Derivation Of Control Law Research Articles

SSR Mitigation of Series-Compensated DFIG Wind Farms by a Nonlinear Damping Controller Using Partial Feedback Linearization

A nonlinear damping controller using partial feedback linearization (PFL) technique is designed with an aim to mitigate subsynchronous resonance (SSR) in series-compensated doubly-fed induction generator (DFIG)-based wind farms, which is integrated to simplified Nordic power system. The controller using PFL technique is implementable into a partially linearized form of a system with DFIG wind farm that results in reduced system order and small computational burden. The derivation of control law does not also demand thorough knowledge of nonlinear and ambiguous system dynamics. The proposed controller design approach has four distinguished steps: 1) scrutinizing partial linearizability, 2) performing partial linearization, 3) assessing stability of internal system dynamics, and 4) obtaining control laws. Small-signal stability analysis is performed that includes electrical damping analysis and eigenvalue analysis. The controller is found to demonstrate a superior performance in SSR mitigation. Time-series simulation is carried out to confirm the veracity of the outcomes obtained from the small-signal stability analysis.

Real-time collision avoidance maneuvers for spacecraft proximity operations via discrete-time Hamilton–Jacobi theory

This study presents a sub-optimal feedback control that implements real-time collision avoidance for spacecraft in proximity operations. The penalty function for avoiding collision with obstacles is first incorporated into the performance index of a typical optimal tracking problem. Then, the infinite-horizon feedback control law is derived by employing generating functions in the framework of discrete-time Hamilton–Jacobi theory. The derived control law, which is an explicit function of the reference states and instantaneous positions of obstacles, allows active spacecraft to avoid collision in real-time. The proposed approach has advantages over conventional optimal collision avoidance approaches in that it does not require iterations with initial guesses, repetitive shooting-based process for multiple boundary conditions, and/or trajectories of obstacles to be known a priori. Numerical simulations demonstrate that the proposed algorithm with a properly designed penalty function is suitable for implementing optimal collision-free transfers in real-time.

Design of a completely model free adaptive control in the presence of parametric, non-parametric uncertainties and random control signal delay

In this paper, an adaptive controller is developed for discrete time linear systems that takes into account parametric uncertainty, internal-external non-parametric random uncertainties, and time varying control signal delay. Additionally, the proposed adaptive control is designed in such a way that it is utterly model free. Even though these properties are studied separately in the literature, they are not taken into account all together in adaptive control literature. The Q-function is used to estimate long-term performance of the proposed adaptive controller. Control policy is generated based on the long-term predicted value, and this policy searches an optimal stabilizing control signal for uncertain and unstable systems. The derived control law does not require an initial stabilizing control assumption as in the ones in the recent literature. Learning error, control signal convergence, minimized Q-function, and instantaneous reward are analyzed to demonstrate the stability and effectiveness of the proposed adaptive controller in a simulation environment. Finally, key insights on parameters convergence of the learning and control signals are provided.

Cross-coupling effect and motion control of an autonomous underwater vehicle with internal actuators

Hybrid autonomous underwater vehicles (AUVs) use internal actuators, e.g., tunnel thruster, moving mass, and ballast chamber, for yaw and pitch steering. Unlike control surfaces, internal actuators perform independently of relative flows around AUVs, thus suitable for missions which require excellent low-speed maneuverability. This research focuses on an investigation into the control design of an REMUS AUV using internal actuators to steer its heading direction. It has been shown that an internal moving mass together with a tunnel thruster is capable of providing actuations to serve the purpose. However, our analysis indicates that a coupling between roll and pitch motion causes the internal actuators to oscillate if depth-plane motion is neglected when deriving control laws for the internal actuators. We present a novel control strategy by taking advantage of the cross-coupling effect when designing the heading autopilot system with internal actuators. The effectiveness and robustness of the proposed design are validated by simulation results.

