Input-output Feedback Linearization Method Research Articles

Model Simplification for Asymmetric Marine Vehicles in Horizontal Motion—Verification of Selected Tracking Control Algorithms

This paper addresses a trajectory tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North–East–Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method, for which the application condition was that the vehicle was symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Adaptive PMSM Control of Ship Electric Propulsion with Energy-Saving Features

Electric ship propulsion is considered one of the most promising alternatives to conventional combustion systems. Its goal is to reduce the carbon footprint and increase a ship’s maneuverability, operational safety, and reliability. The high requirements for ship propulsion make permanent magnet synchronous motors (PMSMs) an attractive solution due to their characteristics. This paper discusses the control problem of a PMSM based on the input–output feedback linearization method combined with the optimal and adaptive control techniques. The method presented here integrates the parameter tuning process with the optimal design of the baseline controller. Since the load disturbances are treated as an additional unknown parameter, there is no need to introduce an integral action to deal with the resulting steady-state error. An important feature of the designed controller is the so-called energetic optimization of the system; i.e., in addition to the aforementioned adaptive and optimal controller, it has a feature of ensuring zero reactive power consumed by the system. The performed simulations of the machine speed stabilization process confirmed the high efficiency of the proposed controller despite the assumed uncertainty of the system parameters and environmental (load) disturbances. Besides achieving high-quality control, an essential feature of this approach is the elimination of the tuning problem.

Distributed Multiagent-Based Event-Driven Fault-Tolerant Control of Islanded Microgrids.

This article proposes an observer-based event-driven fault-tolerant (OBEDFT) secondary control strategy for AC microgrids (MGs) to achieve load voltage regulation. First, the input-output feedback linearization method transforms the voltage regulation issue into an output feedback tracking problem for linear multiagent systems (MASs) with nonlinear dynamics. This transformation provides the necessary preprocessing for load voltage regulation. Then, an OBEDFT secondary control protocol that considers full-state immeasurability is proposed. The actuators of distributed generators (DGs) may experience partial loss of effectiveness (PLOE) and bias faults, and these fault parameters may be heterogeneous and time-varying. The protocol introduces adaptive techniques to avoid information related to fault parameters while using event-driven mechanisms to achieve discrete measurements of neighboring DG. Additionally, the protocol uses boundary layers to construct smooth controllers that prevent the chattering effect caused by nonsmooth controllers. Finally, simulation results confirm the effectiveness of this load voltage regulation strategy.

Modification of Nonlinear Controller for Asymmetric Marine Vehicles Moving in Horizontal Plane

This paper considers a trajectory-tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North-East-Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method for which the application condition is that the vehicle is symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Full State Constrained Flight Tracking Control for Helicopter Systems with Disturbances

In this paper, a full state-constrained anti-disturbance dynamic surface control method is proposed for six-degree-of-freedom unmanned helicopter systems under full state constraints and disturbances. Firstly, due to the underactuated characteristics of six-degree-of-freedom unmanned helicopter systems, an input–output feedback linearization method is used to transform the complex nonlinear systems into facilitated-control nonlinear ones. Based on the transformed systems, the nonlinear disturbance-observer-based control, backstepping control and Barrier Lyapunov function methods are used to construct the flight controller via uniting the state constraint control and dynamic surface control technologies. Then, Lyapunov stability theory is adopted for analysing the closed-loop tracking error systems, which confirms that the tracking errors are bounded under the proposed flight control scheme. Finally, a simulation in the MATLAB/Simulink environment verifies that the unmanned helicopter system can constrain all states under the action of the designed controller, with good dynamic performance.

Design of ship course-keeping system via adaptive control techniques

The paper discusses the problem of ship autopilot design based on the input-output feedback linearization method combined with the adaptive control techniques. At first, the nonlinear ship model of the Norrbin type is linearized with the use of simple system nonlinearity cancellation. Since the exact values of the model parameters are not known to overcome the resulting inaccuracies, these parameters are tuned in such a way as to guarantee the asymptotic stability of the system. Some novelty is that by treating the load disturbance as an additional, unknown parameter of the system, we do not need to introduce an extra integral action to deal with the appearing steady-state error. The simulations of the ship course change process confirmed the high efficiency of the proposed controller despite the assumed uncertainty of the system parameters and environmental disturbances. An important feature of this approach is also the elimination of the tuning problem.

