Showing papers on "Feedback linearization published in 2022"

Disturbance Observer-Based Feedback Linearization Control for a Quadruple-Tank Liquid Level System

Abstract: A novel input/output feedback linearization control method by utilizing nonlinear disturbance observer (NDOB) is proposed for a quadruple-tank liquid level (QTLL) system in this paper. Firstly, the mathematical model of QTLL system is established by using Bernoulli's law and mass conservation. Secondly, in view of the nonlinear and coupling characteristics of the QTLL system, a input/output feedback linearization controller is designed. Then, a NDOB is proposed to estimate disturbances and applied to compensation control. Finally, simulation and experimental results show that the proposed strategy has better control performances than PID control and the disturbance observer-based sliding mode control (DOBSMC).

Event-Triggered Model-Free Adaptive Iterative Learning Control for a Class of Nonlinear Systems Over Fading Channels

Abstract: This article investigates the problem of event-triggered model-free adaptive iterative learning control (MFAILC) for a class of nonlinear systems over fading channels. The fading phenomenon existing in output channels is modeled as an independent Gaussian distribution with mathematical expectation and variance. An event-triggered condition along both iteration domain and time domain is constructed in order to save the communication resources in the iteration. The considered nonlinear system is converted into an equivalent linearization model and then the event-triggered MFAILC independent of the system model is constructed with the faded outputs. Rigorous analysis and convergence proof are developed to verify the ultimately boundedness of the tracking error by using the Lyapunov function. Finally, the effectiveness of the presented algorithm is demonstrated with a numerical example and a velocity tracking control example of wheeled mobile robots (WMRs).

Dynamic Control of Soft Robotic Arm: A Simulation Study

Abstract: In this article, the control problem of one segment pneumatically actuated soft robotic arm is investigated in detail. To date, extensive prior work has been done in soft robotics kinematics and dynamics modeling. Proper controller designs can complement the modeling work since they are able to compensate the effects that have not been considered in the modeling, such as the model uncertainties, system parameter identification error, hysteresis, external forces, disturbances, etc. In this letter, we explored different control approaches (kinematic control, PD+feedback linearization, passivity control, adaptive passivity control) and summarized the advantages and disadvantages of each controller. We further investigated the robot control problem in the practical scenarios when the sensor noise exists, actuator velocity measurement is not available, the hysteresis effect is non-neglectable, as well as the existence of external force. Our simulation results indicated that the adaptive passivity control with sigma modification terms, along with a high-gain observer presents a better performance in comparison with other approaches. Although this paper mainly presented the simulation results of various controllers, the work here will pave the way for practical implementation of soft robot control.

A Trajectory-Based Approach to Discrete-Time Flatness

Abstract: For discrete-time systems, flatness is usually defined by replacing the time-derivatives of the well-known continuous-time definition by forward-shifts. With this definition, the class of flat systems corresponds exactly to the class of systems which can be linearized by a discrete-time endogenous dynamic feedback as it is proposed in the literature. Recently, verifiable necessary and sufficient differential-geometric conditions for this property have been derived. In the present contribution, we make an attempt to take into account also backward-shifts. This extended approach is motivated by the one-to-one correspondence of solutions of flat systems to solutions of a trivial system as it is known from the continuous-time case. If we transfer this idea to the discrete-time case, this leads to an approach which also allows backward-shifts. To distinguish the classical definition with forward-shifts and the approach of this letter, we refer to the former as forward-flatness. We show that flat systems (in the extended sense with backward-shifts) still share many beneficial properties of forward-flat systems. In particular, they still are reachable/controllable, allow a straightforward planning of trajectories and can be linearized by a certain subclass of dynamic feedbacks.

Data-Driven Robust Iterative Learning Consensus Tracking Control for MIMO Multiagent Systems Under Fixed and Iteration-Switching Topologies

Abstract: In the study, a MIMO model-free-adaptive-iterative-learning-control-based (MFAILC-based) consensus tracking scheme for multiagent systems (MASs) has been proposed. The dynamics of agents are heterogeneous and unknown. And the compact form dynamic linearization (CFDL) technique is utilized to describe the unknown nonlinear dynamics of agents along iteration axis. Then, the MIMO MFAILC-based consensus tracking algorithm is proposed for MASs under fixed topology. From the proof, we can obtain that the consensus tracking error can converge to zero along iteration axis asymptotically. Next, the MFAILC-based consensus tracking algorithm is extended to controlling the MASs under iteration-switching topologies and the MASs with external disturbances, respectively. Compared with prior work, the main features of this article are the MFAILC-based consensus strategy can be utilized for MIMO MASs, and the framework of robust MFAILC is built for MIMO MASs with external disturbances. Finally, three simulations are given to verify the effectiveness of the consensus strategy for MASs under fixed and switching topology and MASs with external disturbances, respectively.

