Nonlinear Input Transformation Research Articles

Attitude Control of a 2U Cubesat by Magnetic and Air Drag Torques

This paper describes the development of a magnetic attitude control subsystem for a 2U cubesat. Due to the presence of gravity-gradient torques, the satellite dynamics are open-loop unstable near the desired pointing configuration. Nevertheless, the linearized time-varying system is completely controllable, under easily verifiable conditions, and the system’s disturbance rejection capabilities can be enhanced by adding air drag panels exemplifying a beneficial interplay between hardware design and control. In this paper, conditions for the complete controllability for the case of a magnetically controlled satellite with passive air drag panels are developed, and simulation case studies with the linear quadratic regulator and model predictive control designs applied in combination with a nonlinear time-varying input transformation are presented to demonstrate the ability of the closed-loop system to satisfy mission objectives despite disturbance torques.

Dynamic Model and Nonlinear Control for a Two Degrees of Freedom First Generation Tidal Energy Converter

Abstract: Several manufacturers have developed devices with which to harness tidal/currents power in areas where the depth does not exceed 40 meters. These are the so-called first generation tidal energy converters (TEC). The maintenance tasks carried out on these devices therefore require them to be extracted from their bases to the sea surface and subsequently placed back on the bases. Special high performance ships are required for these tasks, signifying high maintenance costs. The automation of emersion and immersion maneuvers will undoubtedly lead to lower costs, given that ships with less demanding requirements will be required for the aforementioned maintenance tasks. This work presents a very simple dynamic modeling for a first generation TEC composed of only two lumped masses, which are handled solely by hydrostatic forces (conceived as volume-increasing devices). We propose a nonlinear control law based on friction terms compensation for closed loop depth and/or orientation control in order to ensure an adequate behavior when the TEC performs emersion and immersion maneuvers with only passive hydrostatic forces. A control scheme based on nonlinear input transformation, a proportional-derivative (PD) linear action and nonlinear compensation term are also proposed in order to ensure a global asymptotic stability of the TEC posture. Finally, the effectiveness of the dynamic model and the controller approach is demonstrated by means of numerical simulations when the TEC is carrying out an emersion maneuver for the development of blade-cleaning maintenance tasks.

First-principles-driven model-based current profile control for the DIII-D tokamak via LQI optimal control

In tokamak fusion plasmas, control of the spatial distribution profile of the toroidal plasma current plays an important role in realizing certain advanced operating scenarios. These scenarios, characterized by improved confinement, magnetohydrodynamic stability, and a high fraction of non-inductively driven plasma current, could enable steady-state reactor operation with high fusion gain. Current profile control experiments at the DIII-D tokamak focus on using a combination of feedforward and feedback control to achieve a targeted current profile during the ramp-up and early flat-top phases of the shot and then to actively maintain this profile during the rest of the discharge. The dynamic evolution of the current profile is nonlinearly coupled with several plasma parameters, motivating the design of model-based control algorithms that can exploit knowledge of the system to achieve desired performance. In this work, we use a first-principles-driven, control-oriented model of the current profile evolution in low confinement mode (L-mode) discharges in DIII-D to design a feedback control law for regulating the profile around a desired trajectory. The model combines the magnetic diffusion equations with empirical correlations for the electron temperature, resistivity, and non-inductive current drive. To improve tracking performance of the system, a nonlinear input transformation is combined with a linear-quadratic-integral (LQI) optimal controller designed to minimize a weighted combination of the tracking error and controller effort. The resulting control law utilizes the total plasma current, total external heating power, and line averaged plasma density as actuators. A simulation study was used to test the controller's performance and ensure correct implementation in the DIII-D plasma control system prior to experimental testing. Experimental results are presented that show the first-principles-driven model-based control scheme's successful rejection of input disturbances and perturbed initial conditions, as well as target trajectory tracking.

Fixed speed wind farm operation improvement using current-source converter based UPQC

In this paper, a current-source converter based unified power quality conditioner (UPQC) is used for the flexible integration of pitch controlled fixed speed wind generator (FSWG) to IEEE 13 node test feeder. During the normal operation, shunt compensator (SHUC) of the UPQC maintains a unity power factor condition at the Point of Common Coupling (PCC) and when a voltage sag occurs due to grid side fault the series compensator (SERC) of the UPQC injects appropriate deficit voltage to prevent disconnecting of the FSWG and the SHUC of the UPQC provides additional reactive power in fault during. The pitch angle is controlled in order to limit the generator output power to its nominal value for high wind speeds. The nonlinear model of the shunt compensator of the UPQC is modified to a linear model. The modeling technique is not based on the linearization of a set of nonlinear equations around an operating point. Instead, the power balance equation and a nonlinear input transformation are used to derive a linear model independent of the operating point. This model acts as the basis for the design of a decoupled state-feedback controller. The optimal control method linear quadratic regulator (LQR) is used to determine the optimal state-feedback gain matrix. The proposed control approach becomes a robust strategy that is able to keep regulation and stability even under extreme load power factor variations. The In-phase voltage injection method is used for the series compensator of the UPQC. The simulation results carried out by MATLAB/SIMULINK software show the performance of the proposed UPQC and prove the validity of the proposed topology.

