Cascade Design of State Observers

A block approach to designing state observers for nonlinear multivariate systems is developed. A block-observable form of nonlinear systems is elaborated, in which the design of dynamic observation devices is subdivided into sequentially and independently solved elementary subproblems of reduced dimension. Stepwise procedures for choosing state observer controls from high-gain feedback systems are developed. Lower estimates for the finite coefficients of state observers are used in estimating the state vector components with given accuracy via synthesis decomposition. The designed algorithms ensure the invariance of the control operator to parametric uncertainties. By way of application, the state variables of an asynchronous sensorless drive motor are estimated from stator current measurements.     

On the globally defined sensorless control of induction motors

The sensorless control problem of induction motors imposes a current challenge since the nonlinear model of this kind of machines does not exhibit global observability properties, i.e. there are some operation regimes for which speed observability is lost. One way for dealing with this unavoidable limitation, and at the same time provide globally defined controllers, is to consider that the rotor variables are estimated via an open‐loop observer. In this paper a globally defined passivity‐based speed controller that belongs to the aforementioned class is presented. It is shown that the structure of previously reported passivity‐based controllers, developed under the assumption that the mechanical variables are available for measurement, can be extended to operate under sensorless conditions if a speed observer is included in the control scheme. Since the controller design methodology leads to inherent drawbacks regarding robustness issues, to evaluate the usefulness of the proposed scheme a numerically based study is included that cover topics such as parameters and disturbance (load torque) uncertainty. The advantages and limitations of the proposed scheme are established with respect to other globally defined sensorless controllers. Copyright © 2008 John Wiley & Sons, Ltd.     

A survey on sliding mode control strategies for induction motors

A state of the art review of control and estimation methods for induction motor (IM) based on conventional approaches, sliding mode control (SMC) and sensorless SMC is presented. The objective of this survey paper is to summarize the different control approaches for IMs including field oriented control (FOC), direct torque control (DTC), speed observer, observer based flux estimation, sliding mode (SM) flux and speed observer, current regulation by SMC, sensorless SMC, etc. The applications of SMC to IMs has been widespread in recent years. The increasing interest in SMC is because of its interesting features such as invariance, robustness, order reduction and control chattering. Particularly robustness of SM approach with respect to parameter variations and external disturbance is vital for the control system. The review covers the sensorless SMC schemes by integrating controller and observer design to guarantee convergence of the estimates to the real states. It also covers the chattering problems, encountered often in SMC area dealt by using an asymptotic observer.     

An adaptive tracking control from current measurements for induction motors with uncertain load torque and rotor resistance

The problem of controlling sensorless induction motors with uncertain constant load torque and rotor resistance on the basis of stator current measurements only is addressed. A new eighth-order dynamic nonlinear adaptive control algorithm is designed, which relies on a closed loop adaptive observer for the unmeasured state variables (rotor speed and fluxes) and for the uncertain parameters and is not based on non-robust open loop integration of flux dynamics. Local exponential stability of the closed loop tracking and estimation error dynamics is achieved under persistency of excitation conditions which restrict the reference signals and may be interpreted in terms of motor observability and rotor resistance identifiability.     

Adaptive sliding-mode-observer for sensorless induction motor drive using two-time-scale approach

This paper, presents a new sliding-mode-observer design for sensorless vector control of induction motors with rotor resistance estimation using two-time-scale approach. This approach, based on the singular perturbation theory, decomposes the observer error dynamics on two parts; fast part, associated to the stator-current observer, and slow part, associated to the rotor-flux observer. Using this decomposition, the rotor-flux-observer accuracy is guaranteed through the stator-current observer. Consequently, adaptive laws for rotor speed and rotor resistance estimations are easily derived using only measured and estimated stator currents and estimated rotor fluxes. The effectiveness of this new approach has been successfully verified through computer simulations, where the control algorithm is based on the indirect field oriented sliding-mode control.     

Output Tracking Control for Fuzzy Systems Via Output Feedback Design

Fuzzy observer-based control design is proposed to deal with the output tracking problem for nonlinear systems. For the purpose of tracking design, the new concept of virtual desired variables and, in turn the so-called generalized kinematics are introduced to simplify the design procedure. In light of this concept, the design procedure is split into two steps: i) Determine the virtual desired variables from the generalized kinematics; and ii) Determine the control gains just like solving linear matrix inequalities for stabilization problem. For immeasurable state variables, output feedback design is proposed. Here, we focus on a common feature held by many physical systems where their membership functions of fuzzy sets satisfy a Lipschitz-like property. Based on this setting, control gains and observer gains can be designed separately. Moreover, zero tracking error and estimation error are concluded. Three different types of systems, including nonlinear mass-spring systems, dc–dc converters, and induction motors are considered to demonstrate the design procedure. Their satisfactory simulation results verify the proposed approach.     