Observer-based adaptive neural network control for PEMFC air-feed subsystem

Oxygen excess ratio (OER) tracking of polymer electrolyte membrane fuel cell (PEMFC) air-feed subsystem is an interesting topic to obtain a high energy conversion ratio. The control purpose is challenging due to the unknown nonlinear function, time-varying external disturbance and unmeasured variable. To deal with the above problems, a neural network control scheme based on tracking error observer and disturbance observer is proposed. Firstly, a canonical form of the PEMFC air-feed subsystem is developed based on the input–output feedback linearization method. Meanwhile, a tracking error observer which only uses the system output is developed for the reconstruction of the unmeasured variable. Secondly, the neural network based on a novel adaptive learning law is proposed to approximate the unknown nonlinear function. An identification model with a second-order low-pass filter is designed such that the adaptive learning law is adjusted by the observer error and modeling error, simultaneously. Finally, to reduce the effect caused by compound disturbance including the external disturbance and neural network approximation error, a nonlinear disturbance observer is proposed. The main contribution of this study is not only avoiding the prior knowledge of system uncertainty, external disturbance and the unmeasured variable but also improving the OER tracking performance under the measurement noise. Lyapunov theory analysis shows that the system tracking error is uniformly ultimately bounded. Numerical simulations and hardware-in-loop (HIL) experiments show that the proposed neural network control algorithm can maintain OER at the target value even under external disturbance. The experimental results show that the performance indexes including the mean absolute error (MAE), the root mean square error (RMSE) and the standard deviation (SD) of the proposed controller during the whole process are 0.0213, 0.0547 and 0.0538, respectively. Compared with the proportional–integral–derivative (PID) controller (MAE 0.0466, RMSE 0.0762 and SD 0.0745), robust adaptive radial basis function neural network (RBFNN-H∞) controller (MAE 0.0841, RMSE 0.0839 and SD 0.0813) and hybrid robust adaptive radial basis function neural network (HARBFNN-1st) controller (MAE 0.0255, RMSE 0.0613 and SD 0.0603), the proposed controller performs a better performance.

Nonlinear MPC for DFIG-based wind power generation under unbalanced grid conditions

In a modern power system with a high wind power penetrating rate, the control of the doubly-fed induction generator (DFIG) is quite important to ensure high load-following capability. It can be quite challenging when grid voltage unbalance conditions happened. Model predictive control (MPC) is an advanced control strategy that can optimize the DFIG operation, particularly under unbalanced grid voltage conditions. The detailed modeling in the positive and negative synchronous reference frames resulting from the grid unbalance is presented in nonlinear state-space form. An effective linearized technique, i.e., the input-output feedback linearization method, is adopted in the MPC design. The control law is derived by the optimization of two targets that aim to eliminate the pulsations in the active or reactive power. The simulation results prove that power pulsations are effectively suppressed under unbalanced grid voltage conditions while ensuring good track performance.

Parametric uncertainty handling of under-actuated nonlinear systems using an online optimal input–output feedback linearization controller

This research introduces a new online optimal control based on the input–output feedback linearization and a multi-crossover genetic algorithm for under-actuated nonlinear systems having parametric uncertainties. At first, the input–output feedback linearization method is successfully implemented to derive the control law for a two degrees of freedom cart-pole nonlinear system. Then, the regarded optimization algorithm is applied to find the design parameters of the controller for different values of the uncertain variables. Next, an approximation function is suggested to calculate the optimum gains of the controller in the presence of the uncertainties in the system parameters. The simulation results are illustrated to prove the effectiveness and adeptness of the introduced scenario to overcome some common issues in the actual systems, i.e. under-actuating nonlinearities and uncertainties.

Input-Output Feedback Linearization for the Control of a 4 Cable-Driven Parallel Robot

Abstract This paper presents the control of an under-constrained 4 Cable-Driven Parallel Robot (CDPR) using input-output feedback linearization technique. The dynamic model of the CDPR is first formulated by taking into account the Euler angle rates. Following this, the input-output feedback linearization method is implemented to decouple the output and input. A linear feedback controller is then designed using pole placement method to control the CDPR. The control law is then verified by simulation using MATLAB software. Simple trajectories are then tested with and without the presence of noise to analyze the behavior of the control law.

