Robust Adaptive Control of Pulse-width Modulated Rectifiers Based on Adaptive Super-twisting Sliding-mode and State Feedback Controllers

Abstract—This article proposes a new robust adaptive hybrid controller for three-phase pulse-width modulated rectifiers to improve control performance. This hybridization is implemented by combining the second-order sliding mode with the adaptive gain super-twisting control law in the DC bus voltage control loop and state feedback adaptive control in the d-q-axis current control loops. The control objectives are fourfold: (1) driving the DC bus voltage to a reference signal without using a priori knowledge of the plant parameters, (2) forcing the d-q-axis current errors to zero, (3) assuring a satisfactory power factor correction in relation to the AC source, and (4) eliminating the chattering effect. In the closed-loop control system, three-phase source currents and the DC bus voltage are supposed to be available for feedback. As a result, no a priori knowledge of the plant parameters is necessary in the design of the proposed controller. In addition, the proposed controller does not have the disadvantages of singularity, over-parameterization, and chattering phenomenon. Results of experimental studies prove that the proposed control system guarantees the tracking of reference signals with high performance despite all the parameter and external disturbance uncertainties.     

Optimal robust adaptive fuzzy synergetic power system stabilizer design

A new particle swarm optimized robust indirect adaptive power system stabilizer is developed based on recently developed synergetic control methodology. Fuzzy systems are used in an adaptive scheme to approximate the system using a nonlinear model while synergetic control guarantees robustness and the use of a chatter free continuous control law which makes the controller easy to implement. In addition the controller parameters are optimized using PSO approach. Simulation of severe operating conditions of a power system is conducted to validate the effectiveness of the proposed approach while stability is guaranteed via Lyapunov synthesis.     

Transient performance improvement of model reference adaptive control: LMI‐based resetting

In this paper, a resetting mechanism is proposed to enhance the transient performance of model reference adaptive control. While the suggested method has a simple structure, it is capable of taking into account both the desired steady‐state behavior and the transient response, simultaneously. Whenever the transient specification is not satisfying, there is a jump in the controller parameters. This jump is determined by designing an optimal reset law. At the reset times, the after‐reset values of parameters are calculated based on a minimization problem. The considered cost function is a mixed H₂/H_∞ criterion, which minimizes the tracking error. The optimization problem is converted to an LMI formulation, and the reset law is designed by solving this LMI at certain reset times. To verify the effectiveness of the proposed approach, simulation results are presented.     

Reference Model with an Adaptive Hermite Fuzzy Neural Network Controller for Tracking a Synchronous Reluctance Motor

This article presents a reference adaptive Hermite fuzzy neural network controller for a synchronous reluctance motor. Although synchronous reluctance motors are mathematically and structurally simple, they perform poorly under dynamic modes of operation because certain parameters, such as the external load and non-linear friction, are difficult to control. The proposed adaptive Hermite fuzzy neural network controller overcomes this problem, as using the Hermite function instead of the conventional Gaussian function shortens the training time. Furthermore, the proposed adaptive Hermite fuzzy neural network controller uses an online self-tuning fuzzy neural network to estimate the system's lumped uncertainty. The estimation method involves a fuzzy controller with expert knowledge of the initial weight of the neural network. Finally, the Lyapunov stability theory and adaptive update law were applied to guarantee system convergence. In this article, the responsiveness of the adaptive Hermite fuzzy neural network controller and an adaptive reference sliding-mode controller is compared. The experimental results show that the adaptive Hermite fuzzy neural network controller markedly improved the system's lumped uncertainty and external load response.     

Robust and simple adaptive control system design

Recently, the simple adaptive control (SAC) method has attracted considerable interest because of the simple structure of its adaptive controller. The method can only be applied to plants with so-called almost strictly positive real (ASPR) characteristics. Unfortunately, most real plants do not satisfy this condition. Furthermore, real plants contain disturbances such as uncertain elements. This paper deals with such problems and proves that the implementation of a parallel feedforward compensator makes it possible to apply the SAC method to non-ASPR SISO plants with plant uncertainties. Furthermore, a robust SAC algorithm in the presence of a class of external disturbances is also considered. The effectiveness of the parallel feedforward compensator and robust adaptive controller designed in this way is examined through several numerical simulations.     

Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence

This paper provides a modified model reference adaptive control (MRAC) scheme to achieve better transient control performance for systems with unknown unmatched dynamics, where an adaptive law with guaranteed convergence is introduced. We first revisit the standard MRAC system and analyze the tracking error bound by using L₂‐norm and Cauchy‐Schwartz inequality. Based on this analysis, we suggest a feasible way to compensate the undesired transient dynamics induced by the gradient descent–based adaptive laws subject to sluggish convergence or even parameter drift. Then, a modified adaptive law with an alternative leakage term containing the parameter estimation error is developed. With this adaptive law, the convergence of both the estimation error and tracking error can be proved simultaneously. This enhanced convergence property can contribute to deriving smoother control signal and improved control response. Moreover, this paper provides a simple and numerically feasible approach to online verify the well‐known persistent excitation condition by testing the positive definiteness of an introduced auxiliary matrix. Comparative simulations based on a benchmark 3‐DOF helicopter model are given to validate the effectiveness of the proposed MRAC approach and show the improved performance over several other MRAC schemes.     

Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties. How to control such systems effectively is one of the most challenging problems. This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems. The controller can be used in cases where there exist parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The design of the controller is based on the control Lyapunov function method. A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics, nonlinear uncertainties and unknown bounded disturbances. The backstepping procedure is employed to overcome the complexity in the design. With the proposed method, the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system. Furthermore, all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately. Simulation results illustrate the effectiveness of the proposed robust adaptive controller. __________ Translated from Journal of Sichuan University (Engineering Science Edition), 2005, 37(5): 148–153 (in Chinese)     

Adaptive sliding mode control for fuzzy singular systems with time delay and input nonlinearity

This paper addresses the sliding mode control problem for a class of uncertain Takagi‐Sugeno fuzzy singular systems with state delay and subject to input nonlinearity. Our purpose is focused on designing an adaptive sliding mode controller for such a complex system. First, a new fuzzy integral‐type sliding function is designed. Then, an adaptive sliding mode control scheme is established such that the resulting closed‐loop system is insensitive to all admissible uncertainties and satisfies the reaching condition. Moreover, delay‐dependent sufficient conditions are derived such that the admissibility and the L₂‐L_∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delays, external disturbances, and sector nonlinearity input. Finally, the validity and applicability of the proposed theory are illustrated by a numerical example.     

A robust adaptive control with unmodeled dynamic for HVDC transmission systems

Utilizing the feature of quick response of HVDC to improve the performance of AC/DC system has become the emphasis to be researched. This paper introduces firstly the principle of the robust adaptive control of nonlinear systems with unmodeled dynamics, then developed the robust adaptive additional control of HVDC with unmodeled dynamics of generator in order to improve stability of power system. The additional control of HVDC with unmodeled dynamics only uses the local signals and its design is simple, furthermore it can obviously improve the stability of power system in different operational conditions. Experimental results using the presented concepts obtained on single machine infinite bus model are also included. These results prove the efficiency of the control scheme. The design process of controller provided a new idea to design controller by use of simplified model. __________ Translated from Journal of Sichuan University (Engineering Science Edition), 2005, 37(5): 154–158 (in Chinese)     

Online self‐tuning mechanism for direct adaptive control of tall building

The simple adaptive control (SAC) method is known as a remarkable solution to reduce the negative influence of different uncertainties on active control of building structures during an earthquake. The design parameters of this direct adaptive control algorithm are determined after a large number of sensitivity analyses. Furthermore, the selected parameters will not necessarily lead a controller to the optimum performance of the structure. Herein, an innovative online self‐tuning method is firstly introduced to improve the SAC method and cancel out excessive sensitivity analysis. Accordingly, a fuzzy inference system is designed to select the appropriate SAC method, adjusting parameters online instead of using fixed parameters. To show the efficiency of the introduced method, a 20‐story steel building structure equipped with magnetorheological dampers in each story is considered as a benchmark control. The performance of the designed control system is evaluated in different condition of base excitation with and without uncertainty in the model of the proposed structure. The results from the numerical simulations show that the introduced method has better performance than the SAC method with fixed adjusting parameters. The predominance of the method becomes clearer when an input ground motion to the control system has completely different characteristics than the initial designed seismic excitation.     

