Feedback Linearization Approach Research Articles

Combined adaptive neural network and regressor‐based trajectory tracking control of flexible joint robots

By relying on the input–output feedback linearization approach, a novel adaptive controller for flexible joint robots is proposed in this work. First, a model-based controller is developed to get a structure that is useful in the development of the adaptive controller. The adaptive version is developed by using two techniques. To stabilize the output function, an adaptive neural network controller is used, which approximates the non-linear function that contains the uncertainties. The desired rotor position required by the input–output feedback linearization controller is defined with the structure of a link dynamics adaptive regressor-based controller. The main reason to adopt the mentioned structure in the definition of the desired rotor link position is to guarantee its differentiability. Real-time experiment comparisons among the model-based controller, a model-based controller with desired compensation, an adaptive controller based on joint torque feedback, and an adaptive neural network-based controller are carried out. Experimental results support the theory reported in this document and the accuracy of the proposed approach.

Thermoelectric modules in mechatronic systems: Temperature-dependent modeling and control

Active thermal control is crucial in achieving the required accuracy and throughput in many industrial applications, e.g., in the medical, high-power lighting, and semiconductor industry. Thermoelectric Modules (TEMs) can be used to both heat and cool, alleviating some of the challenges associated with traditional electric heater based control. However, the dynamic behavior of these modules is non-affine in their inputs and state, complicating their implementation. To facilitate advanced control approaches a high fidelity model is required. In this paper an approach is presented that increases the modeling accuracy by incorporating temperature-dependent parameters. Using an experimental identification procedure, the parameters are estimated under different operating conditions. The resulting model is used in a feedback linearization approach to linearize the system, facilitating the use of advanced linear control techniques. Moreover, it presents an observer based approach to reconstruct state information in cases where sensor placement is limited. The resulting framework forms a complete approach to temperature-dependent modeling and control of thermoelectric elements.

Fuzzy logic and gradient descent-based optimal adaptive robust controller with inverted pendulum verification

This paper develops an adaptive robust combination of feedback linearization (FL) and sliding mode controller (SMC) based on fuzzy rules and gradient descent laws. The new suggested control algorithm is tested to stabilize a fourth-order under-actuated nonlinear inverted pendulum system. More precisely, the reliable feedback linearization approach and the robust SMC controller are combined to design a stable control effort. In order to enhance the performance of the suggested controller, an adaptation technique as long as fuzzy rules are applied to update the control gains and the boundary layer parameter. Then, a novel evolutionary algorithm termed multi-objective ant lion optimizer (MOALO) is implemented to determine the control coefficients. The analysis and results conducted on the inverted pendulum system demonstrate the desired performance of the proposed control scheme by providing an optimal smooth control input, suitable tracking performance, and proper time responses.

Cooperative Moving-Target Enclosing Control for Multiple Nonholonomic Vehicles Using Feedback Linearization Approach

This article investigates the moving-target circular formation control problem for multiple nonholonomic vehicles under a directed graph. First, a novel moving-target enclosing control scheme is proposed by using the feedback linearization approach, in which the design procedure of the cooperative controller is more straightforward. Compared with the existing literature, the designed controller relaxes some existing constraints and the corresponding stability analysis is more concise. Second, based on the distance measurements, the observers, including sliding-mode observer and relative position observer, are designed to estimate the relative position so that the global position measurements are not required. Therefore, the observer-based controller becomes more suitable for practical application. Numerical simulations are conducted to illustrate the effectiveness of the proposed controllers.

Dynamic modeling and design of controller for the 2-DoF serial chain actuated by a cable-driven robot based on feedback linearization

This study intends to investigate a dynamic modeling and design of controller for a planar serial chain, performing 2-DoF, in interaction with a cable-driven robot. The under study system can be used as a rehabilitation setup which is helpful for those with arm disability. The latter goal can be achieved by applying the positive tensions of the cable-driven robot which are designed based on feedback linearization approach. To this end, the system dynamics formulation is developed using Lagrange approach and then the so-called Wrench-Closure Workspace (WCW) analysis is performed. Moreover, in the feedback linearization approach, the PD and PID controllers are used as auxiliary controllers input and the stability of the system is guaranteed as a whole. From the simulation results it follows that, in the presence of bounded disturbance based on Roots Mean Square Error (RMSE) criteria, the PID controller has better performance and tracking error of the 2-DoF robot joints are improved 15.29% and 24.32%, respectively.

