Magnetic sensor-based simultaneous state and parameter estimation using a nonlinear observer

This paper presents an observer design technique for a newly developed non-intrusive position estimation system based on magnetic sensors. Typically, the magnetic field of an object as a function of position needs to be represented by a highly nonlinear measurement equation. Previous results on observer design for nonlinear systems have mostly assumed that the measurement equation is linear, even if the process dynamics are nonlinear. Hence, a new nonlinear observer design method for a Wiener system composed of a linear process model together with a nonlinear measurement equation is developed in this paper. First, the design of a two degree-of-freedom nonlinear observer is proposed that relies on a Lure system representation of the observer error dynamics. To improve the performance in the presence of parametric uncertainty in the measurement model, the nonlinear observer is augmented to estimate both the state and unknown parameters simultaneously. A rigorous nonlinear observability analysis is also presented to show that a dual sensor configuration is a sufficient and necessary condition for simultaneous state and parameter estimation. Finally, the developed observer design technique is applied to non-intrusive position estimation of the piston inside a pneumatic cylinder. Experimental results show that both position and unknown parameters can be reliably estimated in this application.     

Global sampled‐data output‐feedback stabilization for nonlinear systems with unknown measurement sensitivity

This paper investigates the problem of global output‐feedback stabilization by sampled‐data control for nonlinear systems with unknown measurement sensitivity. By employing the technique of output‐feedback domination, a sampled‐data output‐feedback control law together with a sampled‐data state observer is explicitly constructed. By an exquisite selection of both the domination gain and sampling period, the resultant control law is a globally asymptotic stabilizer even in the presence of unknown measurement sensitivity. The novelty of this paper is the development of a distinct approach which can tackle the problem of output‐feedback stabilization for the nonlinear systems with unknown measurement sensitivity.     

Survey on Passivity Based Control of Induction Machine

Induction machines (IM) constitute a theoretically interesting and practically important class of nonlinear systems. They are frequently used as wind generators for their power/cost ratio. They are described by a fifth‐order nonlinear differential equation with two inputs and only three state variables available for measurement. The control task is further complicated by the fact that IM are subject to unknown (load) disturbances and the parameters can be of great uncertainty. One is then faced with the challenging problem of controlling a highly nonlinear system, with unknown time‐varying parameters, where the regulated output, besides being unmeasurable, is perturbed by an unknown additive signal. Passivity‐based control (PBC) is a well‐established structure‐preserving design methodology which has shown to be very powerful to design robust controllers for physical systems described by Euler‐Lagrange equations of motion. PBCs provide a natural procedure to "shape" the potential energy yielding controllers with a clear physical interpretation in terms of interconnection of the system with its environment and are robust vis á vis to unmodeled dissipative effects. One recent approach of PBC is the Interconnection and Damping Assignment Passivity‐Based Control (IDA‐PBC) which is a very useful technique to control nonlinear systems assigning a desired (Port‐Controlled Hamiltonian) structure to the closed‐loop. The aim of this paper is to give a survey on different PBC of IM. The originality of this work is that the author proves that the well known field oriented control of IM is a particular case of the IDA‐PBC with disturbance.     

Almost Disturbance Decoupling for a Class of Nonlinear Systems Subject to Time‐Delays Via Sampled‐Data Output Feedback Control

This paper considers the problem of almost disturbance decoupling (ADD) via sampled‐data output feedback control for a class of uncertain nonlinear systems subject to time‐delays. Based on output feedback domination approach, a sampled‐data output feedback controller is designed to globally stabilize the system under a lower‐triangular linear growth condition. Gronwall‐Bellman‐like inequality and inductive method are introduced to estimate the state growth in the presence of time‐delays, uncertain nonlinearities and unknown disturbances. The proposed controller can attenuate the influence of disturbances on the output to an arbitrary degree in the L₂ gain sense. Finally, simulation results show the effectiveness of the control method.     

Nonlinear predictive control of irregularly sampled multirate systems using blackbox observers

This work aims the development of an inferential nonlinear model predictive control (NMPC) scheme based on a nonlinear fast rate model that is identified from irregularly sampled multirate data, which is corrupted with unmeasured disturbances and measurement noise. The model identification is carried out in two steps. In the first step, a MISO fast rate nonlinear output error (NOE) model is identified from the irregularly sampled output data. In the second step, a time varying nonlinear auto-regressive (NAR) type model is developed using the residuals generated in the first step. The deterministic and stochastic components of the observer are parameterized using generalized ortho-normal basis filters (GOBF). The identified NOE and NAR models are combined to form MISO state observers. We then proceed to use these identified observers to formulate a nonlinear MPC strategy for controlling irregularly sampled multirate systems. The identified observers are used to generate inter-sample estimates of the irregularly sampled outputs and for performing future trajectory predictions. The efficacy of the proposed modeling and control scheme is demonstrated using simulations on a benchmark continuous fermentation process. This process exhibits input multiplicity and change in the sign of steady state gain in the operating region. The validity of the proposed modeling and control scheme is also established by conducting identification and control experiments on a laboratory scale heater-mixer setup. The proposed NMPC gives satisfactory regulatory as well as servo performance over a wide operating range in the irregularly sampled multirate scenario.     

