Class Of SISO Nonlinear Systems Research Articles

Using Memoryless Output Feedback to Semiglobally Stabilize a Class of SISO Nonlinear Systems With Input Delay

Using the semiglobal control idea from the recent work (Wang and Lin, 2022), we present a different semiglobal method without invoking the dynamic extension technique to prove that in the single-input-single-output (SISO) case, certain nonaffine systems with input delay are semiglobally asymptotically stabilizable (SGAS) via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -dimensional memoryless output feedback. A dynamic output compensator is constructed and composed of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -dimensional nonlinear observer and an observer-based controller, both of them with saturated states. As a consequence, an affine system in a lower triangular form with input delay is shown to be SGAS by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -dimensional memoryless output feedback. These results provide some answers to the open question in (Wang and Lin, 2022) where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(2n-1)$</tex-math></inline-formula> -dimensional output feedback controllers were found by a dynamic extension method: when and how to design delay-free, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -dimensional SGAS output feedback controllers for a significant class of SISO nonaffine systems?

Fuzzy Disturbance Observer Design for a Class of Nonlinear SISO Systems

Fuzzy Disturbance Observer Design for a Class of Nonlinear SISO Systems

Robust Output Feedback Passivity-Based Variable Structure Controller Design for Nonlinear Systems

This paper examines the use of an output feedback variable structure controller with a nonlinear sliding surface for a class of SISO nonlinear systems in the presence of matched disturbances. With only the measurable system output, the discontinuous observer reconstructs the system states and ensures that the estimation errors exponentially approach zero. Using the estimation states, the proposed nonlinear sliding surface with variable damping ratio can simultaneously achieve low overshoot and short settling time. Then the passivity-based controller including a discontinuous term can guarantee that the closed-loop system asymptotically converges to the sliding surface. Compared with other sliding mode controllers, the proposed passivity-based control scheme has better transient performance and effectively reduces the control gain. Finally, simulation results demonstrate the validity of the proposed method.

Robust predictive tracking control for a class of nonlinear systems

A robust predictive tracking control (RPTC) approach is developed in this paper to deal with a class of nonlinear SISO systems. To improve the control performance, the RPTC architecture mainly consists of a robust fuzzy PID (RFPID)-based control module and a robust PI grey model (RPIGM)-based prediction module. The RFPID functions as the main control unit to drive the system to desired goals. The control gains are online optimized by neural network-based fuzzy tuners. Meanwhile using grey and neural network theories, the RPIGM is designed with two tasks: to forecast the future system output which is fed to the RFPID to optimize the controller parameters ahead of time; and to estimate the impacts of noises and disturbances on the system performance in order to create properly a compensating control signal. Furthermore, a fuzzy grey cognitive map (FGCM)-based decision tool is built to regulate the RPIGM prediction step size to maximize the control efforts. Convergences of both the predictor and controller are theoretically guaranteed by Lyapunov stability conditions. The effectiveness of the proposed RPTC approach has been proved through real-time experiments on a nonlinear SISO system.

Direct Adaptive Fuzzy Control of SISO Nonlinear Systems with Input–Output Nonlinear Relationship

Because the nonlinear relationship between the input and output generally exists in many actual systems. In this paper, a new design method of direct adaptive fuzzy controller is proposed for this class of SISO nonlinear systems. The adaptive law and constraint conditions of the system parameters are given in this study. The stability of the closed-loop system is proved with all state variables being uniformly bounded in the Lyapunov sense. Additionally, the convergence of the fuzzy control system is analyzed. Finally, the simulation results obtained for the practical example show the feasibility, effectiveness and widely use of the designed method.

An Improved Multi-Level Adaptive Control Algorithm Based on Parameters Self-Tuning for a Class of SISO Nonlinear Systems

In this paper, a multi-level adaptive control algorithm using parameters self-tuning is proposed for improving the tracking performance of a class of SISO nonlinear systems. This scheme is comprised of the pseudo partial derivative estimation law and the adaptive control law. The adaptive control law is derived from a novel higher order weighted one-step-ahead criterion function which exploits more previous control information. In order to identify the laws’ penalty factors which partly imply the dynamics of the system, an approach of parameters self-tuning is proposed with on-line recursive gradient algorithm. This design is model free and depends directly on the pseudo partial derivative updating on-line with the input and output data Simulation examples are provided to illustrate the effectiveness of the proposed method.

