Nonlinear Identification Techniques Research Articles

A Self-Calibration Method for Robot End-Effector Using Spherical Constraints

A self-calibration method utilizing spherical constraints is proposed for calibration of robot end-effectors. The method establishes a mathematical model to account for both the geometric errors of the robot and the deformation errors of the end-effector. A nonlinear least-squares parameter identification technique based on spherical constraints is employed to achieve autonomous calibration of the end-effector. Contrasted with methodologies relying on point plane or distance constraints, this novel technique delivers superior positioning accuracy, streamlined operational procedures and enhanced efficiency. Both simulation and experimental validation confirm that the self-calibration method using spherical constraints improves the positioning accuracy of the robot end-effector from 3 mm to 0.3 mm, showing the effectiveness of the method.

Efficient Algorithm for Pulmonary Nonlinear Model Online Estimation of Patients Under Assisted Ventilation

An efficient algorithm to estimate a respiratory system nonlinear model of sedated patients under assisted ventilation is presented. The considered model comprises an airways resistance and a volume-dependant compliance and, for each respiratory cycle, the proposed algorithm provides online the model parameters guaranteeing a minimum accuracy, above a user-defined threshold. Relying on standard nonlinear identification techniques, it exhibits computational burden reduction features, which contribute to its suitability for its online application.

Equivariant Observers for Second-Order Systems on Matrix Lie Groups

This paper develops an equivariant symmetry for second order kinematic systems on matrix Lie groups and uses this symmetry for observer design. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of the group with the inputs lying in the tangent of the tangent bundle known as the double tangent bundle. We provide a simple parameterization of both the tangent bundle state space and the input space (the fiber space of the double tangent bundle) and then introduce a semi-direct product group and group actions onto both the state and input spaces. We show that with the proposed group actions the second order kinematics are equivariant. An equivariant lift of the kinematics onto the symmetry group is derived and used to design nonlinear observers on the lifted state space using nonlinear constructive design techniques. The observer design is specialised to kinematics on groups that themselves admit a semi-direct product structure and include applications in rigid-body motion amongst others. A simulation based on an ideal hovercraft model verifies the performance of the proposed observer architecture.

Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework

In this paper, the periodic solutions of nonlinear mechanical systems are studied starting from the nonlinear state-space model estimated using the nonlinear subspace identification (NSI) technique. In its standard form, NSI needs the input–output data from a nonlinear structure undergoing broadband excitation and requires the prior knowledge of the locations and kind of nonlinearities to be estimated. The method allows the estimation of the nonlinear features of the system and the indirect study of its periodic solutions using a single broadband excitation, without the need of feedback control loops. To this end, the nonlinear frequency response curves of the system are estimated merging the harmonic balance method with the NSI technique and using a continuation approach. Then, a monodromy-based stability analysis is developed in the nonlinear state-space framework to study the stability of the periodic solutions of the system and to track its bifurcations. The method is validated considering conservative nonlinearities on two numerical examples and one experimental application, the latter comprising a double-well oscillator with period-doubling phenomena. The effects of noise and nonlinear modeling errors are also evaluated.

Design of multivalued frequency response filters by using nonlinear feedback

This contribution introduces the design of multivalued multiband frequency response filters exploiting nonlinear feedback design techniques. The interest in this topic is related to the possibility of analysing in real-time sinusoidal signals unveiling whether their main frequency components increase or decrease along different complex paths and in fixed sets of windows. This can be done by using the effects of frequency hysteresis, peculiar characteristic of the proposed devices.

Core volume reduction based on non-linear inductors for a PV DC–DC converter

The main objective of this paper is to analyze and achieve inductor core volume reduction based on non-linear inductance design techniques for a PV DC–DC Converter, and to perform a comparison of volume and efficiency among usual design techniques. The volume reduction in PV systems is a crucial design parameter for microinverters, leading to development of new techniques for this area. The paper performs a design-oriented approach of two different non-linear inductance techniques to compare with usual techniques for inductor design of a buck-boost converter applied as a power point tracker in a photovoltaic system. One technique performs the inclusion of an auxiliary winding in ferrite E core inductor, and the other consists of sendust core design aiming for inductance variability regarding its natural magnetic saturation properties. The design of all inductors and experimental results will be presented, besides the possibility of volume reduction by applying non-linear inductance techniques.