Orders & Contracts

This paper develops an adaptive robust combination of feedback linearization (FL) and sliding mode controller (SMC) based on fuzzy rules and gradient descent laws. The new suggested control algorithm is tested to stabilize a fourth-order under-actuated nonlinear inverted pendulum system. More precisely, the reliable feedback linearization approach and the robust SMC controller are combined to design a stable control effort. In order to enhance the performance of the suggested controller, an adaptation technique as long as fuzzy rules are applied to update the control gains and the boundary layer parameter. Then, a novel evolutionary algorithm termed multi-objective ant lion optimizer (MOALO) is implemented to determine the control coefficients. The analysis and results conducted on the inverted pendulum system demonstrate the desired performance of the proposed control scheme by providing an optimal smooth control input, suitable tracking performance, and proper time responses.

Robust LQR-Based Neural-Fuzzy Tracking Control for a Lower Limb Exoskeleton System with Parametric Uncertainties and External Disturbances.

The design of an accurate control scheme for a lower limb exoskeleton system has few challenges due to the uncertain dynamics and the unintended subject's reflexes during gait rehabilitation. In this work, a robust linear quadratic regulator- (LQR-) based neural-fuzzy (NF) control scheme is proposed to address the effect of payload uncertainties and external disturbances during passive-assist gait training. Initially, the Euler-Lagrange principle-based nonlinear dynamic relations are established for the coupled system. The input-output feedback linearization approach is used to transform the nonlinear relations into a linearized state-space form. The architecture of the adaptive neuro-fuzzy inference system (ANFIS) and used membership function are briefly explained. While varying mass parameters up to 20%, three robust neural-fuzzy datasets are formulated offline with the joint error vector and LQR control input. Thereafter, to deal with external interferences, an error dynamics with a disturbance estimator is presented using an online adaptation of the firing strength matrix. The Lyapunov theory is carried out to ensure the asymptotic stability of the coupled human-exoskeleton system in view of the proposed controller. The gait tracking results for the proposed control scheme (RLQR-NF) are presented and compared with the exponential reaching law-based sliding mode (ERL-SM) controller. Furthermore, to investigate the robustness of the proposed control over LQR control, a comparative performance analysis is presented for two cases of parametric uncertainties and external disturbances. The first case considers the 20% raise in mass values with a trigonometric form of disturbances, and the second case includes the effect of the 30% increment in mass values with a random form of disturbances. The simulation runs have shown the promising gait tracking aspects of the designed controller for passive-assist gait training.

Energy Shaping and Partial Feedback Linearization of Mechanical Systems with Kinematic Constraints

Abstract Traditionally, the energy shaping for mechanical systems requires the elimination of holonomic and nonholonomic constraints. In recent years, it was argued that such elimination might be unnecessary, leading to a possible simplification of the matching conditions in energy shaping. On the other hand, the partial feedback linearization (PFL) approach has been widely applied to unconstrained mechanical systems, but there is no general result for the constrained case. In this regard, this paper formalizes the PFL for mechanical systems with kinematic constraints and extends the energy shaping of such systems by including systems with singular inertia matrix and non-workless constraint forces, which can arise from the coordinate selection and PFL. We validated the proposed methodology on a 5-DoF portal crane via simulation.

Toward a Reinforcement Learning Environment Toolbox for Intelligent Electric Motor Control.

Electric motors are used in many applications, and their efficiency is strongly dependent on their control. Among others, linear feedback approaches or model predictive control methods are well known in the scientific literature and industrial practice. A novel approach is to use reinforcement learning (RL) to have an agent learn electric drive control from scratch merely by interacting with a suitable control environment. RL achieved remarkable results with superhuman performance in many games (e.g., Atari classics or Go) and also becomes more popular in control tasks, such as cart-pole or swinging pendulum benchmarks. In this work, the open-source Python package gym-electric-motor (GEM) is developed for ease of training of RL-agents for electric motor control. Furthermore, this package can be used to compare the trained agents with other state-of-the-art control approaches. It is based on the OpenAI Gym framework that provides a widely used interface for the evaluation of RL-agents. The package covers different dc and three-phase motor variants, as well as different power electronic converters and mechanical load models. Due to the modular setup of the proposed toolbox, additional motor, load, and power electronic devices can be easily extended in the future. Furthermore, different secondary effects, such as converter interlocking time or noise, are considered. An intelligent controller example based on the deep deterministic policy gradient algorithm that controls a series dc motor is presented and compared to a cascaded proportional-integral controller as a baseline for future research. Here, safety requirements are particularly highlighted as an important constraint for data-driven control algorithms applied to electric energy systems. Fellow researchers are encouraged to use the GEM framework in their RL investigations or contribute to the functional scope (e.g., further motor types) of the package.