Privacy-Preserving Sliding Mode Control for Voltage Restoration of AC Microgrids Based on Output Mask Approach

Abstract: Although privacy-preserving is often considered in energy management and energy scheduling of microgrids (MGs), to the best of authors’ knowledge, there are almost no literatures on distributed secondary control of MGs with privacy-preserving. To fill this gap, this article investigates the privacy-preserving problem for voltage restoration of an ac MG. First, the model of the MG is transformed into a linear multiagent system model by feedback linearization. Furthermore, output mask approach, which avoids divulging the initial condition by inserting a dynamic mask on the exchanged state information, is adopted to make the distributed generator agents exactly converge to the reference value rather than the value with a preset certain convergence error by differential private. Meanwhile, the sliding mode control scheme with simple structure is adopted to accelerate the convergence speed of the masked system. However, it is difficult to design the controller directly because of the strong nonlinearity brought by the mask function. To solve this problem, we first implement the controller for the original system, and then extend it to the masked system. After that, we carry out the consensus analysis of the controlled masked system. Finally, the effectiveness of the proposed control scheme is validated in the MATLAB/Simulink environment.

Position Feedback Control of Lagrangian Robotic Systems via an Affine PD-Based Control Law. Part 1: Design of LMI Conditions

Abstract: Among the appropriate methods to describe the morphology of a robotic system, we note the development of a nonlinear dynamic model defined by the equations of the robot’s motion. Thus, the control design method can be based on the linearization of the nonlinear model. Therefore, in this work, we rely on the difference between the nonlinear model of Lagrangian robotic systems and the approximated linear dynamics to obtain a dynamical model that satisfies a certain Lipschitz condition. Thus, we introduce an affine PD-based control law in the obtained dynamic model to develop by three methods the stability conditions using the Schur complement, the Young inequality and the S-procedure lemma. These conditions are described by Linear Matrix Inequalities (LMIs). Finally, we present some results by adopting, as an illustrative example, the manipulator robot with two degrees of freedom, as a Lagrangian robotic system.

Singular Zone in Quadrotor Yaw–Position Feedback Linearization

Abstract: Feedback linearization-based controllers are widely exploited in stabilizing a tilt rotor (eight or twelve inputs); each degree of freedom (six degrees of freedom in total) is manipulated individually to track the desired trajectory, since no singular decoupling matrix is introduced while applying this method. The conventional quadrotor (four inputs), on the other hand, is an under-actuated MIMO system that can directly track four independent degrees of freedom at most. Common selections of these outputs can be yaw–position and attitude–altitude. It is reported that no singularity is found in the decoupling matrix while applying feedback linearization in the yaw–position-tracking problem. However, in this research, we argue the existence of the ignored singular zone within the range of interest, which can cause the failure in the controller design. This paper visualizes this noninvertible area and details the process of deduction for the first time. An attempt (switch controller) to avert the singular problem is later discussed with the verification by simulation in Simulink and MATLAB. All the results are sketched in the roll–pitch diagram.

Nonlinear Model Predictive Control Using Feedback Linearization for a Pressurized Water Nuclear Power Plant

Abstract: The present work aims to introduce a nonlinear control scheme that combines intelligent feedback linearization (FBL) and a model predictive control (MPC) for a pressurized water reactor (PWR). The nonlinear plant model that is considered in this study is described by the first-principles approach, and it consists of 38 state variables. First, system identification using a dynamic neural network (DNN) structure is performed to obtain a standard affine nonlinear system. The quasi-Newton algorithm is employed to find the best DNN model. Then, an FBL is formulated to address the nonlinearity of the DNN model. An MPC controller is developed based on the FBL system to improve the system performance. The designed controller is compared with a linear MPC controller that is based on state-space models to evaluate the performance of the proposed controller. The proposed approach improves the load-following operation and offers better disturbance rejection capability than the conventional MPC. In addition, numerical measures are employed to compare and analyze the performances of the two control strategies.