T-形磁通集聚器磁场放大特性及影响因素研究

针对微型磁传感器对弱磁场测量灵敏度低的问题,利用软磁材料对外磁场的集聚放大作用来提高磁测系统的灵敏度。重点针对T-形磁通集聚器的轴向磁场放大特性及影响因素进行了分析,并设计了相应的磁通集聚器并进行试验测试。试验表明所设计的T-形磁通集聚器具有很好的磁场线性放大作用,可用于提高弱磁场的测量精度。磁力线在磁通集聚结构内部流动的过程中发生了磁通泄漏现象;T-形磁通集聚器对外部磁场放大了约21倍;磁通集聚器的相对磁导率及空气间隙与外部磁场的放大倍数都呈非线性的关系,结构的长宽之比与外部磁场的放大倍数呈单调递增关系,结构厚度对其几乎没有影响。该研究结果能够为磁通集聚器结构设计及优化方面提供一定的参考价值。     

Sampled-data chain-observer design for a class of delayed nonlinear systems

The problem of observer design is addressed for a class of triangular nonlinear systems with not-necessarily small delay and sampled output measurements. One more difficulty is that the system state matrix is dependent on the un-delayed output signal which is not accessible to measurement, making existing observers inapplicable. A new chain observer, composed of m elementary observers in series, is designed to compensate for output sampling and arbitrary large delays. The larger the time-delay the larger the number m. Each elementary observer includes an output predictor that is conceived to compensate for the effects of output sampling and a fractional delay. The predictors are defined by first-order ordinary differential equations (ODEs) much simpler than those of existing predictors which involve both output and state predictors. Using a small gain type analysis, sufficient conditions for the observer to be exponentially convergent are established in terms of the minimal number m of elementary observers and the maximum sampling interval.     

Optimum filtering and control of randomly sampled systems

Kalman's concept of optimum filtering is interpreted in such a way that it can be applied to both nonlinear and linear systems with Gaussian or non-Gaussian statistics. The essential idea is to synthesize a generalized Kalman filter in two stages, a) propagation and b) measurement and correction. The analysis of each stage is independent of the other, and the generalized results are quite simple. In the present paper, the application of the above result is confined to linear systems: 1) Optimum filtering and interpolation of randomly sampled signals; for the interpolation problem it is assumed that the signals are measured exactly at the sampling instant. 2) Optimum filtering of related continuous and randomly sampled signals. 3) Optimum control of randomly sampled linear systems with quadratic cost criterion.     

State observers are unnecessary for induction motor control

Induction motors constitute a theoretically interesting and practically important class of nonlinear systems, which are evolving into a benchmark example for nonlinear control. They are described by a fifth-order nonlinear differential equation with two inputs, and only three state variables available for measurement. A lot of research in the field has been devoted to the design of observers which, combined with a suitable control strategy, would yield stable behaviour. Our contribution in this paper is to show that the control objective can be achieved without reconstruction of the motor state. Specifically, we present a globally stable nonlinear dynamic output feedback controller for torque tracking of induction motors which does not rely on state reconstruction ideas. Another important feature of our sheme is that the control law is globally defined, even in startup. This stems from the fact that we do not aim at linearizing the system dynamics, but instead exploit the energy dissipation properties of the motor model. For the sake of illustration we present the result for a model described in the stator frame (ab model), but the theory applies as well to models expressed in a rotating frame (dq model). We also show how, as a particular case of torque tracking, we can solve the rotor speed tracking problem.     

On nonlinear H∞ control under sampled measurements

This paper deals with the nonlinear H_∞ control problem with sampled measurement feedback. This problem has already been studied in Suzuki et al. (1995), where, using a certainty equivalence principle, a control solution involving a state estimator with a linear injection gain is proposed. Using the same general framework, we propose a more refined estimator with a nonlinear injection gain. This gain is shown to be connected to a periodic solution of a Hamilton-Jacobi inequality with jumps     

Parameterization of Sampled‐Data H∞ Output Feedback Controllers for General Nonlinear Systems

In this paper, we consider the H^∞ control problem for general nonlinear systems under sampled measurements. Sufficient conditions for the existence of H^∞ output feedback controllers are derived. The major contribution of this paper is to characterize a family of H^∞ output feedback controllers for nonaffine nonlinear systems under sampled measurements.     

A quadrature-based method of moments for nonlinear filtering

According to the nonlinear filtering theory, optimal estimates of a general continuous-discrete nonlinear filtering problem can be obtained by solving the Fokker-Planck equation, coupled with a Bayesian update rule. This procedure does not rely on linearizations of the dynamical and/or measurement models. However, the lack of fast and efficient methods for solving the Fokker-Planck equation presents challenges in real time nonlinear filtering problems. In this paper, a direct quadrature method of moments is introduced to solve the Fokker-Planck equation efficiently and accurately. This approach involves representation of the state conditional probability density function in terms of a finite collection of Dirac delta functions. The weights and locations (abscissas) in this representation are determined by moment constraints and modified using the Bayes’ rule according to measurement updates. As demonstrated by numerical examples, this approach appears to be promising in the field of nonlinear filtering.     