LESO Based Dynamic Surface Control for Hypersonic Flight Vehicle

In the presence of model parametric uncertainties and external disturbances, a LESO-based dynamic surface control approach is designed for the longitudinal model of Hypersonic Flight Vehicle (HFV). Via Nonlinear Dynamic Inversion (NDI) technique, the decoupling of altitude and velocity is realized. Combining with conventional back-stepping technique, a low pass filter (LPF) is introduced to attain the derivation of virtual control laws, which avoids the problem of "differentiation explosion". A linear extended state observer (LESO) is designed for the precise estimation and compensation of "lumped disturbance" containing parametric uncertainties and external disturbances, which tremendously improves the ability of disturbance rejection of the system. The stability of the proposed approach is analyzed by means of Lyapunov theory. The simulation results demonstrate that the proposed methodology has good command tracking performance, and the approach is robust in the presence of lumped disturbances.

An expert 2DOF fractional order fuzzy PID controller for nonlinear systems

This work presents a generic two-degree-of-freedom fractional order fuzzy PI-D (2DOF FOFPI-D) controller dedicated to a class of nonlinear systems. The control law for proposed scheme is derived from basic 2DOF fractional order PID controller in discrete domain. Expert intelligence is embedded in overall derived control law by utilizing formula-based fuzzy design methodology. The controller structure comprises of fractional order fuzzy PI (FOFPI) and fractional order derivative filter to handle multiple issues and provides flexibility in design and self-tuning control feature. Further, the proposed scheme is compared with its integer order counterpart and 2DOF PI-D controller for coupled nonlinear 2-link robotic arm in real operating environment. The parameters of designed controllers are optimally tuned using multi-objective non-dominated sorting genetic algorithm-II for attaining low variation in control effort and error index. Intensive simulation studies are performed to analyze trajectory tracking, model uncertainty, disturbance due to cogging, sensor noise and noise as well as disturbance rejection simultaneously. Results demonstrate the superior performance of 2DOF FOFPI-D controller as compared to other designed controllers in the facets of different operating conditions.

Well-Posedness and Output Regulation for Implicit Time-Varying Evolution Variational Inequalities

A class of evolution variational inequalities (EVIs), which comprises ordinary differential equations (ODEs) coupled with variational inequalities (VIs) associated with time-varying set-valued mappings, is proposed in this paper. We first study the conditions for existence and uniqueness of solutions. The central idea behind the proof is to rewrite the system dynamics as a differential inclusion which can be decomposed into a single-valued Lipschitz map, and a time-dependent maximal monotone operator. Regularity assumptions on the set-valued mapping determine the regularity of the resulting solutions. Complementarity systems with time-dependence are studied as a particular case. We then use this result to study the problem of designing state feedback control laws for output regulation in systems described by EVIs. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available, In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed. As applications, we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints. Another application is seen in designing control inputs for regulation in power converters.

On the Selection of a Control Law for Multiply Connected Inertial Objects

A comparative analysis of the control law applied to complex dynamic objects that exhibit drift and lag is performed. The selection of a proportional–integral–derivative control law based on transient processes with optimum performance indicators is evaluated. An estimate of the external disturbances of the system is given and the advantage of the selection arrived at is proved.

A Novel Error-Compensation Control for a Class of High-Order Nonlinear Systems With Input Delay.

A novel tracking error-compensation-based adaptive neural control scheme is proposed for a class of high-order nonlinear systems with completely unknown nonlinearities and input delay. In the tracking errors of existing papers, there exist the following difficulties: first, output curve always lags behind the desired trajectory, second, some big peak errors cause a decrease in tracking precision, and third, a big initial value of the modified tracking error can make the closed-loop system unstable. To tackle them, three corresponding error-compensation terms are constructed, including a prediction and compensation term, an auxiliary signal produced by the constructed auxiliary system, and a damping term. However, inequality amplification caused by high order will weaken the effectiveness of the proposed error-compensation scheme, and the control precision will decrease under an assumption that the lower bounds of the unknown control coefficients should be exactly known. To overcome aforementioned difficulties, in the derivation of the first virtual control law, the radial basis function neural network is used to approximate a hybrid term online constructed by unknown nonlinearities, a lumped control coefficient achieved by state transformation, and the dynamic of the proposed error-compensation terms and desired signal. Meanwhile, input delay is coped with a robust compensation signal constructed based on a finite integral of the past control values. Finally, it is proven that all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the proposed method.