Takagi–Sugeno Fuzzy Unknown Input Observers to Estimate Nonlinear Dynamics of Autonomous Ground Vehicles: Theory and Real-Time Verification

In this article, we address the simultaneous estimation problem of the lateral speed, the steering input, and the effective engine torque, which play a fundamental role in vehicle handling, stability control, and fault diagnosis of autonomous ground vehicles. Due to the involved longitudinal-lateral coupling dynamics and the presence of unknown inputs (UIs), a new nonlinear observer design technique is proposed to guarantee the asymptotic estimation performance. To this end, we make use of a specific Takagi-Sugeno (TS) fuzzy representation with nonlinear consequents to exactly model the nonlinear vehicle dynamics within a compact set of the vehicle state. This TS fuzzy modeling not only allows reducing significantly the real-time computational effort in estimating the vehicle variables but also enables an effective way to deal with unmeasured nonlinearities. Moreover, via a generalized Luenberger observer structure, the UI decoupling can be achieved without requiring a priori UI information. Using Lyapunov stability arguments, the UI observer design is reformulated as an optimization problem under linear matrix inequalities, which can be effectively solved with standard numerical solvers. The effectiveness of the proposed TS fuzzy UI observer design is demonstrated with real-time hardware-in-the-loop experiments.

Data-driven linear parameter-varying modelling of the steering dynamics of an autonomous car

Developing automatic driving solutions and driver support systems requires accurate vehicle specific models to describe and predict the associated motion dynamics of the vehicle. Despite of the mature understanding of ideal vehicle dynamics, which are inherently nonlinear, modern cars are equipped with a wide array of digital and mechatronic components that are difficult to model. Furthermore, due to manufacturing, each car has its personal motion characteristics which change over time. Hence, it is important to develop data-driven modelling methods that are capable to capture from data all relevant aspects of vehicle dynamics in a model that is directly utilisable for control. In this paper, we show how Linear Parameter-Varying (LPV) modelling and system identification can be applied to reliably capture personalised model of the steering system of an autonomous car based on measured data. Compared to other nonlinear identification techniques, the obtained LPV model is directly utilisable for powerful controller synthesis methods of the LPV framework.

Integral Backstepping Control of Three phase Grid Connected Photovoltaic Systems for Power Optimization

We propose in this paper a nonlinear controller to optimize the operation of a photovoltaic device consisting of a PV generator, a three-phase inverter, and an LCL filter. Unlike traditional systems, this system is reliable and is not expensive, thanks to the absence of the DC-DC converter. In reality, we are trying to achieve two goals: (i) Search track and extract the maximum power from the PV generator (MPPT requirement); (ii) Inject this power into the network in the form of an alternating current which has the same pulsation as that of the network (UPF requirement). To achieve these objectives, the proposed controller was designed using non-linear design techniques, based on the nonlinear modeling of the photovoltaic system. Numerical simulation and its results showed the performance of the nonlinear controller and its ability to confront the challenges described in this article (MPP and UPF requirement), external disturbances and abrupt climatic changes.

Error-Driven Nonlinear Feedback Design for Fuzzy Adaptive Dynamic Surface Control of Nonlinear Systems With Prescribed Tracking Performance

This paper addresses an error-driven nonlinear feedback design technique to improve the dynamic performance of fuzzy adaptive dynamic surface control (DSC) for a class of uncertain multiple-input-multiple-output nonlinear systems with prescribed tracking performance. The highlight of the error-driven nonlinear feedback technique is that the feedback gain self-regulates versus different levels of output and virtual tracking errors, this reflects the classical control design criterions commendably: relatively high feedback gains can be implemented to guarantee disturbances and uncertainties attenuation and so on to improve the control performance when small tracking errors are measured, and relatively small feedback gains can be implemented to circumvent the problems of actuator and states saturations when large tracking errors are measured. The complexity problem of the traditional backstepping design is circumvented owe to the peculiarity of DSC method. Caused by the compound error functions of nonlinear feedback dynamics, a nonquadratic Lyapunov function is used to deduce the conditions of closed-loop stability. Fuzzy logic systems and error transformation-based method are used in the online learning of completely unknown dynamics and the prescribed performance tracking, respectively. Comparative results are presented to demonstrate the effectiveness and preponderance of the proposed control scheme with comparison to existing ones.

A Novel Nonlinear System Identification for Cerebral Autoregulation in Human: Computer Simulation and Validation.

