Recursive Identification for MIMO Fractional-Order Hammerstein Model Based on AIAGS

In this paper, adaptive immune algorithm based on a global search strategy (AIAGS) and auxiliary model recursive least square method (AMRLS) are used to identify the multiple-input multiple-output fractional-order Hammerstein model. The model’s nonlinear parameters, linear parameters, and fractional order are unknown. The identification step is to use AIAGS to find the initial values of model coefficients and order at first, then bring the initial values into AMRLS to identify the coefficients and order of the model in turn. The expression of the linear block is the transfer function of the differential equation. By changing the stimulation function of the original algorithm, adopting the global search strategy before the local search strategy in the mutation operation, and adopting the parallel mechanism, AIAGS further strengthens the original algorithm’s optimization ability. The experimental results show that the proposed method is effective.

Discrete indirect adaptive sliding mode control for uncertain Hammerstein nonlinear systems

The robustness issue of uncertain nonlinear systems’ control has attracted the attention of numerous researchers. In this paper, we propose three techniques to deal with the uncertain Hammerstein nonlinear model. First, a discrete sliding mode control (SMC) is developed, which is based on converting the original nonlinear system into a linearized one in the vicinity of the operating region using Taylor series expansion. However, the presence of relatively high nonlinearities and parameter variations leads to the deterioration of the desired performances. In order to overcome these problems and to improve the performance of classical SMC, we propose two solutions. The first one is based on the synthesis of a discrete SMC, taking into account the presence of nonlinearity. The second solution is a new discrete adaptive SMC for input–output Hammerstein model. In order to show the effectiveness of the proposed controllers, a detailed robustness analysis is clearly developed. Simulation examples are reported at the end of the paper.

Rate-Dependent Modeling of Piezoelectric Actuators for Nano Manipulation Based on Fractional Hammerstein Model

Piezoelectric actuators (PEAs), as a smart material with excellent characteristics, are increasingly used in high-precision and high-speed nano-positioning systems. Different from the usual positioning control or fixed frequency tracking control, the more accurate rate-dependent PEA nonlinear model is needed in random signal dynamic tracking control systems such as active vibration control. In response to this problem, this paper proposes a Hammerstein model based on fractional order rate correlation. The improved Bouc-Wen model is used to describe the asymmetric hysteresis characteristics of PEA, and the fractional order model is used to describe the dynamic characteristics of PEA. The nonlinear rate-dependent hysteresis model can be used to accurately describe the dynamic characteristics of PEA. Compared with the integer order model or linear autoregressive model to describe the dynamic characteristics of the PEA Hammerstein model, the modeling accuracy is higher. Moreover, an artificial bee colony algorithm (DE-ABC) based on differential evolution was proposed to identify model parameters. By adding the mutation strategy and chaos search of the genetic algorithm into the previous ABC, the convergence speed of the algorithm is faster and the identification accuracy is higher, and the simultaneous identification of order and coefficient of the fractional model is realized. Finally, by comparing the simulation and experimental data of multiple sets of sinusoidal excitation with different frequencies, the effectiveness of the proposed modeling method and the accuracy and rapidity of the identification algorithm are verified. The results show that, in the wide frequency range of 1–100 Hz, the proposed method can obtain more accurate rate-correlation models than the Bouc-Wen model, the Hammerstein model based on integer order or the linear autoregressive model to describe dynamic characteristics. The maximum error (Max error) is 0.0915 μm, and the maximum mean square error (RMSE) is 0.0244.

Recursive least squares identification of heat exchanger system using block-structured models

This study provides a recursive parametric identification scheme for a liquid-saturated steam heat exchanger system. The recursive identification scheme uses block-structured Wiener and Hammerstein models as model structure and recursive least squares estimation scheme as the parameter estimation method. The estimated block-oriented model provides higher accuracy of estimation than linear models provided in the literature. From the simulation results, it is observed that the Wiener model can provide 88% goodness-of-FIT, whereas Hammerstein model can provide 96% goodness-of-FIT using the said technique.

Identification of the Thermoelectric Cooler Using Hybrid Multi-Verse Optimizer and Sine Cosine Algorithm Based Continuous-Time Hammerstein Model

This paper presents the identification of the ThermoElectric Cooler (TEC) plant using a hybrid method of Multi-Verse Optimizer with Sine Cosine Algorithm (hMVOSCA) based on continuous-time Hammerstein model. These modifications are mainly for escaping from local minima and for making the balance between exploration and exploitation. In the Hammerstein model identification a continuous-time linear system is used and the hMVOSCA based method is used to tune the coefficients of both the Hammerstein model subsystems (linear and nonlinear) such that the error between the estimated output and the actual output is reduced. The efficiency of the proposed method is evaluated based on the convergence curve, parameter estimation error, bode plot, function plot, and Wilcoxon’s rank test. The experimental findings show that the hMVOSCA can produce a Hammerstein system that generates an estimated output like the actual TEC output. Moreover, the identified outputs also show that the hMVOSCA outperforms other popular metaheuristic algorithms.

Dual-Input Slope Seeking Control of Continuous Micro-Algae Cultures with Experimental Validation

This paper investigates the application of adaptive slope-seeking strategies to dual-input single output dynamic processes. While the classical objective of extremum seeking control is to drive a process performance index to its optimum, this paper also considers slope seeking, which allows driving the performance index to a desired level (which is thus sub-optimal). Moreover, the consideration of more than one input signal allows minimizing the input energy thanks to the degrees of freedom offered by the additional inputs. The actual process is assumed to be locally approachable by a Hammerstein model, combining a nonlinear static map with a linear dynamic model. The proposed strategy is based on the interplay of three components: (i) a recursive estimation algorithm providing the model parameters and the performance index gradient, (ii) a slope generator using the static map parameter estimates to convert the performance index setpoint into slope setpoints, and (iii) an adaptive controller driving the process to the desired setpoint. The performance of the slope strategy is assessed in simulation in an application example related to lipid productivity optimization in continuous cultures of micro-algae by acting on both the incident light intensity and the dilution rate. It is also validated in experimental studies where biomass production in a continuous photo-bioreactor is targeted.

Noise Reduction in the Swept Sine Identification Procedure of Nonlinear Systems

The Hammerstein model identification technique based on swept sine excitation signals proved in numerous applications to be particularly effective for the definition of a model for nonlinear systems. In this paper we address the problem of the robustness of this model parameter estimation procedure in the presence of noise in the measurement step. The relationship between the different functions that enter the identification procedure is analyzed to assess how the presence of additive noise affects model parameters estimation. This analysis allows us to propose an original technique to mitigate the effects of additive noise in order to improve the accuracy of model parameters estimation. The different aspects addressed in the paper and the technique for mitigating the effects of noise on the accuracy of parameter estimation are verified on both synthetic and experimental data acquired with an ultrasonic system. The results of both simulations and experiments on laboratory data confirm the correctness of the assumptions made and the effectiveness of the proposed mitigation methodology.

A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control

A continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein’s model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem.