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In this study a control-oriented model is proposed to represent a wide range of non-linear discrete-time dynamic plants. As a testimony to the efficiency of the model structure for control system design, a pole placement controller is designed for non-linear discrete-time plants. Mathematically the solution of the controller output is converted into resolving a polynomial equation in the current control term u( t), which significantly reduces the difficulties encountered in non-linear control system synthesis and computational complexities. The integrated procedure provides a straightforward methodology to use in linear control system design techniques when designing non-linear control systems. For a demonstration of the effectiveness of the proposed methodology used to deal with practical problems, pole placement controllers are designed for three non-linear plants, including the Hammerstein model, a laboratory-scale liquid level system and a continuous stirred tank reactor. The simulation results are presented with graphical illustrations.

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In this study, a novel output feedback terminal sliding mode control (TSMC) approach is proposed for a class of second order nonlinear systems in light of the equivalent output injection sliding mode observer (SMO) method and TSMC principle. The SMO method is applied to reconstruct full states in finite time and the non‐singular TSMC algorithm is designed to stabilize system states to equilibrium points in finite time. The corresponding stability analysis is presented. An indispensable illustrative example is bench tested to validate the effectiveness of the proposed approach.

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two subalgorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance.

This paper is a summary of the research development in the rational (total) nonlinear dynamic modelling over the last two decades. Total nonlinear dynamic systems are defined as those where the model parameters and input (controller outputs) are subject to nonlinear to the output. Previously this class of models has been known as rational models, which is a model that can be considered to belong to the Non-linear AutoRegressive Moving Average with eXogenous input (NARMAX) model subset and is an extension of the well-known polynomial NARMAX model. The justification for using the rational model is that it provides a very concise and parsimonious representation for highly complex non-linear dynamic systems and has excellent interpolatory and extrapolatory properties. However model identification and controller design are much more challenging compared to the polynomial models. This has been a new and fascinating research trend in the area of mathematical modelling, control and applications, but still within a limited research community. This paper brings several representative algorithms together, developed by the authors and their colleagues, to form an easily referenced archive for promotion of the awareness, tutorial, applications, and even further research expansion.

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