Cerebral autoregulation in healthy humans was studied using a novel methodology adapted from Bendat nonlinear analysis technique. A computer simulation of a high-pass filter in parallel with a cubic nonlinearity followed by a low-pass filter was analyzed. A linear system transfer function analysis showed an incorrect estimate of the gain, cut-off frequency, and phase of the high-pass filter. By contrast, using our nonlinear systems identification, yielded the correct gain, cut-off frequency, and phase of the linear system, and accurately quantified the nonlinear system and following low-pass filter. Adding the nonlinear and linear coherence function indicated a complete description of the system. Cerebral blood flow velocity and arterial pressure were measured in six data sets. Application of the linear and nonlinear systems identification techniques to the data showed a high-pass filter, like the linear transfer function, but the gain was smaller. The phase was similar between the two techniques. The linear coherence was low for frequencies below 0.1Hz but improved by including a nonlinear term. The linear + nonlinear coherence was approximately 0.9 across the frequency bandwidth, indicating an improved description over the linear system analysis of the cerebral autoregulation system.

Neural Network Based Nonlinear Autoregressive Models for CNC Machine Process

Tool wear monitoring and control in the machining operations is necessary to enhance the productivity and decrease the operation cost. The identification of CNC machine process model and its control is so difficult due to its high non-linearity. Therefore, neural networks (NNs) one of the non-linear identification techniques, have been applied in addition to system identification field for the identification and control of nonlinear systems. In this paper, auto-regression recurrent neural network model structures NNARX and NNARMAX is proposed for CNC machine modeling with its cutting condition and vibration signals as input to obtain an accurate nonlinear system model for prediction of tool wear and surface roughness. Finally, the modeled neural network model structures for prediction of tool wear and surface roughness is validated with the observed tool wear and surface roughness for the accuracy analysis of modeled neural network model structures.

Tracking of Vehicle Motion on Highways and Urban Roads Using a Nonlinear Observer

This paper focuses on the development and use of a nonlinear observer for tracking of vehicle motion trajectories while using a radar sensor. Previous results on vehicle tracking have typically used an interacting multiple model filter that needs different models for different modes of vehicle motion. This paper uses a single nonlinear vehicle model that can be used for all modes of vehicle motion. Previous nonlinear observer design results from the literature do not work for the nonlinear system under consideration due to the wide range of operating conditions that need to be accommodated. Hence, a new nonlinear observer design technique that utilizes better bounds on the coupled nonlinear functions in the dynamics is developed. The exponential stability of the observer is established using Lyapunov techniques. The observer design with the developed technique is then implemented in both simulations and experiments. Experimental results show that the observer can simultaneously and accurately estimate longitudinal position, lateral position, and velocity and orientation variables for the vehicle from radar measurements. Results are presented both for tracking of vehicle maneuvers on highways and of maneuvers on urban roads at traffic intersections where turns and significant changes in vehicle orientation can occur.

Comparative Analysis of Evolutionary Computation Based Gain Scheduling Control for Ball and Plate Stabilization System

The platform stabilization systems used in marine, airborne or land vehicle applications are controlled with very different control methods basically including linear, nonlinear and artificial intelligence-based design techniques. Nowadays, evolutionary computation based optimization algorithms also provide new opportunities to engineers in order to design a gain scheduling controller. In this study, an evolutionary computation based gain scheduling controller is proposed for a ball and plate system so as to examine its control performances on a stabilization system. For this purpose, the swarm intelligence based Particle Swarm Optimization (PSO) and evolutionary algorithm based Differential Evolution (DE) algorithms are chosen due to their better performance than the other evolutionary computation algorithms. The results are comparatively investigated by using time domain and frequency domain analysis methods. Additionally, the robustness analysis is also applied to examine the tuning performances of these controllers in case of changing system parameters in the range of ±50%.

Free‐Decay Nonlinear System Identification via Mass‐Change Scheme

Methods for nonlinear system identification of structures generally require input‐output measured data to estimate the nonlinear model, as a consequence of the noninvariance of the FRFs in nonlinear systems. However, providing a continuous forcing input to the structure may be difficult or impracticable in some situations, while it may be much easier to only measure the output. This paper deals with the identification of nonlinear mechanical vibrations using output‐only free‐decay data. The presented method is based on the nonlinear subspace identification (NSI) technique combined with a mass‐change scheme, in order to extract both the nonlinear state‐space model and the underlying linear system. The technique is tested first on a numerical nonlinear system and subsequently on experimental measurements of a multi‐degree‐of‐freedom system comprising a localized nonlinearity.