Adaptive Attitude Controller Design for a Rigid Satellite with Feedback Linearization Approach

This paper investigates a novel adaptive attitude controller design for rigid microsatellite based on feedback linearization approach, in which an accurate attitude pointing is required within a strict power limitation for space environment. The control strategy is performed to guarantee the stability of the satellite attitude under the effect of uncertain actuator parameters such as torque magnitude error and misalignment. The controller estimates the total torque fault through an observer in order to provide a reliable attitude control during the satellite manoeuvre. The stability of the closed-loop dynamic of the designed control law is proven via Lyapunov analysis. Finally, a comparative study with the well-known controllers from the literature is examined through numerical simulations to demonstrate the feasibility and effectiveness of the proposed control method.

Trajectory Tracking of a Flexible Robot Manipulator by a New Optimized Fuzzy Adaptive Sliding Mode-Based Feedback Linearization Controller

This work presents a novel fuzzy adaptive sliding mode-based feedback linearization controller for trajectory tracking of a flexible robot manipulator. To reach this goal, after deriving the dynamical equations of the robot, the feedback linearization approach is utilized to change the nonlinear dynamics to a linear one and find the control law. Then, the sliding mode control strategy is implemented to design a stabilizer for trajectory tracking of the flexible robot. In order to adaptively tune the parameters of the designed controller, the gradient descent approach and the chain derivative rule are employed. Moreover, the Takagi–Sugeno–Kang fuzzy system is applied to regulate the controller gains. Finally, a multiobjective particle swarm optimization algorithm is used to find the optimum fuzzy rules. The conflicting objective functions considered as the integrals of the absolute values of the state error and the control effort should be minimized, simultaneously. The simulation results illustrate the effectiveness and capability of the introduced scenario in comparison with other methods.

Coupling analysis and control of axial and torsional vibrations in a horizontal drill string

Vertical drilling methods have been often used for oil and gas extraction so far. In some places, for further extraction and access to the locations that cannot be obtained by the vertical drilling (due to its restrictions); horizontal drilling has become more popular. In horizontal drilling, a variety of longitudinal, torsional and lateral vibrations occur. These vibrations, if left uncontrolled, can damage the drilling rig and equipment, as well as reduce the efficiency of the drilling process and increase the processing time. The purpose of this research is to obtain the coupled axial and torsional vibration equations by analysing the vibrational modes in the horizontal section of the horizontal drilling. The obtained equations, which are in the form of continuous vibrations, are discretized by the mode summation method, and then the stability of the horizontal drilling string is investigated, and the controller is designed to stabilize the unstable process. In this research, the friction coefficient has been modeled randomly to be closer to the actual conditions. The controller was initially designed with four inputs, and then its inputs were reduced to the two inputs. First, the feedback linearization approach plus the pole placement method have been used to design the controller. To show the efficiency of the controller performance, uncertainties in the parameters of the forces are considered.

Fault-tolerant control for four-wheel independent actuated electric vehicle using feedback linearization and cooperative game theory

This paper presents a novel fault-tolerant control (FTC) approach based on the cooperative game to guarantee the stability of four-wheel independent drive electric vehicles, in which four different players are modeled and interacted to find a solution to the FTC problem. First, a feedback linearization approach is employed to handle the nonlinearities in the system. Then, to study the interaction among actuators in an actuator failure scenario, the FTC problem can be viewed as a cooperative game so that its four players, namely the four in-wheel motors can cooperate to provide more stability of the vehicle. The distributed model predictive control theory is adopted as a general framework, the Pareto strategies among the players are derived using an interactive model based on a convex iterative method. Furthermore, the conditions that guarantee the practical stability of the closed-loop system are provided. The intrinsic differences between the cooperative game and noncooperative game are investigated via a numerical simulation. The effectiveness and real-time of the proposed control strategy are verified in a real-time hardware-in-the-loop test, and the results prove that the control strategy can effectively guarantee the stability of the vehicle in various actuator failure scenarios.