A Linearization of Centroidal Dynamics for the Model-Predictive Control of Quadruped Robots

Abstract: Centroidal dynamics, which describes the overall linear and angular motion of a robot, is often used in locomotion generation and control of legged robots. However, the equation of centroidal dynamics contains nonlinear terms mainly caused by the robot's angular motion and needs to be linearized for deriving a linear model-predictive motion controller. This paper proposes a new linearization of the robot's centroidal dynamics. By expressing the angular motion with exponential coordinates, more linear terms are identified and retained than in the existing methods to reduce the loss from the model linearization. As a consequence, a model-predictive control (MPC) algorithm is derived and shows a good performance in tracking angular motions on a quadruped robot.

Sampled-Data Stabilization With Control Lyapunov Functions via Quadratically Constrained Quadratic Programs

Abstract: Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap between design with continuous time models and the discrete time sampled implementation of the resulting controllers, often leading to poor performance on hardware platforms. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CLF-based controllers, specified as quadratically constrained quadratic programs (QCQPs). Assuming feedback linearizability and stable zero-dynamics of a system’s continuous time model, we derive practical stability guarantees for the resulting sampled-data system. We demonstrate improved performance of the proposed approach over continuous time counterparts in simulation.

Data-Driven Adaptive Control: An Incremental Triangular Dynamic Linearization Approach

Abstract: This brief investigates the data-driven control problem for a class of nonlinear systems. An incremental triangular dynamic linearization (ITDL) model is presented to equivalently describe these systems, and it contains three parameters including a single time-varying parameter, all of which have clear physical meanings. The ITDL model has obvious advantages compared with the existing partial form dynamic linearization (PFDL) model, although it is a special case of the PFDL model in form. An online estimation algorithm is designed for the single time-varying parameter, and then an adaptive control law is designed. The convergence and stability of the closed-loop system are analyzed, and the corresponding explicit conditions are derived. Finally, a comparative simulation study is conducted to illustrate the effectiveness of the proposed method.

Nonlinear Estimation and Control of Bending Soft Pneumatic Actuators Using Feedback Linearization and UKF

Abstract: In this article, we combine nonlinear estimation and control methods for precise bending angle control in soft pneumatic actuators driven by a pressure source and single low-cost on/off solenoid valve. First, a complete model for the soft actuator is derived, which includes both the motion and pressure dynamics. An unscented Kalman filter (UKF) is used to estimate the velocity state and filter noisy measurements from a pressure sensor and an embedded resistive flex sensor. Then, a feedback linearization approach is used with pole placement and linear quadratic regulator (LQR) controllers for bending angle control. To compensate for model uncertainties and improve reference tracking, integral action is incorporated to both controllers. The closed-loop performance of the nonlinear estimation and control approach is experimentally evaluated with a soft pneumatic network actuator. The simulation and experimental results show that the UKF provides accurate state estimation from noisy sensor measurements. The results demonstrate the effectiveness and robustness of the proposed observer-based nonlinear controllers for bending angle trajectory tracking.

Decoupling Control of Cascaded Power Electronic Transformer Based on Feedback Exact Linearization

Abstract: This article addresses the decoupling control design for the cascaded power electronic transformer (PET) in input-series–output-parallel connection. Due to the coupling and interaction between the submodules and between substages, in essence it is a complex nonlinear system. A nonlinear control strategy based on feedback exact linearization (FEL) is developed to decouple all the control objectives so as to realize the dc-link and output voltages fast stabilizing and the submodule balancing without coupling and interactions. Based on the separation of the ac current time-scale and dc voltage time-scale, the FEL control law is derived, and the specific tuning process of control parameters is given for desired control bandwidths. Taken the dynamic influences of the current-loop, filter, and delay into account, further analyses are made and compared with a dual active bridge (DAB) balancing control-based strategy to show the improvement on decoupling effect and dynamic performance of the proposed control. Finally, the simulation and experimental results verify the theoretical analysis, which exhibit better dynamic features and minimal coupling effect under the condition of bidirectional power changes and parameter inconsistency and uncertainty.

Control of a DC motor using feedback linearization and gray wolf optimization algorithm

Abstract: The aim of this study is to investigate nonlinear DC motor behavior and to control velocity as output variable. The linear model is designed, but as it is experimentally verified that it does not describe the system well enough it is replaced by the nonlinear one. System’s model has been obtained taking into account Coulomb and viscous friction in the firmly nonlinear environment. In the frame of the paper the dynamical analysis of the nonlinear feedback linearizing control is carried out. Furthermore, a metaheuristic optimization algorithm is set up for finding the coefficient of the proportional-integral feedback linearizing controller. For this purpose Gray wolf optimization technique is used. Moreover, after the introduction of the control law, analysis of the pole placement and stability of the system is establish. Optimized nonlinear control signal has been applied to the real object with simulated white noise and step signal as disturbances. Finally, for several desired output signals, responses with and without disruption are compared to illustrate the approach proposed in the paper. Experimental results obtained on the given system are provided and they verify nonlinear control robustness.

Nonlinear Subsynchronous Oscillation Damping Controller for Direct-Drive Wind Farms With VSC-HVDC Systems

Abstract: Due to the subsynchronous interaction between the grid-side converter (GSC) of wind farms and the rectifier (REC) of voltage source converter-based high-voltage direct current (VSC-HVDC) transmission system, subsynchronous oscillations (SSOs) may occur in direct-drive wind farms with VSC-HVDC systems. Considering the nonlinearities and uncertainties of the system, a nonlinear SSO mitigation strategy is proposed in this article based on the feedback linearization theory and sliding mode control (SMC). The feedback linearization theory is used to eliminate the nonlinearities, and the SMC is adopted to improve the robustness against uncertainties and disturbances. The proposed feedback linearization SMC (FLSMC) takes the advantages of feedback linearization control (FLC) and SMC. The FLC transforms the nonlinear forms of the GSC and REC into the linear forms through the coordinate transformation and feedback. Considering that the FLC is sensitive to parameter uncertainties and external disturbances, the SMC is combined with the FLC to improve the system robustness. An eigenvalue analysis and time-domain simulations are carried out, which demonstrates that the FLC outperforms over the traditional proportional–integral control for the SSO mitigation and decoupling. Meanwhile, the FLSMC shows better robustness against parameter uncertainties and external disturbances over the FLC and traditional damping control.

Prescribed performance model-free adaptive sliding mode control of a shape memory alloy actuated system

Abstract: This paper concentrates on a simple and robust control method for the discrete time nonlinear systems to fulfill the requirement of predefined accuracy. A sliding mode control method is designed by introducing equivalent dynamic linearization technique according to the input/output (I/O) information merely. A square-root type error transformation method is presented for the tracking error to be restricted within a preassigned zone. The performance of presented control method is demonstrated through experiments on a nonlinear system. Experiment results show that the presented control method has a superior tracking accuracy compared with PID controller and model-free adaptive control (MFAC).

Determination of Conditions on Feedback Gains for the Position Control of Robotic Systems Under an Affine PD-Based Control Law

Abstract: Among the most important tasks, in order to control the robotic system to achieve some desired goal, is the design of the controller to be applied as well as the right choice of gains to be used. Despite the presence of several effective controllers that can be used, it remains the judicious choice of the adequate values of the feedback gains that will define the control and then the stabilization of the robot system from some initial configuration towards a desired one. This work mainly proposes some conditions that can help to make the right choice of the feedback gains to solve the problem of position control of robotic systems via an affine PD-based control law. Such control law is designed through the linearization of the nonlinear dynamics of the robotic system around the desired state. The methodology used is mainly based on the linear matrix inequality (LMI) techniques and lies on determining the conditions on the feedback gains ensuring the stability of the linear dynamic model and the nonlinear dynamics under the adopted controller. An illustrative example of a two-degree-of-freedom manipulator robot is considered to illustrate the different adopted determination methods of conditions on the feedback gains.

Controller-Dynamic-Linearization-Based Data-Driven ILC for Nonlinear Discrete-Time Systems With RBFNN

Abstract: In this article a novel data-driven iterative learning control (ILC) approach is proposed for unknown nonlinear nonaffine repetitive discrete-time systems, where the dynamic linearization (DL) technique in the iteration domain is applied both on the controlled nonlinear system and on the unknown nonlinear ideal learning controller. Through updating the weight matrix of a radial basis function neural network (RBFNN), the learning control gain of the obtained iterative learning law is automatically tuned in reaching the optimal learning controller using only the input-output data of the nonlinear system. The uniformly ultimately bounded property is established for the tracking error of the proposed ILC scheme in the iteration domain through rigorous theoretical analysis. The effectiveness and applicability are validated by a simulation example and further demonstrated by simulation on a high-speed train model.