Adaptive output feedback integral sliding mode attitude tracking control of spacecraft without unwinding

This article studies an output feedback attitude tracking control problem for rigid spacecraft in the presence of parameter uncertainties and external disturbances. First, an anti-unwinding attitude control law is designed using the integral sliding mode control technique to achieve accurate tracking responses and robustness against inertia uncertainties and external disturbances. Next, the derived control law is combined with a suitable tuning law to relax the knowledge about the bounds of uncertainties and disturbances. The stability results are rigorously proved using the Lyapunov stability theory. In addition, a new finite-time sliding mode observer is developed to estimate the first time derivative of attitude. A new adaptive output feedback attitude controller is designed based on the estimated results, and angular velocity measurements are not required in the design process. A Lyapunov-based analysis is provided to demonstrate the uniformly ultimately bounded stability of the observer errors. Numerical simulations are given to illustrate the effectiveness of the proposed control method.

A Linear Formulation for Model Predictive Perimeter Traffic Control in Cities

An alternative approach for real-time network-wide traffic control in cities that has recently gained a lot of interest is perimeter flow control. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the inter-regional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions, so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of the current work is to study three aspects that are not covered in the perimeter control literature, which are: (a) the treatment of some model parameters that are not measurable in real life implementations and can affect the performance of the controller (e.g. advanced online estimation schemes can be developed for this purpose), (b) integration of appropriate external demand information that has been considered system disturbance in the derivation of feedback control laws in previous works, and (c) mathematical formulation of the original nonlinear problem in a linear form, so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem, as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. Preliminary simulation results for the case of a macroscopic environment (plant) are presented, in order to demonstrate the efficiency of the proposed approach. Results for the closed-loop model predictive control scheme are presented for the nonlinear case, which is used as “benchmark”, as well as the linear case.

Semi-Analytical Modeling and Vibration Control of a Geometrically Nonlinear Plate

This paper presents the dynamic modeling of a piezolaminated plate considering geometrical nonlinearities. The piezo-actuator and piezo-sensor are connected via proportional derivative feedback control law. The Hamilton’s principle is used to extract the strong form of the equation of motion with the reflection of the higher order strain terms by means of the strain–displacement relationship of the von Karman type. Then the nonlinear partial differential equation (PDE) obtained is converted to a nonlinear algebraic equation by employing the combination of harmonic balance method and single-mode Galerkin’s technique. Finally, the vibration suppression performance and sensitivity of the dynamic response is evaluated for various control parameters and magnitudes of external disturbance.

Robust reliable control of uncertain nonlinear stochastic systems subject to actuator fault

This paper addresses the issue of robust reliable stabilization for a class of uncertain nonlinear stochastic systems with both discrete and distributed time-varying delays and possible occurrence of actuator faults. By constructing a new Lyapunov functional and using linear matrix inequality technique, a new set of sufficient conditions is established for the stochastic stability of the uncertain nonlinear stochastic systems. Then, sufficient conditions are obtained for the solvability of the robust stabilization problem via robust reliable controller. More precisely, the derived control law guarantees the robust stabilization of nonlinear stochastic systems in the presence of known actuator failure matrix and uncertainties. Further, the results are extended to study the stabilization of stochastic systems with unknown actuator failure matrix. Moreover, the obtained criteria are formulated in terms of LMIs and also the reliable controller can be designed in terms of the solutions to certain linear matrix inequalities. Finally, numerical examples with simulation result are presented to demonstrate the validity and less conservatism of the obtained results.