Parameter‐dependent Riccati equation–based output feedback adaptive control

A parameter‐dependent Riccati equation approach is proposed to design and analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment an existing fixed‐gain observer‐based output feedback control law. Although the formulation is in the setting of model reference adaptive control, the realization of the adaptive controller does not require implementing the reference model. In this regard, the increased complexity of implementing the adaptive controller, above that of a fixed‐gain control law, is less than that of other methods. The error signals are shown to be uniformly ultimately bounded, and an estimate for the ultimate bound is provided. The issue of sensor noise is addressed by introducing an error filter. The control design process and the theoretical results are illustrated using a model for wing rock dynamics.     

Quaternion-based adaptive control for trajectory tracking of quadrotor unmanned aerial vehicles

The problem of trajectory tracking of aerial vehicles with four rotors and dynamic parameter uncertainties is addressed in this article. By exploiting the cascade structure of the translational and attitude dynamics of the quadrotor, a nonlinear hierarchical adaptive control is proposed. The attitude control law is designed based on the unit quaternion, therefore, the singularities of the Euler angles and angle-axis representation are avoided. Instead of relying on the stability properties of time-varying cascade systems, the stability of the whole closed-loop system is proven by an appropriate Lyapunov function. In addition, a novel method to compute the desired orientation based on the desired Cartesian trajectories and position control inputs is proposed. A set of simulations results are presented to assess the performance of the proposed adaptive controller.     

并联型有源滤波器直流电压的简单自适应控制

提出了一种基于二次性能指标的简单自适应控制算法，通过采用滞环电流控制产生了脉宽调制的开关信号，设计了并联型有源滤波器直流电压控制器。仿真结果表明，与常规的比例–积分控制相比，对并联型有源滤波器直流电压采用简单自适应控制可获得更好的动态性能，且负载变化时的鲁棒性更好。     

Adaptive controller design and disturbance attenuation for SISO linear systems with zero relative degree under noisy output measurements

In this paper, we present robust adaptive controller design for SISO linear systems with zero relative degree under noisy output measurements. We formulate the robust adaptive control problem as a nonlinear H^∞‐optimal control problem under imperfect state measurements, and then solve it using game theory. By using the a priori knowledge of the parameter vector, we apply a soft projection algorithm, which guarantees the robustness property of the closed‐loop system without any persistency of excitation assumption of the reference signal. Owing to our formulation in state space, we allow the true system to be uncontrollable, as long as the uncontrollable part is stable in the sense of Lyapunov, and the uncontrollable modes on the jω‐axis are uncontrollable from the exogenous disturbance input. This assumption allows the adaptive controller to asymptotically cancel out, at the output, the effect of exogenous sinusoidal disturbance inputs with unknown magnitude, phase, and frequency. These strong robustness properties are illustrated by a numerical example. Copyright © 2009 John Wiley & Sons, Ltd.     

Reduced‐order robust adaptive control design of uncertain SISO linear systems

In this paper, a stability and robustness preserving adaptive controller order‐reduction method is developed for a class of uncertain linear systems affected by system and measurement noises. In this method, we immediately start the integrator backstepping procedure of the controller design without first stabilizing a filtered dynamics of the output. This relieves us from generating the reference trajectory for the filtered dynamics of the output and thus reducing the controller order by n, n being the dimension of the system state. The stability of the filtered dynamics is indirectly proved via an existing state signal. The trade‐off for this order reduction is that the worst‐case estimate for the expanded state vector has to be chosen as a suboptimal choice rather than the optimal choice. It is shown that the resulting reduced‐order adaptive controller preserves the stability and robustness properties of the full‐order adaptive controller in disturbance attenuation, boundedness of closed‐loop signals, and output tracking. The proposed order‐reduction scheme is also applied to a class of single‐input single‐output linear systems with partly measured disturbances. Two examples are presented to illustrate the performance of the reduced‐order controller in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Filtered adaptive constrained sampled-data control for uncertain multivariable nonlinear systems