Passivity based-control technique incorporating genetic algorithm for design of a free piston Stirling engine

In this paper, a novel design philosophy of free piston Stirling engines based on passivity based-control technique incorporating genetic algorithm is presented. First, the design problem of an FPSE is expressed as a physical nonlinear servo control system with unknown parameters. Accordingly, the desired motions of power piston and displacer (i.e. design objectives) are regarded as the reference trajectories of the control loop. Then, the unknown design parameters of the nonlinear control system including cross sectional-area of the displacer rod, mass and spring stiffness of the power piston and displacer, phase difference, hot gas temperature, and control coefficients are found using a GA along with an error-based objective function. Next, the estimated values of unknown parameters are used to simulate the control system performance. Subsequently, the simulated control system response is compared to the desired trajectories. It is found that the simulated displacements and velocities for both pistons as well as the corresponding limit cycles are close to the desired references of the control system. Finally, simulated performance of the FPSE is verified through experimental results. The outcomes of this research clearly reveal the effectiveness of the proposed nonlinear control-based design technique of the free piston Stirling engine (SUTECH-SR-1).

Development of nonlinear disturbance observer based control and nonlinear PID: A personal note

This paper gives an overview of early development of nonlinear disturbance observer design technique and the disturbance observer based control (DOBC) design. Some critical points raised in the development of the methods have been reviewed and discussed which are still relevant for many researchers or practitioners who are interested in this method. The review is followed by the development of a new type of nonlinear PID controller for a robotic manipulator and its experimental tests. It is shown that, under a number of assumptions, the DOBC consisting of a predictive control method and a nonlinear disturbance observer could reduce to a nonlinear PID with special features. Experimental results show that, compared with the predictive control method, the developed controller significantly improves performance robustness against uncertainty and friction. This paper may trigger further research and interests in the development of DOBC and related methods, and building up more understanding between this group of control methods with comparable ones (particularly control methods with integral action).

Control of pendular motion on tethered satellites systems

PurposeThis paper aims to present the control laws to be used in the control of pendular motion on tethered satellite systems in space during orbiting by using a nonlinear design technique.Design/methodology/approachThis work presents both physical and mathematical models represented in a circular orbit. Euler equation of the rigid body is applied under reasonable assumption so as to form the equations of pendular motion. These equations are then used to develop the control laws using a nonlinear design technique. The control laws are required to drive the in-plane angles and out-of-plane angles of the pendular motion to the required trajectories. Simulations are then conducted to study the control results.FindingsSimulation results show that the control laws in both plane angles of motions considered are able to move the pendular motion to the required trajectory. It was also eminent that a lot of effort is required in the case of the reference trajectory that corresponds to the constant inside-plane. To control the pendular motion of the plane, one requires an extended period of time and it should be controlled within a reasonable range. In the outside-of-plane pendular motion, minimal or no effort is required for the control. The reason is that the trajectory is natural planar.Practical implicationsThis research is expected to provide a dynamic control strategy for all tethered satellite space systems.Originality/valueThe research proposes a combined dynamic method for the purpose of improving the control of all types of tether satellites.

Predictor-corrector framework for the sequential assembly of optical systems based on wavefront sensing.

Alignment of optical components is crucial for the assembly of optical systems to ensure their full functionality. In this paper we present a novel predictor-corrector framework for the sequential assembly of serial optical systems. Therein, we use a hybrid optical simulation model that comprises virtual and identified component positions. The hybrid model is constantly adapted throughout the assembly process with the help of nonlinear identification techniques and wavefront measurements. This enables prediction of the future wavefront at the detector plane and therefore allows for taking corrective measures accordingly during the assembly process if a user-defined tolerance on the wavefront error is violated. We present a novel notation for the so-called hybrid model and outline the work flow of the presented predictor-corrector framework. A beam expander is assembled as demonstrator for experimental verification of the framework. The optical setup consists of a laser, two bi-convex spherical lenses each mounted to a five degree-of-freedom stage to misalign and correct components, and a Shack-Hartmann sensor for wavefront measurements.

Modelling and control of an alkaline water electrolysis process

In this research, an alkaline water electrolysis process is modelled. The electrochemical electrolysis is carried out in an electrolyzer composed of 12 series-connected steel cells with a solution 30% wt of potassium hydroxide. The electrolysis process model was developed using a nonlinear identification technique based on the Hammerstein structure. This structure consists of a nonlinear static block and a linear dynamic block. In this work, the nonlinear static function is modelled by a polynomial approximation equation, and the linear dynamic is modelled using the ARX structure. To control the current feed to the electrolyzer an unconstraint predictive controller was implemented, once the unconstrained MPC was simulated, some restrictions are proposed to design a constrained MPC (CMPC). The CMPC aim is to reduce the electrolyzer's energy consumption (power supply current). Simulation results showed the advantages of using the CMPC since the energy (current) overshoots are avoided.