Direct discrete time design of robust state derivative feedback control laws

ABSTRACTThis paper is concerned with the problem of designing robust state derivative feedback control laws in discrete time. The main contribution consists of a method for recasting a continuous time state space model in the form of a discrete time model formulated in terms of the state derivative. Uncertain input delays and parametric uncertainties in polytopic form can be propagated from the original state space representation to the resulting state derivative model. Therefore, robust control techniques originally developed for discrete time state space models can be directly employed to design the state derivative feedback law. Three computational examples are presented for illustration. The first example highlights the importance of accounting for the effect of sampling in the design procedure. More specifically, a linear quadratic regulation problem involving the state derivative is addressed. The second example involves the design of a robust predictive controller in the presence of input constraints and uncertain time delay. Finally, the third example is concerned with robust pole placement in the presence of parametric uncertainty.

Active control of bending waves propagating in an orthotropic rectangular panel

Due to the recent advances in microprocessors, active control of a flexible structure has become a realizable method for suppressing the vibration. Conventional modal-based method encounters difficulties in controlling a distributed parameter structure, since such a structure has an infinite number of vibration modes. To overcome this problem, active wave control has been studied in recent years. This paper presents an active wave control of an orthotropic rectangular panel by expanding the conventional active wave control method for a two-dimensional structural case. First, a transfer matrix method for a rectangular panel is introduced to describe the wave dynamics of the structure. This is followed by the derivation of feedforward control laws for absorbing reflected waves or eliminating transmitted waves. In the proposed method, the control laws are including the modal actuation scheme for uncontrolled direction. Then, from a viewpoint of numerical analyses, basic properties of the proposed method are verified. It is found that the reflected wave absorbing control enables the inactivation of all vibration modes in the controlled direction and the transmitted wave eliminating control enables the generation of an almost vibration-free state.

Wave absorption of an orthotropic rectangular panel based on direct feedback

This paper presents a new methodology of realizing an active wave control for an orthotropic rectangular panel. In general, an ideal wave controller is expressed by non-causal function which is impossible to be realized practically. The static direct feedback is introduced to overcome this problem. Firstly, a transfer matrix method for an orthotropic rectangular panel is introduced to describe the wave dynamics of the structure. This is followed by the derivation of feedback control laws for absorbing reflected waves. Then, static direct feedback is presented to realize the perfect wave absorption at single frequency. Finally, from a viewpoint of numerical analyses, control effects of the proposed method are verified by evaluating the absolute displacement distribution. It is found that the reflected wave absorbing control enables the inactivation of all vibration modes in the controlled direction.

Underwater soft-bodied pulsed-jet thrusters: Actuator modeling and performance profiling

A new kind of underwater vehicle is developed by taking inspiration from cephalopods. Its actuation routine is scrutinized via a suitable model. Similar to octopuses and squids, these vehicles consist of an elastic, hollow shell capable of undergoing sequential stages of ingestion and ejection of ambient fluid, which is driven by the recursive inflation and deflation of the shell. The shell actively collapses, and in this way it expels water through a funnel; then it passively returns to the inflated shape, drawing ambient fluid into the cavity. By doing so, a pulsed-jet propulsion routine is performed that enables the vehicle to propel itself in water. Due to their soft nature, the actuation of these vehicles is largely dependent on the subtle management of the elastic response of the shell throughout the propulsion routine. A kinematic model of the actuation mechanism, thoroughly corroborated by experimental validation, is devised which elucidates the relationship between the active (collapse) and passive (refill) stages of the actuation. Upon association with the dynamics of the vehicle, this model permits the derivation of the generic performance profiles of this new kind of vehicle. It is acknowledged that, for given design specifications, an optimal swimming speed exists in coincidence with the coordinated operation between the crank mechanism driving the shell contraction and the onset of elastic energy, which determines the speed of inflation of the shell. These results are invaluable in the definition of rigorous design criteria and derivation of ad-hoc control laws for a new breed of optimized soft-bodied, pulsed-jet, unmanned underwater vehicles.