A filtered adaptive constrained sampled-data controller for uncertain multivariable nonlinear systems in the presence of various constraints is synthesized in this paper. A piecewise constant adaptive law drives that estimation error dynamics to zero at each sampling time instant yields adaptive parameters. The filtered control scheme consists of two components. Based on an estimation/cancellation strategy, a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters, whereas a constraint violation avoidance control law is designed to solve an online constrained optimization problem. Although a reduced sampling time helps to minimize the estimation error caused by the neglect of unknowns, the resulting aggressive signals put more restrictions on the control law. Greater sacrifice of tracking performance is required to satisfy the constraints. The constraints violation avoidance control law is in favor of a larger sampling time. Sufficient conditions are given to guarantee the stability of the closed-loop system with the sampled-data controller, where the input/output signals are held constant over the sampling period. Numerical examples are provided to validate the theoretical results, comparisons between the constrained sampled-data controller and unconstrained adaptive controller with the implementation of different sampling times are carried out.     

A robust adaptive pole‐placement controller without strictly positive real condition

This paper considers the adaptive pole‐placement control problem for system (1) with unmodelled dynamics η_n dominated by a small constant ε multiplied by a quantity independent of ε but tending to infinity as the past input, output, and noise grow. Using bounded external excitation and randomly varying truncation techniques, we give a design method of adaptive pole‐placement controller. It is shown that the closed‐loop system is globally stable, the estimation error for the parameter contained in the modelled part is of order ε, and the closed‐loop system under the adaptive pole‐placement control law is suboptimal in the sense of $$\mathop{\lim\sup}\limits_{{n\to\infty }}{1\over n}\mathop{\sum}\limits_{i=0}^n{\left({A^{*}(z)y_{n}‐L(z)C(z)w_{n}‐B(z)R(z)y_{n}^{*}}\right)^{2}{\leq}O({\varepsilon}^{2})+\gamma^{2}\mathop{\sum}\limits_{j=1}^q{b_{j}^{2}}}$$\nopagenumbers\end while the SPR condition used usually in other papers is replaced by a stability condition. Copyright © 2001 John Wiley & Sons, Ltd.     

Enhancing optimal controllers via techniques from robust and adaptive control

Optimal control strategies for both non-linear and linear plants and indices are notoriously sensitive to modelling errors and external noise disturbances. In this paper a general framework to enhance robustness of an optimal control law is presented, with emphasis on the non-linear case. The framework allows a blending of off-line non-linear optimal control, on-line linear robust feedback control for regulation about the optimal trajectory and on-line adaptive techniques to enhance performance/robustness. The adaptive-Q techniques are those developed in previous work based on the Youla-Kucera parametrization for the class of all stabilizing two-degree-of-freedom controllers. Some general fundamental stability properties are developed which are new, at least for the non-linear plant and linear robust controller case. Also, performance enhancement results in the presence of unmodelled linear dynamics based on an averaging analysis are reviewed. A convergence analysis based on averaging theory appears possible in principle for any specific non-linear system but is beyond the scope of the present paper. Certain model reference adaptive control algorithms come out as special cases. A non-linear optimal control problem is studied to illustrate the efficacy of the techniques, and the possibility of further performance enhancement based on functional learning is noted.     

Application of adaptive lattice filters to internal model control

An adaptive internal model control (IMC) framework is proposed in this article for infinite impulse response systems. The innovation in this study stems from the relaxed assumption that the controller needs to know a priori the system order. To bypass this restriction, a lattice filter identifies the system's order as well as its reflection coefficients. Within the IMC structure, a lattice‐based controller is utilized in the forward path in cascade with a low‐pass detuning filter. The controller self‐configures its structure according to the estimated system order, while the filter's bandwidth increases as the identifier estimates more accurately the system dynamics. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive fuzzy sliding mode control of Lorenz chaotic system

By using the exponential reaching law technology, a sliding mode controller was designed for Lorenz chaotic system subject to an unknown external disturbance. On this basis, considering the unknown disturbance, an adaptive law was introduced to adaptively estimate the parameters of the disturbance bounds. Furthermore, to eliminate the chattering resulting from the discontinuous switch controller and to guarantee system transient performance, a new adaptive fuzzy sliding mode controller was designed. The results of the simulation show the effectiveness of the proposed control scheme. Translated from Journal of Harbin Institute of Technology, 2006, 38(4): 499–502 [译自: 哈尔滨工业大学学报]