating two-dimensional NACA 0012 airfoil.

Error model-based iterative compensation method for improving the estimation of frequency response function

For the estimation of frequency response function (FRF) using the window-based spectral estimation method, the error models of the FRF estimation are introduced, including window interpolation error and transient error models, and an error model-based iterative compensation (EMIC) method is then proposed to improve the FRF estimation accuracy. The specific iteration steps of the proposed EMIC method are presented, fast computations are adopted in the steps as far as possible; and that, iteration convergence and noise uncertainty are analyzed. The analyses reveal that, the proposed EMIC method is almost always convergent as long as the error of the FRF pre-estimation is small, intercepting enough data and using a window which has smaller and fewer side DFT bins as well as smaller front-end value for FRF estimation can result in better iteration convergence; whereas, the proposed EMIC method will slightly increase the noise uncertainty of FRF estimation compared with that without iterative compensation because it removes the window interpolation effects on noise just like removing the error. To verify the effectiveness and practicability of the proposed EMIC method, model simulation and actual sensor data verification are implemented, and multi existing methods are employed for comparison. The results show that, the proposed EMIC method can largely decrease the error of the FRF estimated by the window-based spectral estimation method, it has the best maximum error restraining capabilities especially in the resonance frequency band and relatively better comprehensive error restraining capabilities especially when the data is not long enough compared with the mentioned existing methods, also, the time consumption of the proposed EMIC method is acceptable and is usually seconds or less; and that, the theoretical analyses, model simulation results and actual data verification results are consistent with each other. Consequently, the proposed EMIC method is proven to be effective and practical for improving the FRF estimation of a stable LTI system from its step or impulse response data.

Proportional-Integral-Derivative Controller Performance Assessment and Retuning Based on General Process Response Data.

In this paper, the current research status of controller performance assessment is reviewed in brief. Solving the problem of proportional–integral–derivative performance assessment usually requires step response data, and several methods are combined and extended. Using the integral of signals, implicit model information contained in process response data becomes explicit, and then the least squares approach is adopted to construct a detailed low-order process model based on process response data in more general types. A one-dimensional search algorithm is used to attain better estimation of process time delay, and integral equation approach is extended to be useful for more general process response. Based on the obtained model, a performance benchmark is established by simulating model output. Appropriate retuning methods are selected when the index of absolute integral error (IAE) indicates bad performance. Simulations and experiments verify the effectiveness of the proposed method. Issues about estimation of process time delay, data preprocessing, and parameter selection are studied and discussed.

Identifying DQ-Domain Admittance Models of a 2.3-MVA Commercial Grid-Following Inverter via Frequency-Domain and Time-Domain Data

In this paper, we present two methods to identify the admittance of a 2.3-MVA commercial grid-following inverter through frequency-domain data and time-domain data. In addition to the well-known harmonic injection method to obtain the admittance at frequency points followed by vector fitting, we adopt a step response-based method where the step response data of the converter are collected and their s-domain expressions are obtained. In turn, the s-domain admittance model of the converter is found. The two methods can be used for cross validation. Step responses and frequency-domain responses obtained from the two methods are compared. Results show that the time-domain data-based method leads to an admittance comparable with that from the frequency-domain measurement in the range less than 60 Hz. In addition, two insights are obtained from the frequency-domain admittance measurements. First, when the dq-frame is aligned to the point of common coupling (PCC) voltage, the per unit DQ-domain admittance directly reflects operating conditions. Second, existence of negative-sequence control can be detected via sequence-domain admittances.

Synthesis of A Digital PID/LQR Control System for Duty-Cycle Modulation Buck Converters

<p>This research paper presents a synthesis approach of a digital optimal PID/LQR control system for DCM (duty-cycle cycle modulation) Buck converters. The step response of the DCM Buck converter is obtained under Multisim virtual simulation framework. The related data file is saved as *.SCP format, and imported into EditPad Lite7 editor, then exported as Matlab file to be processed. The transfer function of the DCM Buck converter is computed from the imported step response data. Then, using the zoh (zero order holder) discretization method with 100 ms resampling period, the z-transfer function of the DCM Buck converter is computed, and that of the analog optimal PID/LQR(linear quadratic regulator) controller is calculated using Tustin’s discretization technique. Furthermore, the step response of the related closed loop digital PID control system is simulated and compared to that of the original analog PID/LQR control system. The simulation results obtained are presented in order to show the high precision as well as the reliability of Matlab-based synthesis of digital optimal PID/LQR control systems for DCM Buck converters.</p>

Efficient low-order system identification from low-quality step response data with rank-constrained optimization