Model-based control designs for offshore hydraulic winch systems

Model-based control designs have an advantage in controlling complex systems, and in assuring global system stability, in comparison to ordinary linear controllers such as PID controllers. This paper attempts to promote the use of model-based control designs in industrial applications, particularly in the marine system industry. A simple pendulum system is used as an example help to compare a backstepping sliding mode controller with a PID controller, and to display the main steps in deriving such a model based control design in a consistent manner, and to highlight the benefits using model-based control laws in comparison to standard PID based control laws. The results from this example indicate that the model based controller is barely affected by changes in system parameters in comparison to the PID controller which must be retuned each time the system parameters are changed. This indicates that a lookup table of controller gains and interpolation is needed if a PID controller is to be used for controlling a system with changing system parameters and/or highly nonlinear dynamics. Furthermore, an offshore hydraulic winch system is used as an in-depth case study in which the system is thoroughly analyzed. Based on simple fluid dynamics, mechanics and dynamics in general, a simplified state space model, but a highly nonlinear model that only describes the main characteristics of the hydraulic system is developed and used in the derivation of a speed controller and a torque controller for the hydraulic winch system. A process plant model describing the hydraulic winch system, together with a lumped wire-load model, is used in simulations to test and verify the derived control laws, which seem to be well-suited for controlling the hydraulic system. Based on the observations and results obtained in this work, it is indicated that a PID controller would not be able to control the hydraulic winch system with a large stability region, as well as a model-based controller, if a huge amount of work was not done in tuning and making lookup tables and interpolation algorithms for controller gains. This argues for the use of model-based control designs in industrial applications containing nonlinear dynamics and/or varying system parameters.

Potential function-based path-following control of an autonomous underwater vehicle in an obstacle-rich environment

This paper presents the development of simple but powerful path-following and obstacle-avoidance control laws for an underactuated autonomous underwater vehicle (AUV). Potential function-based proportional derivative (PFPD) as well as a potential function-based augmented proportional derivative (PFAPD) control laws are developed to govern the motion of the AUV in an obstacle-rich environment. For obstacle avoidance, a mathematical potential function is used, which formulates the repulsive force between the AUV and the solid obstacles intersecting the desired path. Numerical simulations are carried out to study the efficacy of the proposed controllers and the results are observed. To reduce the values of the overshoots and steady-state errors identified due to the application of PFPD controller a PFAPD controller is designed that drives the AUV along the desired trajectory. From the simulation results, it is observed that the proposed controllers are able to drive the AUV to track the desired path, avoiding the obstacles in an obstacle-rich environment. The results are compared and it is observed that the PFAPD outperforms the PFPD to drive the AUV along the desired trajectory. It is also proved that it is not necessary to employ highly complicated controllers for solving obstacle-avoidance and path-following problems of underactuated AUVs. These problems can be solved with the application of PFAPD controllers.

Three-Phase Three-Wire Active Power Filter With D Digital Control to Accommodate Filter-Inductance Variation

This paper presents a shunt active power filter (APF) with division–summation (D– $\Sigma )$ digital control and based on a three-phase three-wire inverter configuration. The APF shapes source current by introducing one degree of freedom to compensate load harmonic currents. The adopted D– $\Sigma $ digital control approach can accommodate filter-inductance variation, reducing core size significantly, and it can derive control laws directly. An average power method is adopted in this paper for determining the fundamental current at the source side, which can readily be implemented without complex calculation, frame transformation, and extra filter. In the design and implementation, the inductances corresponding to various inductor currents were estimated at the startup and stored in the microcontroller for scheduling loop gain cycle by cycle, which can ensure the system stability. Measured results from a 5-kVA three-phase APF have confirmed the analysis and discussion of the APF.