Direct fuzzy adaptive control based on sliding surface for a class of SISO non-linear systems

In this work we are interested in direct fuzzy adaptive control. The continuous SISO non-linear system is presented by the Takgi-Sugeno type fuzzy state model. The strategy of reference model direct adaptive control theory is presented then the adaptive fuzzy adjustment algorithm is presented. The control law includes two terms. The first is responsible to stabilise the plant is computed based on PDC method. The second constitutes the feed forward gain. All the parameters of the controller are adjusted online. The adjustment algorithm of the controller parameters exploits the sliding surface to profit of robustness of sliding mode control. The stability analysis of the closed-loop system has been proven using the Lyapunov approach. The single synchronous generator coupled to the infinite-bus power system is used to check the performances of the proposed control scheme.

A Nonlinear Control Method Based on ANFIS and Multiple Models for a Class of SISO Nonlinear Systems and Its Application

This paper presents a novel nonlinear control strategy for a class of uncertain single-input and single-output discrete-time nonlinear systems with unstable zero-dynamics. The proposed method combines adaptive-network-based fuzzy inference system (ANFIS) with multiple models, where a linear robust controller, an ANFIS-based nonlinear controller and a switching mechanism are integrated using multiple models technique. It has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system. Moreover, it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance. As a result, the controller has the following three outstanding features compared with existing control strategies. First, this method relaxes the assumption of commonly-used uniform boundedness on the unmodeled dynamics and thus enhances its applicability. Second, since ANFIS is used to estimate and compensate the effect caused by the unmodeled dynamics, the convergence rate of neural network learning has been increased. Third, a "one-to-one mapping" technique is adapted to guarantee the universal approximation property of ANFIS. The proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system, respectively, where its effectiveness has been justified.

Subsystem backstepping design for controlling a class of nonlinear SISO systems with cascade structure

This paper presents a controller design, referred to as the subsystem backstepping design (SSBD), for a class of nonlinear SISO mechatronic systems that comprise several cascaded subsystems. Compared with the conventional integrator backstepping design (CIBD) that deals with a first-order equation at each design step, the SSBD manages at each design step a subsystem that can be of high order. This both simplifies the design procedure and also makes controller parameters conveniently determined according to dynamic characteristics of each subsystem as in the conventional cascade control design with multiple feedback loops. However, in contrast to the conventional cascade control design, the SSBD does not require the inner feedback loop to respond much faster than the outer feedback loop, while guaranteeing system stability for a class of nonlinear systems. In addition, a variant of the SSBD, called internal model principle-based SSBD (IMP-SSBD), is presented to both further demonstrate the advantages of the SSBD procedure over the CIBD and also achieve robust tracking performance. The effectiveness of the proposed scheme is demonstrated through experimental studies of a harmonic drive system suffering from transmission compliance and periodic disturbances.

Neural Network Adaptive Control for a Class of SISO Nonlinear Systems

An adaptive neural network control scheme is presented for a class of SISO affine nonlinear systems. Parameters in neural networks are updated using a gradient descent method. No robustifying control term is used in controller. The convergence of adaptive parameters and tracking error and the boundedness of all states in the corresponding closed-loop system are demonstrated by Lyapunov stability theorem. Simulation results demonstrate the effectiveness of the approach.

Direct Adaptive Fuzzy Output Feedback Control for a Class of SISO Nonlinear Systems with Unknown Control Direction

AbstractIn this paper, a direct adaptive output feedback control scheme using fuzzy systems is presented for a class of uncertain SISO nonlinear systems with unknown control direction. Within this scheme, a high-gain observer is employed to estimate the unavailable system states, a fuzzy system is employed to generate directly the control input signal with only output feedback, and the Nussbaum-type function is used to deal with the unknown control direction. The stability of the closed-loop system is performed using a Lyapunov approach. Simulation results are provided to verify the effectiveness of the proposed design.

Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance

AbstractIn this paper, we investigate the problem of output‐feedback tracking control for a class of nonlinear SISO systems in the strick‐feedback form, which are subject to both uncertain delay‐related functions and disturbances. A reduced‐order observer is first introduced to provide the estimates of the unmeasured states. Then, an output‐feedback controller is recursively designed based on the backsteppng method. By constructing an appropriate Lyapunov–Krasovskii functional, we prove that all the signals in the closed‐loop system are bounded. The tracking performance is guaranteed by suitably choosing the design parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed control algorithm. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction

In this paper, a direct fuzzy adaptive robust control approach is proposed for a class of SISO nonlinear systems with completely unknown virtual control directions, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, fuzzy logic systems are employed to approximate the combined nonlinear uncertainties, a dynamic signal and Nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions, respectively. It is proved that the proposed robust fuzzy adaptive scheme can guarantee the all signals in the closed-loop system are semi-globally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated via three examples.

Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input

Based on the universal approximation property of the fuzzy-neural networks, an adaptive fuzzy-neural observer design algorithm is studied for a class of nonlinear SISO systems with both a completely unknown function and an unknown dead-zone input. The fuzzy-neural networks are used to approximate the unknown nonlinear function. Because it is assumed that the system states are unmeasured, an observer needs to be designed to estimate those unmeasured states. In the previous works with the observer design based on the universal approximator, when the dead-zone input appears it is ignored and the stability of the closed-loop system will be affected. In this paper, the proposed algorithm overcomes the affections of dead-zone input for the stability of the systems. Moreover, the dead-zone parameters are assumed to be unknown and will be adjusted adaptively as well as the sign function being introduced to compensate the dead-zone. With the aid of the Lyapunov analysis method, the stability of the closed-loop system is proven. A simulation example is provided to illustrate the feasibility of the control algorithm presented in this paper.

An indirect model reference robust fuzzy adaptive control for a class of SISO nonlinear systems

In this paper we are interested in robust adaptive fuzzy control of nonlinear SISO systems in the presence of parametric uncertainties. The plant model structure is represented by the Takagi-Sugeno (T-S) type fuzzy system. An indirect adaptive fuzzy controller based on model reference control scheme is proposed to provide asymptotic tracking of reference signal. The controller parameters are computed at each time. The plant state tracks asymptotically the state of the reference model for any bounded reference input signal. Inverted pendulum and mass spring damper are used to check the performance of the proposed controller.

Model-matching Quantization for a Class of SISO Nonlinear Systems

Model-matching Quantization for a Class of SISO Nonlinear Systems

An indirect adaptive fuzzy sliding mode controller for a class of SISO non-linear systems

In this paper, we propose an indirect adaptive fuzzy controller for a class of SISO non-linear systems. The plant model structure is represented by a Takagi-Sugeno (T-S) type fuzzy system. The parameters of the T-S fuzzy model are adjusted online; the proposed algorithms are based on sliding manifold. The indirect adaptive fuzzy controller is based on a adjustable T-S fuzzy parameters model and sliding mode theory. The analysis of the stability of the adaptive algorithms is based on the Lyapunov approach. The plant state tracks asymptotically any bounded reference input signal. Inverted pendulum and mass spring damper are two examples used to check performances of the proposed fuzzy adaptive control scheme.

Adaptive Neural Control of SISO Time-Delay Nonlinear Systems with Unknown Hysteresis Input

In this paper, adaptive variable structure neural control is investigated for a class of SISO nonlinear systems in a Brunovsky form with state time-varying delays and unknown hysteresis input. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The effect of the unknown hysteresis with the Prandtl-Ishlinskii model is mitigated using the proposed adaptive control. By utilizing the integral-type Lyapunov function, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the approach.

Adaptive robust motion control of SISO nonlinear systems with implementation on linear motors

For the purpose of controlling an X– Y table driven by linear motors with a high precision, an adaptive robust motion tracking control method is first introduced. The controller is developed based upon a class of SISO nonlinear systems whose nonlinear part can be linearly parameterized. The advantage of such a controller is that parametric uncertainties and unknown disturbances can be dealt with, which is essential for a high precision of the control of linear-motor-driven X– Y table. With the prior knowledge of the bounds of the system parameters, a discontinuous projection is utilized in the adaptive law to ensure the boundedness of the parameters estimates. The algorithm is then implemented on a real X– Y table driven by the linear motors. In the modeling of such a system, fiction effects are also considered, which is useful for the derivation of the adaptive law. Experiments on the X– Y table are carried out and the results show excellent tracking performance of the system.

Cascade Observers for Nonlinear Systems and Application to Nonlinear Output Feedback Control

In this paper, we present a new observer, namely a cascade observer, for a general class of nonlinear SISO systems. Inspired by but different from a high-gain observer, the cascade observer features a cascade structure and adaptive observer gains. In doing so the cascade observer attempts to overcome some of the typical problems that may pose to a high-gain observer. As in the case of a high-gain observer, the cascade observer structure is simple and universal in the sense that it is independent of the system dynamics and parameters. It is shown that the estimation errors converge to zero and all the internal variables are globally uniformly bounded. Based on the cascade observer, an adaptive output feedback controller is designed for a class of SISO nonlinear systems represented globally by a nth-order differential equation. The output feedback controller has the same structure as a state feedback controller. Globally uniformly ultimate boundedness of tracking errors is achieved for the nonlinear systems with unknown parameters.