Trajectory Tracking and Path Following for Underactuated Marine Vehicles

In this paper, we present a control strategy for trajectory tracking and path following of generic paths for underactuated marine vehicles. Our work is inspired and motivated by previous works on ground vehicles. In particular, we extend the definition of the hand position point, introduced for ground vehicles, to autonomous surface vehicles and autonomous underwater vehicles, and then use the hand position point as output for a control strategy based on the input–output feedback linearization method. The presented strategy is able to deal with external disturbances affecting the vehicle, e.g., constant and irrotational ocean currents. Using the Lyapunov analysis, we are able to prove that the closed-loop system has an external dynamics that is globally exponentially stable and an internal dynamics that has ultimately bounded states, both for the trajectory tracking and the path following control problems. Finally, we present a simulation case study and experimental results in order to validate the theoretical results.

Minimum-Rank Dynamic Output Consensus Design for Heterogeneous Nonlinear Multi-Agent Systems

In this paper, we propose a new and systematic design framework for output consensus in heterogeneous Multi-Input Multi-Output (MIMO) general nonlinear Multi-Agent Systems (MASs) subjected to directed communication topology. First, the input-output feedback linearization method is utilized assuming that the internal dynamics is Input-to-State Stable (ISS) to obtain linearized subsystems of agents. Consequently, we propose local dynamic controllers for agents such that the linearized subsystems have an identical closed-loop dynamics which has a single pole at the origin whereas other poles are on the open left half complex plane. This allows us to deal with distinct agents having arbitrarily vector relative degrees and to derive rank-$1$ cooperative control inputs for those homogeneous linearized dynamics which results in a minimum rank distributed dynamic consensus controller for the initial nonlinear MAS. Moreover, we prove that the coupling strength in the consensus protocol can be arbitrarily small but positive and hence our consensus design is non-conservative. Next, our design approach is further strengthened by tackling the problem of randomly switching communication topologies among agents where we relax the assumption on the balance of each switched graph and derive a distributed rank-$1$ dynamic consensus controller. Lastly, a numerical example is introduced to illustrate the effectiveness of our proposed framework.

Modulation of Parkinsonian State With Uncertain Disturbance Based on Sliding Mode Control.

Parkinson's disease (PD) is a degenerative disorder of central nervous system that endangers the olds' health seriously. The motor symptoms of PD can be attributed to the distorted relay reliability of thalamus to cortical sensorimotor input that results from the increase of inhibitory input from internal segment of the globus pallidum (GPi). Based on this, we construct the GPi-thalamocortical computational model to generate the normal and pathological firing patterns by varying GPi spike train input. A kind of closed-loop deep brain stimulation (DBS) strategy is proposed here. Our control objective is to make the controlled membrane potential of the thalamic neuron return to the normal firing pattern. The control input that directly acts on the thalamus is the DBS waveform, which is adjusted in real time according to the feedback signal. Aimed at a certain system without the change of object parameters or stochastic disturbance, the input-output feedback linearization method is able to eliminate the error between the system output and the desired output. When uncertain elements taken into consideration in the system, the simulation results indicate that sliding mode control scheme provides better effectiveness and higher robustness.

Passivity-Based Control With Nonlinear Damping for Type 2 STATCOM Systems

This paper presents a passivity-based control (PBC) for a type 2 static synchronous compensator (STATCOM) based on an Euler-Lagrange model. The proposed method is designed based on a Lyapunov function by considering dissipation to improve transient performance. An additional nonlinear damping term is designed to regulate the capacitor voltage. It is guaranteed that the equilibrium point of the system is locally exponentially stable in the operating range. The performance of the proposed method is validated via a 100 Mvar STATCOM system connected to the 345-kV grid system in SimPowerSystems, MATLAB/Siumlink. To compare with the input-output feedback linearization method, the proposed control method has improved convergence and reduction of oscillations of the active current and DC voltage, as shown in simulation results. Lastly, it shows that the proposed method is robust to model mismatches as the variation of the grid voltage and the degradation of the capacitance.

On Consensus of Nonlinear Multi-Agent Systems with Output Constraints

Abstract: This paper proposes a unified approach to analyze and synthesize consensus control laws for nonlinear leaderless multi-agent systems (MASs) subjected to output constraints. First, we employ the input-output feedback linearization method to derive the linearized models of agents. Accordingly, the consensus problem under output constraints for the initial nonlinear MAS is transformed into an equivalent consensus problem under state constraints for the linearized MAS, which is then reformulated as a network of Lur’e systems. Next, a sufficient condition for consensus and the design of consensus controller gain are derived from solutions of a distributed LMI convex problem. Finally, a numerical example is introduced to illustrate the proposed theoretical approach.