Adaptive actuator fault-tolerant control for non-minimum phase air-breathing hypersonic vehicle model

Abstract: In this paper, the tracking control problem of non-minimum phase flexible air-breathing hypersonic vehicles (AHSV) is investigated subject to actuator fault, external disturbances and parameters uncertainties. The study is began with a series of control-oriented manipulations: first, the input-output dynamics are derived by using feedback linearization method and the internal dynamics of AHSV are constructed; then, the zero dynamics stability analysis is conducted to verify the non-minimum phase characteristic of AHSV. In order to realize output tracking of the non-minimum phase system with sufficient accuracy, an adaptive fault tolerant controller (FTC) is proposed based on an output-redefinition making the zero-dynamics with respect to the new output stable. Additionally, robust adaptive laws are utilized for the estimation of unknown parameters and actuator failure compensation of the AHSV model. Furthermore, the stability of the closed-loop system is analyzed based on the Lyapunov stability theory. At last, the numerical simulation results are provided to demonstrate the effective tracking performance of the proposed FTC scheme.

A two‐loop group formation tracking control scheme for networked tri‐rotor UAVs using an ARE‐based approach

Abstract: Cooperative control of networked unmanned aerial vehicles (UAVs) has received significant research interest over the last decade due to its potential applications in military security and surveillance, search and rescue, planetary exploration, precision agriculture, and so on. Many of these practical activities can be formulated as a group formation tracking problem with multiple targets to track. This paper aims to address such problems via designing a cooperative control scheme for networked tri‐rotor UAVs connected with directed graph topology. The proposed methodology consists of a two‐loop control scheme—the inner loop applies a robust feedback linearization technique to linearize the coupled, nonlinear dynamics of the tri‐rotor UAVs; while the outer loop facilitates an ARE‐based cooperative group formation tracking scheme. Tri‐rotor UAVs are considered in this paper instead of quad‐rotor UAVs, which are more common in drone applications, to conquer a major limitation of the quad‐rotor UAVs that it cannot alter its attitude independently while hovering at a particular height. A rigorous theoretical proof is given to establish the two‐loop control scheme exploiting the Lyapunov stability approach and algebraic Riccati equation (ARE)‐based optimal control policy. An in‐depth case study on a multitarget surveillance mission has been performed in this paper using a virtual reality software simulation platform to demonstrate the usefulness and efficacy of the proposed scheme.

Efficient feedback linearization control for an IPMSM of EVs based on improved firefly algorithm.

Abstract: The conventional direct torque control (DTC) has high torque and stator flux fluctuation that causes the stator current distortion. This paper presents an efficient control method based on the feedback-linearization direct torque control (FL-DTC) method for an interior permanent magnet synchronous motor (IPMSM) drive by using an improved firefly algorithm. The proposed approach can greatly restrain the poor performance of torque and stator flux. Thus, it is suitable for IPMSM drives in electric vehicles. First, a decoupled linear model is derived to implement the proposed efficient feedback linearization control for the IPMSM. Two phase voltages in d-q axes and two additional control inputs take shape into an isomorphism mapping with the concept of orthogonal transformation. The torque generation is related to the additional control. Second, the Hamiltonian efficient control theory combined with an improved firefly algorithm is applied to obtain an analytical solution. An efficient linearization controller is designed with a cost function considering the maximum voltage of the inverter. Finally, simulation and experiment are carried out to compare the performance of the proposed efficient FL-DTC with the improved firefly algorithm and the conventional direct torque control. The results show that the proposed control method can reduce the torque and flux ripples at a steady state and maintains a good dynamic response with the variations of speed and torque.

Coordinated Time-Varying Low Gain Feedback Control of High-Speed Trains Under a Delayed Communication Network

Abstract: The coordinated control problem for a multiple high-speed train (HST) system subject to unknown communication delays is systematically investigated in this paper. Taking into consideration the inertial lag of the servo motor, a third-order nonlinear control model is constructed to capture the dynamics of a train in real-world operations. By virtue of the backstepping linearization technique, the coordinated control of trains is formulated as a stabilization problem for a linear multiple-input multiple-output system with an unknown input delay. Distributed control laws with a time-varying low gain parameter are designed, besides solving the stabilization problem, to guarantee a fast convergency rate during the train status adjustment process. Numerical examples are provided to illustrate that the time-varying low gain parameter design achieves better control performance compared with the traditional constant low gain feedback design in terms of the convergency rate and the system overshot, and that the proposed control method is effective in train tracking distance adjustment.