State feedback tracking control for indirect field-oriented induction motor using fuzzy approach

This paper deals with the synthesis of fuzzy controller applied to the induction motor with a guaranteed model reference tracking performance. First, the Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear system in the synchronous d-q frame rotating with field-oriented control strategy. Then, a fuzzy state feedback controller is designed to reduce the tracking error by minimizing the disturbance level. The proposed controller is based on a T-S reference model in which the desired trajectory has been specified. The inaccessible rotor flux is estimated by a T-S fuzzy observer. The developed approach for the controller design is based on the synthesis of an augmented fuzzy model which regroups the model of induction machine, fuzzy observer, and reference model. The gains of the observer and controller are obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation and experimental results are given to show the performance of the observer-based tracking controller.     

Sigma function in observer design for states and perturbations

For nonlinear systems operating under uncertainty, this paper involves the principle of motion separation to design a state observer with nonlinear corrections in the form of sigma functions. For the systems representable in the regular form with respect to the external perturbations, the above approach yields the current estimates of the unmeasurable state variables and external perturbations without extending the dynamic order of the observer by a model that simulates the action of the external perturbations. The developed algorithms are applied in the control system of an asynchronous drive with an incomplete set of measuring devices.     

A unified observer for robust sensorless control of DC–DC converters

Due to the large variety of converters' configurations, many different sensorless controllers are available in the literature, each one suited for a particular converter. The need for different configurations, especially on the same power supply, make it clear the advantage of having a shared control algorithm. This paper presents a unified nonlinear robust current observer for buck, boost and buck–boost converters in synchronous and asynchronous configurations. The unified observer speeds up the design, tuning and the implementation, and requires a memory cheaper code, easier to certify. Simulation and experimental results are presented to validate the approach in different scenarios.     

Adaptive state observers for sensorless control of switched reluctance motors

In this paper, we address the problem of state observation for sensorless control of switched reluctance motors (SRMs), that is, the regulation of the motor measuring only the voltage and the current of the electrical supply. Instrumental for the construction of the observer is the derivation of algebraic relations, which define regression models, between the unknown rotor flux and the measured quantities. With the knowledge of the flux, it is shown that the mechanical coordinates can be estimated with suitably tailored adaptive nonlinear observers. Replacing the observed states, in a certainty equivalent manner, with a full information stabilizing law completes the sensorless controller design. In contrast with other motors, there is no universally accepted mathematical model to describe the dynamics of SRMs. To widen our target audience, we present the results for four different mathematical models reported in the literature. Simulation results with a precise (finite element) model of the SRM are used to illustrate the performance of the proposed observer and sensorless control.     

On Maximum Stability Margin Design of Nonlinear Uncertain Systems: Fuzzy Control Approach

This paper studies the maximum stability margin design for nonlinear uncertain systems using fuzzy control. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear uncertain system. Next, based on the fuzzy model, the maximum stability margin for a nonlinear uncertain system is studied to achieve as much tolerance of plant uncertainties as possible using a fuzzy control method. In the proposed fuzzy control method, the maximum stability margin design problem is parameterized in terms of a corresponding generalized eigenvalue problem (GEVP). For the case where state variables are unavailable, a fuzzy observer‐based control scheme is also proposed to deal with the maximum stability margin for nonlinear uncertain systems. Using a suboptimal approach, we characterize the maximum stability margin via fuzzy observer‐based control in terms of a linear matrix inequality problem (LMIP). The GEVP and LMIP can be solved very efficiently via convex optimization techniques. Simulation examples are given to illustrate the design procedure of the proposed method.     

Observer-based variable universe adaptive fuzzy controller without additional dynamic order

A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output (SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme.     