In the presence of low-quality industrial process data, generic step response identification methods typically show unsatisfactory performance and heavily rely on manual intervention of technical personnel. This erects obvious obstacles for the advancement of intelligent manufacturing in process industries. To address these challenges, we propose a novel rank-constrained optimization approach to low-order system identification from step response data, which yields much more accurate and robust estimates than existing modeling methods. By exploiting the inherent low-rank structure of the Hankel matrix of ideal step response, parameters of a low-order process can be accurately recovered by solving a rank-constrained program, which effectively bypasses the two-step procedure in some state-of-the-art algorithms involving significant error accumulation. The alternating direction method of multipliers is adopted to effectively solve the nonconvex error minimization problem and circumvent poor local optima. Case studies on both numerical examples and industrial datasets demonstrate that, the proposed method not only gives much better modeling accuracy, but also secures reliable and robust estimates even for raw low-quality industrial data. This is particularly helpful for automated execution of the identification routine without human intervention, with success percentage over 99% that is remarkably higher than the state-of-the-art.

Identification scheme for fractional Hammerstein models with the delayed Haar wavelet

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix (HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.

Identification of fractional-order transfer functions using exponentially modulated signals with arbitrary excitation waveforms

This paper proposes a new identification method based on an exponential modulation scheme for the determination of the coefficients and exponents of a fractional-order transfer function. The proposed approach has a broader scope of application compared to a previous method based on step response data, in that it allows for the use of arbitrary input signals. Moreover, it dispenses with the need for repeated simulations during the search for the best fractional exponents, which significantly reduces the computational workload involved in the identification process. Two examples involving measurement noise at the observed system output are presented to illustrate the effectiveness of the proposed method when compared to a conventional output-error optimization approach based on the polytope algorithm. In both examples, the proposed method is found to provide a better trade-off between computational workload and accuracy of the parameter estimates for different realizations of the noise.

Step Response-Based Identification of Fractional Order Time Delay Models

An identification method for fractional order models with time delay is presented. The proposed method, based on the output error optimization, simultaneously estimates model orders, coefficients and time delay from a single noisy step response. Analytical expressions for logarithmic derivatives of the step input are derived to evaluate the Jacobian and the Hessian required for the Newton’s algorithm for optimization. A simplified initialization procedure is also outlined that assumes an integral initial order and uses estimated coefficients as the initial guess. Simulation results are presented to demonstrate the efficacy of the proposed approach. Convergence of the Newton’s method and the Gauss–Newton scheme are also studied in simulation. Identification results from noisy step response data for time delay models with different structures are presented.

Multivariable Dynamic Input Shaping for Two-Axis Fast Steering Mirror

A two-axis Fast Steering Mirror (FSM) is a commonly used mechanical component used in optical imaging and laser beam steering. This paper shows how inverse kinematic analysis and dynamic input shaping can be used to compute the two-axis input signals for the actuation of a FSM to be able to track a desired output trajectory. The approach is based on quasi-static kinematic analysis and dynamic modeling of a two-axis FSM multivariable motion from experimental step response data. It is shown how open-loop tracking can be improved by properly designed dynamic input shaping signals that take into account the inverse kinematics and dynamic response of the FSM.

Switchable PID Controller Tuning Based on Golden Section Reduction Rule

Resulting from the complexity and sensitivity instinct, high-order control system design is always a challenge faced by engineers from process industry. To solve this challenging task, a switchable control scheme consisted of two sub-controllers tuned based on two complementary simplified models respectively is proposed in this paper, and golden section is introduced into process model reduction to simplify parameter tuning. Inspired by adaptive control strategy, the controller switch mechanism depends on the time domain response similarity between the original high-order model and the simplified model. Besides, PID controller structure and corresponding parameter tuning method, such as Ziegler-Nichols method and SIMC method, are remained to guarantee the facility and efficiency of sub-controller design. The proposed method has been tested on several examples (balanced, lag-dominant, and a delay-dominant process) and the comparison with other tuning method based on step-response data resulting in favorable control performance.

Method of automatic steering system design and parameter optimisation for small tractors

In order to improve the operational efficiency and quality of small tractors, the original manual steering system needs to be renovated to include automatic steering functionality, which is the basis of autonomous navigation. Here, a modification method based on the steering circuit of a Dongfanghong SG250 tractor and a method to calculate the virtual steering angle is proposed. A small tractor steering model is established from the step response data of the system, and a PD controller for this model is also designed. The PD controller can also adapt to varying tractor speeds for optimal functionality in changing operational conditions, and a parameter optimisation approach for the speed-adaptive PD controller is proposed. Test results show that at a speed of 0.5 m s−1, the steady-state error in the step response is 0.32°, the percentage error is 2.3%, the overshoot is 1.86°, and the percentage overshoot is 13.7%. For a ramp response, the average signal latency is 0.82 s and the steady-state error is 0.25°. The ability of the PD to adapt to changing speeds is also tested at different speeds. The results show that the steering system performs well.