Hardware implementation of an electrostatic MEMS-actuator linearization

In this paper, an electrostatic actuator linearization will be introduced, which is based on an existing hardware-efficient iterative square root algorithm. The algorithm is solely based on add and shift operations while just needing n/2 iterations for an n bit wide input signal. As a practical example, the nonlinear input transformation will be utilized for the design of the primary mode controller of a capacitive MEMS gyroscope and an implementation of the algorithm will be instantiated in the Verilog hardware description language. Furthermore, an implementation of an improved version of the algorithm will be given reducing the number of needed iterations to n/2 − 1 for an n bit wide input signal while just requiring an acceptable additional amount of hardware resources. Finally, measurement results will validate the feasibility of the presented control concept and its hardware implementation.

Nonlinear EGR and VGT Control with Integral Action for Diesel Engines

Nonlinear EGR and VGT Control with Integral Action for Diesel Engines - A nonlinear multivariable control design with integral action is proposed and investigated for control of Exhaust Gas Recirculation (EGR) and Variable Geometry Turbine (VGT) in heavy duty Diesel engines. The main control goal is to regulate oxygen/fuel ratio and intake manifold EGR-fraction, and they are specified in an outer loop. These are chosen as main performance variables since they are strongly coupled to the emissions. An existing nonlinear control design based on feedback linearization is extended with integral action. In particular; the control design method utilizes a control Lyapunov function, inverse optimal control, and a nonlinear input transformation. Comparisons between different control structures are performed in simulations showing the following four points. Firstly, integral action is necessary to handle model errors so that the controller can track the performance variables specified in the outer loop. Secondly the proposed control design handles the nonlinear effects in the Diesel engine that results in less control errors compared to a control structure with PID controllers. Thirdly, it is important to use the input transformation and it is sufficient to use a control structure with PID controllers and input transformation to handle the nonlinear effects. Fourthly, the proposed control design is sensitive to model errors in the input transformation while a control structure with PID controllers and input transformation handles these model errors.

Output tracking control of mobile manipulators based on dynamical sliding-mode control

A dynamical sliding-mode controller is devised to track the output of mobile manipulators. During the investigation, firstly a reduced dynamic model considering the dynamics of the driving motor is developed for mobile manipulators. Then, the system is decomposed into four lower-dimensional subsystems by means of diffeomorphism and nonlinear input transformation. Moreover, a design method of the dynamical sliding-mode controller that is applied to the output tracking of mobile manipulators is proposed. The simulation results indicate that the dynamical sliding-mode controller can not only track the given trajectory correctly but also reduce the chattering of sliding-mode control system considerably.

Current-Source Converter Based STATCOM: Modeling and Control

STATCOM is a FACTS controller that is used in power systems to regulate the line voltage, enhance the power transmission capacity and extend the transient stability margin. STATCOM is conventionally realized by a voltage-source converter; however, being a current injection device, its performance can be improved when realized by a current-source converter (CSC) that can generate a controllable current directly at its output terminals. In this paper, a STATCOM based on the current-source converter topology is proposed. The nonlinear model of the current-source converter, which is the source of the difficulties in the controller design, has been modified to a linear model through a novel modeling technique. The proposed modeling technique is not based on the linearization of a set of nonlinear equations around an operating point. Instead, the power balance equation and a nonlinear input transformation are used to derive a linear model independent of the operating point. This model acts as the basis for the design of a decoupled state-feedback controller. The proposed STATCOM has been simulated using the PSCAD/EMTDC package. The simulation results show that a CSC-based STATCOM can result in excellent current and voltage waveforms as well as very short response time while operating at a low switching frequency. This makes the proposed scheme suitable for high power applications.

Data-based mechanistic modelling and forecasting of hydrological systems

The paper presents a data-driven approach to the modelling and forecasting of hydrological systems based on nonlinear time-series analysis. Time varying parameters are estimated using a combined Kalman filter and fixed-interval-smoother, and state-dependent parameter relations are identified leading to nonlinear extensions to common time-series models such as the autoregressive exogenous (ARX) and general transfer function (TF). This nonlinear time-series technique is used as part of a data-based mechanistic modelling methodology where models are objectively identified from the data, but are only accepted as a reasonable representation of the system if they have a valid mechanistic interpretation. To this end it is shown that the TF model can represent a general linear storage model that subsumes many common hydrological flow forecasting models, and that the rainfall-runoff process can be represented using a nonlinear input transformation in combination with a TF model. One advantage of the forecasting models produced is that the Kalman filter can be used for real-time state updating leading to improved forecasts and an estimate of associated forecast uncertainty. Rainfall-runoff and flood routing case studies are included to demonstrate the power of the modelling and forecasting methods. One important conclusion is that optimal system identification techniques are required to objectively identify parallel flow pathways.

Nonlinear feedback control for a four‐steering‐wheel mobile robot

AbstractA mobile robot with four steered and driven wheels moving on planar surfaces under nonholonmic constraints is considered. For this system the equation of motion is derived, which can be reduced to a model of a two‐steering‐wheel vehicle under certain assumptions. For reduced state‐space model a nonlinear state‐space transformation and a nonlinear input transformation is derived so that the model becomes exactly linearized. Additionally to the exact state‐space linearization, the systems for the two positions in the plane and the orientation of the mobile robot are decoupled. These three linear and noninteracting systems can then easily be stabilized by linear control theory.