Sensorless adaptive output feedback control of wind energy systems with PMS generators

This paper addresses the problem of controlling wind energy conversion (WEC) systems involving permanent magnet synchronous generator (PMSG) fed by IGBT-based buck-to-buck rectifier–inverter. The prime control objective is to maximize wind energy extraction which cannot be achieved without letting the wind turbine rotor operate in variable-speed mode. Interestingly, the present study features the achievement of the above energetic goal without resorting to sensors of wind velocity, PMSG speed and load torque. To this end, an adaptive output-feedback control strategy devoid of any mechanical sensor is developed (called sensorless), based on the nonlinear model of the whole controlled system and only using electrical variables measurements. This control strategy involves: (i) a sensorless online reference-speed optimizer designed using the turbine power characteristic to meet the maximum power point tracking (MPPT) requirement; (ii) a nonlinear speed regulator designed by using the backstepping technique; (iii) a sensorless interconnected adaptive state observer providing online estimates of the rotor position as well as speed and load/turbine torque. The proposed output-feedback control strategy is backed by a formal analysis showing that all control objectives are actually achieved. Several simulations show that the control strategy enjoys additional robustness properties.     

Sensorless Control of Induction Machine Supplied by Current Source Inverter

The paper describes the voltage control technique of induction machines supplied by a current source inverter. The control system is based on proposed new multi‐scalar variables, which are named “r.” The control system contains the output filter capacitor's model. In the sensorless control system the Z type backstepping speed observer was applied. The mathematical dependences are confirmed by simulation and experimental research.     

A Robust Backstepping Sensorless Control for Interior Permanent Magnet Synchronous Motor Using a Super‐Twisting Based Torque Observer

In order to achieve high‐performance speed regulation for sensorless interior permanent magnet synchronous motors (IPMSMS), a robust backstepping sensorless control is presented in this paper. Firstly, instead of a real mechanical sensor, a robust terminal sliding mode observer is used to provide the rotor position. Then, a new super‐twisting algorithm (STA) based observer is designed to obtain estimates of load torque and speed. The proposed observer ensures finite‐time convergence, maintains robust to uncertainties, and eliminates the common assumption of constant or piece‐wise constant load torque. Finally, a sensorless scheme is designed to realize speed control despite parameter uncertainties, by combining the robust backstepping control with sliding mode actions and the presented sliding mode observers. The stability of the observer and controller are verified by using Lyapunov's second method to determine the design gains. Simulation results show the effectiveness of the proposed approach.     

Output feedback control with disturbance rejection of a class of nonlinear MIMO systems

Output feedback control with disturbance rejection is developed for a class of nonlinear multi-input-multi-output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance. In the design of an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. The control methodology is robust to bounded disturbances that are both constant and time-varying, with effective performance. The adaptive laws are derived based on the Lyapunov synthesis method; therefore closed-loop asymptotic stability is also guaranteed. Moreover, chattering can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed controller. The text was submitted by the authors in English.     

Observers for state-affine systems

A system whose discrete-time model is linear in state variables and nonlinear in control variables is considered. Under the assumption of generic observability (under single experiment) an exact observer algorithm is suggested. Also, it is shown that the existence of a general nonlinear asymptotic observer implies the existence of a linear one. Two design procedures for asymptotic observers are presented. Surprisingly, one of them extends to a rather complete solution for continuous-time systems with piecewise constant controls provided discrete output measurements are more frequent than switches of control values.     

Second order sliding mode block control of single‐phase induction motors

The authors propose a robust nonlinear controller based on a block control linearization technique combined with a second order sliding mode super‐twisting algorithm for controlling the rotor speed of single‐phase induction motors. The block control approach is used to design a sliding manifold in terms of the stator current and its desired value. The super‐twisting sliding mode algorithm is applied then to render the designed manifold be attractive. A nonlinear observer is designed to estimate the unmeasured variables (rotor flux linkages and torque load). Copyright © 2012 John Wiley & Sons, Ltd.     

基于自适应观测器的无速度传感器感应电机控制

针对采用极点配置的自适应速度观测器存在不稳定区域的问题,建立了全阶自适应状态观测器并给出了观测器的速度辨识律.应用Lyapunov稳定性理论,观测器的增益借助于MATLAB LMI工具箱求解两个双线性矩阵不等式得到.在MATLAB 6.5/SIMULINK环境下,建立了无速度传感器感应电机直接转矩控制的仿真实验平台,给出了无速度传感器直接转矩控制的仿真结果.仿真结果表明本文给出的自适应观测器在全速范围内具有很好的稳态性能,并具有很好的鲁棒性.同时,在以TMS320F240为核心的感应电机直接转矩控制系统上进行了速度辨识实验,实验结果验证了方案的有效性.