Dynamics modeling and control of a transport aircraft for ultra-low altitude airdrop

The nonlinear aircraft model with heavy cargo moving inside is derived by using the separation body method, which can describe the influence of the moving cargo on the aircraft attitude and altitude accurately. Furthermore, the nonlinear system is decoupled and linearized through the input–output feedback linearization method. On this basis, an iterative quasi-sliding mode (SM) flight controller for speed and pitch angle control is proposed. At the first-level SM, a global dynamic switching function is introduced thus eliminating the reaching phase of the sliding motion. At the second-level SM, a nonlinear function with the property of “smaller errors correspond to bigger gains and bigger errors correspond to saturated gains” is designed to form an integral sliding manifold, and the overcompensation of the integral term to big errors is weakened. Lyapunov-based analysis shows that the controller with strong robustness can reject both constant and time-varying model uncertainties. The performance of the proposed control strategy is verified in a maximum load airdrop mission.

Adaptive control of Parkinson's state based on a nonlinear computational model with unknown parameters.

The objective here is to explore the use of adaptive input-output feedback linearization method to achieve an improved deep brain stimulation (DBS) algorithm for closed-loop control of Parkinson's state. The control law is based on a highly nonlinear computational model of Parkinson's disease (PD) with unknown parameters. The restoration of thalamic relay reliability is formulated as the desired outcome of the adaptive control methodology, and the DBS waveform is the control input. The control input is adjusted in real time according to estimates of unknown parameters as well as the feedback signal. Simulation results show that the proposed adaptive control algorithm succeeds in restoring the relay reliability of the thalamus, and at the same time achieves accurate estimation of unknown parameters. Our findings point to the potential value of adaptive control approach that could be used to regulate DBS waveform in more effective treatment of PD.

Modeling Single-Phase Inverter and Its Decentralized Coordinated Control by Using Feedback Linearization

It is a very crucial problem to make a microgrid operated reasonably and stably. Considering the nonlinear mathematics model of inverter established in this paper, the input-output feedback linearization method is used to transform the nonlinear mathematics model of inverters to a linear tracking synchronization and consensus regulation control problem. Based on the linear mathematics model and multiagent consensus algorithm, a decentralized coordinated controller is proposed to make amplitudes and angles of voltages from inverters be consensus and active and reactive power shared in the desired ratio. The proposed control is totally distributed because each inverter only requires local and one neighbor’s information with sparse communication structure based on multiagent system. The hybrid consensus algorithm is used to keep the amplitude of the output voltages following the leader and the angles of output voltage as consensus. Then the microgrid can be operated more efficiently and the circulating current between DGs can be effectively suppressed. The effectiveness of the proposed method is proved through simulation results of a typical microgrid system.

Following control for a UUV using temporary path generation guidance

A path following control algorithm for an unmanned underwater vehicle (UUV) using temporary path generation guidance was proposed in this paper. Owing to different initial states of the vehicle, such as position and orientation, the path following control in the horizontal plane may yield a poor performance. To deal with the negative effect induced by initial states, a temporary path generation was presented based on the relationship between the original reference path and the vehicle’s initial states. With different relative positions between the vehicle and reference path, including out of straight lines, as well as inside and outside a circle, the related temporary paths guiding the vehicle to the reference path were able to be generated in real time. The vehicle was guided to steer along the temporary path until it reached the tangent point at the reference path, where the controller was designed using the input-output feedback linearization method. Simulation results demonstrated that the proposed algorithm is effective under the three different situations mentioned above.

거리 정보를 이용한 되먹음 선형화 기법 무인기 편대 비행제어

This paper addresses how to make a formation of multiple unmanned aerial vehicles (UAVs) using only the relative range information. Since the relative range can easily be measured by an on-board range sensor like the laser range finder, the proposed method does not require any expensive and heavy wireless communication system to share the navigation information of each vehicle. Based on the two-dimensional (2-D) nonlinear equations of motion, we propose a nonlinear formation controller using the typical input-output feedback linearization method. The performance of the proposed formation controller is verified by various numerical simulations.