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

In this paper, the global sampled‐data output‐feedback stabilization problem is considered for a class of stochastic nonlinear systems. First, based on output‐feedback domination technique and emulation approach, a systematic design procedure for sampled‐data output‐feedback controller is proposed for a class of stochastic lower‐triangular nonlinear systems. It is proved that the proposed sampled‐data output‐feedback controller will stabilize the given stochastic nonlinear system in the sense of mean square exponential stability. Because of the domination nature of the proposed control approach, it is shown that the proposed control approach can also be used to handle the global sampled‐data output‐feedback stabilization problems for a more general class of stochastic non‐triangular nonlinear systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

Almost disturbance decoupling for a class of nonlinear systems via sampled‐data output feedback control

This paper addresses the problem of almost disturbance decoupling (ADD) using sampled‐data output feedback control for a class of continuous‐time nonlinear systems. Under a lower‐triangular linear growth condition, a sampled‐data output feedback controller is constructed based on the output feedback domination approach, and a Gronwall–Bellman‐like inequality is established in the presence of disturbances. Even though a sampled‐data controller is employed for easy computer implementation, the proposed controller is still able to achieve ADD under the commonly used continuous‐time requirement, that is, the disturbances' effect on the output is attenuated to an arbitrary degree of accuracy in the L₂ gain sense. Copyright © 2015 John Wiley & Sons, Ltd.     

Input-to-state stabilization for nonlinear dual-rate sampled-data systems via approximate discrete-time model

The problem of state feedback stabilization of nonlinear sampled-data systems is considered under the “low measurement rate” constraint. A dual-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state. Given an approximate discrete-time model of a sampled nonlinear plant and given a family of controllers that stabilizes the plant model in input-to-state sense, we show that under some standard assumptions the closed loop dual-rate sampled data system is input-to-state stable in the semiglobal practical sense.     

Nonlinear H∞-control of time-varying systems: aunified distribution-based formalism for continuous and sampled-datameasurement feedback design

Nonlinear H_∞-controller synthesis is presented for time-varying systems via sampled-data measurement feedback. The H _∞-control problem for a nonlinear system with a sampled-data measurement output is shown to be equivalent to the H_∞-control problem for a certain nonlinear system with a time-continuous measurement output. Special mathematical tools are developed to straightforwardly derive a local solution of the sampled-data measurement feedback (SMF) H_∞-control problem from that of the time-continuous measurement feedback (CMF) H _∞-control problem     

Stabilization of nonlinear systems with limited information feedback

This note is concerned with the problem of stabilizing a nonlinear continuous-time system by using sampled encoded measurements of the state. We demonstrate that global asymptotic stabilization is possible if a suitable relationship holds between the number of values taken by the encoder, the sampling period, and a system parameter, provided that a feedback law achieving input-to-state stability with respect to measurement errors can be found. The issue of relaxing the latter condition is also discussed.     

Multirate versions of sampled-data stabilization of nonlinear systems

The problem of state feedback sampled-data stabilization of nonlinear systems is considered under the “low measurement rate” constraint and in the presence of (not necessarily small) time delay in the measurement channel. A multirate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state from the delayed measurements. For both the controller emulation approach and the approach based on approximate discrete-time model of the system, we show that under standard assumptions the closed-loop multirate sampled data system is asymptotically stable in the semiglobal practical sense. An illustrative example of sampled-data control of vertical take off and landing aircraft is discussed.     

Discrete time output feedback sliding mode control for nonlinear MIMO system: a stepper motor case

This article, presents discrete sliding mode control algorithm using multirate output feedback for control of stepper motor. The algorithm developed by the authors uses past output samples and past control inputs. When all the states of the system are neither physical variable nor available for measurement, multirate output feedback can be used. The stepper motor is known to be a differentially flat system. The dynamics of the stepper motor are highly nonlinear, hence feedback linearization based on endogenous feedback has been used. The linear model is obtained and multirate output feedback-based discrete sliding mode control has been designed. The discrete sliding mode control with multirate output feedback has been applied for regulator as well as tracking case for the motor. The proposed algorithm uses only two outputs. It is essentially shown that first output needs to be sampled only once and second output must be sampled at least thrice in every τ sampling interval in order to achieve acceptable performance. The system parameter variation has been considered and the results obtained are found to be satisfactory. Thus, it has been shown that discrete sliding mode control algorithm using multirate output feed back can be extended to a class of nonlinear MIMO system.     

H∞ control via measurement feedback for affine nonlinear systems

This paper summarizes some recent results on the problem of disturbance attenuation via measurement feedback, with internal stability, for an affine nonlinear system. The solution of the problem is shown to be related to the existence of solutions of a pair of Hamilton-Jacobi inequalities in n independent variables, associated with state feedback and, respectively, output-injection design.