Control Design of Nonlinear Spacecraft System Based on Feedback Linearization Approach

In this paper, based on simple quadratic matrix algebra, feedback linearization and neural network methods, the kinematics and almost perturbation decoupling and tracking performances of nonlinear spacecraft attitude control represented by improved Rodriguez parameters are studied. A nonlinear robust attitude controller is proposed to ensure the global stability and the almost disturbance decoupling performance without any learning or adaptation rules used in neural network approach and without having to solve the complex Hamilton-Jacobi equation of H-infinity control approach. This study presents an example that cannot be solved by the first paper on the problem of almost disturbance decoupling, to illustrate the point that this method can easily solve the tracking and almost disturbance decoupling performance. In addition, we propose a novel algorithm and two theorems that design a controller with almost disturbance decoupling and tracking performances. On the basis of meeting the standards we proposed, we successfully carried out some simulations on the spacecraft system to solve the effects of external disturbance torques.

Autonomous Landing Design of UAVs using Feedback Linearization Controller with Anti Windup Scheme

This paper presents autonomous landing controller design of unmanned aerial vehicles (UAVs). Feedback linearization approach with anti windup scheme is designed as autonomous landing controller. Anti windup basically controls the integrator component accumulation in the autopilot design and restricts the output within saturation limits. Autonomous landing of a fixed wing UAV consists of approach, glideslope and flare phases. During approach, aerial vehicle aligns itself with runway and reduces its lateral deviations with respect to runway central line. In glide slope phase, aerial vehicle maintains a fixed flight path angle and descends with a constant sink rate. In flare phase, aerial vehicle follows an exponential trajectory and descends with a lower sink rate which keeps reducing further as it goes to lower altitudes. Flare controller is designed with integrator and antiwindup scheme is used to handle the controller output within saturation limits. Landing is primarily a longitudinal mode operation but due to disturbances and coupling lateral and directional modes also gets activated. In this paper pitch angle, roll angle and yaw angle nonlinear dynamic equations are linearized to obtain the control commands in terms of elevator deflection, aileron deflection and rudder deflections. Similarly total velocity of aerial vehicle being an important parameter is controlled using thrust command. A first order linearized model of velocity is used to obtain thrust control command. Autonomous landing of UAV with feedback linearization controller and anti windup scheme is simulated with Six-DOF model of AE2 UAV. The algorithm is implemented with wind disturbances to show the autonomous landing performance of UAV.

Position‐heading quadrotor control using LPV techniques

This work presents a solution to the position-heading control problem of a small quadrotor. The main idea of this study is to exploit the advantages of the linear parameter varying (LPV) control approach together with a feedback linearisation approach for designing a cascade control structure without the need to perform simplifications with respect to the reference dynamic model used in the literature. The use of a LPV representation of the attitude subsystem allows to consider it as independent of the position one, allowing the use of a cascade control structure. For the inner attitude control loop, the proposed quasi-LPV-linear-quadratic regulator (LQR) controller and proportional-integral observer (PIO) are solved in an optimal manner by solving a set of linear matrix inequalities (LMIs). While for the outer position control loop, a feedback linearisation approach is developed before designing the corresponding controller and PIO also minimising the LQR problem by means of LMIs. Furthermore, another outer loop, interchangeable with the position one, such that controls the velocities in the body frame is proposed. This velocities controller is also solved in an optimal manner using a combination of feedback linearisation and LPV techniques. The proposed solutions are applied to an AscTec Hummingbird unmanned aerial vehicle in simulation.

A coordinated control for voltage and transient stability of multi-machine power grids relying on wind energy

This paper proposes a new nonlinear control approach to coordinate doubly fed induction generator (DFIG)-based wind turbines and static synchronous compensator (STATCOM) controllers in multi-machine power systems. Its main objectives are to improve the transient and voltage stability of the inter-connected multi-machine power system via simultaneous design of the voltage of the DFIGs’ rotors and reference current of STATCOM. The nonlinear approach is based on a multi input-multi output (MIMO) zero dynamics (ZD) technique augmented by a super twisting sliding mode control (STSMC) to reduce the effects of the linearization error. The proposed approach was implemented to the Kundur’s four-machine two-area power system and the IEEE 39-bus power system. Its performance was assessed in the presence of various faulty scenarios and disturbances. The effectiveness of the proposed approach (ZD-STSMC) was evaluated via eigenvalue analysis, transient simulations and transient stability margin analysis (by critical clearing time (CCT)). The merits of the proposed design are further compared to those of the exact feedback linearization (EFL) approach. Enhancing the power and voltage stability of large scale power systems, damping power oscillations and providing faster post-fault recovery time are among the positive features of the proposed approach.

A Feedback Linearization-Based Motion Controller for a UWMR with Experimental Evaluations

SummaryIn this paper, the feedback linearization approach is used to introduce a motion controller for unicycle-type wheeled mobile robots (UWMRs). The output function is defined as a linear combination of the error state. The novel scheme is firstly tested in numerical simulation and compared with its corresponding experimental result. Three controllers are taken from the literature and compared to the proposed approach by means of experiments. The gains of the experimentally tested controllers are selected to obtain identical energy consumption. The Optitrack commercial vision system and Pioneer P3-DX UWMR are used in real-time experimental tests. In addition, two sets of experimental results for different motion tasks are provided. The results show that the proposed controller presents the best tracking accuracy.

Nonlinear Multi-Agent Optimal Load Frequency Control Based on Feedback Linearization of Wind Turbines

Large scale power systems have distributed structure since power generation units are distributed in the network. In such systems, where the communications are sometimes imperfect, centralized control structures have concerns to be applied. For such inherently distributed systems, multi-agent control structures are more appropriate. On the other hand, power systems have nonlinear dynamics. When all generation units are synchronous generators, linear approximation of swing equation of generators is a common choice. However, by penetration of renewable energy generation units, those have highly nonlinear dynamics, nonlinear control approaches should be applied. In this paper, a nonlinear multi-agent feedback linearization approach is adopted for optimal load frequency control of a power system with wind generation units. Multiagent controllers with both distributed and decentralized structures are proposed. Centralized feedback controller is also applied for comparison purposes. The parameters of the controllers are optimized using gray wolf optimization algorithm to improve time response of the system and reduce generation costs. IEEE 30-bus system with six synchronous generators and four wind turbines is considered as a test system. Simulation results verify the inefficiency of centralized controller and show that distributed control structure can produce a balanced performance in terms of time response and is better from the cost reduction view point than the decentralized controller.

Configuration-Dependent Optimal Impedance Control of an Upper Extremity Stroke Rehabilitation Manipulandum.

Robots are becoming a popular means of rehabilitation since they can decrease the laborious work of a therapist, and associated costs, and provide well-controlled repeatable tasks. Many researchers have postulated that human motor control can be mathematically represented using optimal control theories, whereby some cost function is effectively maximized or minimized. However, such abilities are compromised in stroke patients. In this study, to promote rehabilitation of the stroke patient, a rehabilitation robot has been developed using optimal control theory. Despite numerous studies of control strategies for rehabilitation, there is a limited number of rehabilitation robots using optimal control theory. The main idea of this work is to show that impedance control gains cannot be kept constant for optimal performance of the robot using a feedback linearization approach. Hence, a general method for the real-time and optimal impedance control of an end-effector-based rehabilitation robot is proposed. The controller is developed for a 2 degree-of-freedom upper extremity stroke rehabilitation robot, and compared to a feedback linearization approach that uses the standard optimal impedance derived from covariance propagation equations. The new method will assign optimal impedance gains at each configuration of the robot while performing a rehabilitation task. The proposed controller is a linear quadratic regulator mapped from the operational space to the joint space. Parameters of the two controllers have been tuned using a unified biomechatronic model of the human and robot. The performances of the controllers were compared while operating the robot under four conditions of human movements (impaired, healthy, delayed, and time-advanced) along a reference trajectory, both in simulations and experiments. Despite the idealized and approximate nature of the human-robot model, the proposed controller worked well in experiments. Simulation and experimental results with the two controllers showed that, compared to the standard optimal controller, the rehabilitation system with the proposed optimal controller is assisting more in the active-assist therapy while resisting in active-constrained case. Furthermore, in passive therapy, the proposed optimal controller maintains the position error and interaction forces in safer regions. This is the result of updating the impedance in the operational space using a linear time-variant impedance model.