Partial Feedback Linearization Research Articles

On the analysis and control of a bipedal legged locomotion model via partial feedback linearization

In this study, we introduce a new model for bipedal locomotion that enhances the classical spring-loaded inverted pendulum (SLIP) model. Our proposed model incorporates a damping term in the leg spring, a linear actuator serially interconnected to the leg, and a rotary actuator affixed to the hip. The distinct feature of this new model is its ability to overcome the non-integrability challenge inherent in the conventional SLIP models through the application of partial feedback linearization. By leveraging these actuators, our model enhances the stability and robustness of the locomotion mechanism, particularly when navigating across varied terrain profiles. To validate the effectiveness and practicality of this model, we conducted detailed simulation studies, benchmarking its performance against other recent models outlined in the literature. Our findings suggest that the redundancy in actuation introduced by our model significantly facilitates both open-loop and closed-loop walking gait, showcasing promising potential for the future of bipedal locomotion, especially for bio-inspired robotics applications in outdoor and rough terrains.

Dynamics modeling and path following controller of tractor-trailer-wheeled robots considering wheels slip

To improve the payload capacity and maneuverability of a Differentially-Driven Wheeled Robot (DDWR), a wheeled vehicle, which is called trailer, is connected to the DDWR. In all of the previous studies of DDWRs with a trailer, the robot wheels are subject to pure rolling constraints. However, when these multibody systems move with high velocities/accelerations, transfer a heavy payload, or travel on a slippery surface, they experience slipping and/or skidding. In the present study, a Tractor-Trailer Wheeled Mobile Robot (TTWMR) is modeled whose wheels may slip in lateral and longitudinal directions. To this end, Lagrange formalism is employed along with the LuGre friction model to derive dynamics of the considered multibody system. Next, the problem of path following for the trailer is addressed. Toward this goal, the partial feedback linearization technique will be utilized. The obtained simulation results prove the superiority of the performance of the suggested method in comparison to the previous studies. Additionally, the response of the system in the presence of the external disturbances and uncertainties in system parameters will be examined.

СИНТЕЗ ДВОКОНТУРНИХ СИСТЕМ КЕРУВАННЯ НАПРУГОЮ РЕВЕРСИВНИХ ПІДВИЩУВАЛЬНИХ DC-DC ПЕРЕТВОРЮВАЧІВ

The paper deals with the design and analysis of cascaded DC-link voltage control systems for bidirectional buck-boost DC-DC converters. Its model is significantly nonlinear and non-minimum-phase, which makes it impossible to achieve high dynamic quality indicators using standard methods of linear control theory. A new method for design and analysis of DC-DC converters control systems based on partial feedback linearization and the subsequent application of linear PI voltage and current controllers is proposed. It provides that the resulting model is composed of the feedback inter-connected linear asymptotically stable subsystems with bilinear properties. The resulting system is linearized in the vicinity of the trajectories corresponding to the power balance equation. Such form allows to apply the theory of cas-caded systems with two time-scale separation of the control loops dynamics. It not only ensures system stability but also allows to specify the process quality indicators using methods available to control engineers. References 14, figures 9.

Low voltage ride-through augmentation of DFIG wind turbines by simultaneous control of back-to-back converter using partial feedback linearization technique

This paper proposes a nonlinear controller for doubly fed induction generator (DFIG) wind turbines using partial feedback linearization (PFL) technique. The controller generates switching signals for driving both the rotor side converter and grid side converter simultaneously enhancing the low voltage ride through (LVRT) capability over a wide range of operating conditions. The proposed PFL method has been implemented into a partially linearized form of a nonlinear system, where the transformed system has been made autonomous and reduced in order. All calculations in the proposed method except for the control laws have been carried out offline resulting in reduced design and implementation complexity, small computational burden, and offline control tuning with fast tracking performances. The step-by-step approach of control design and implementation includes system modeling and partial linearization, control law derivation, software implementation, and controller tuning. The effectiveness of the proposed controller has been evaluated through electromagnetic transient simulations. The simulations have demonstrated that the controller has successfully augmented the LVRT capability of DFIG wind turbines and has remained robust against diverse wind conditions and voltage sags.

New fixed-time synchronization results for discontinuous dynamic networks: A novel two-stage analysis approach

This paper concerns the issue of fixed-time synchronization (FXTS) for complex networks composed of dynamical nodes with discontinuous dynamics, abbreviated as discontinuous dynamic networks, under the concept of Filippov solution. In terms of [Formula: see text]-norm and [Formula: see text]-norm, two types of simple control schemes without the linear feedback part are, respectively, designed to compel the considered discontinuous dynamic network to fixed-timely synchronize with a desired trajectory. By utilizing a novel two-stage analysis approach, some new FXTS criteria are derived. Compared with the existing research works, the established theoretical results not only are more relaxed, but also improve the estimation accuracy of synchronous settling time. Finally, the validity of the analytical results is verified via numerical simulations.

Robust output-feedback orbital stabilization for underactuated mechanical systems via high-order sliding modes

The manuscript deals with the robust orbital stabilization for a class of disturbed Euler–Lagrange systems with one degree of underactuation. The proposed strategy relies on the virtual holonomic constraints approach, using incomplete state measurements. First, a high-order sliding-mode extended observer estimates the state and the disturbances affecting the input channel. Then, proposing a new set of coordinates, the so-called virtual holonomic constraints, a robust output partial-feedback linearization approach takes the system into a double integrator with a particular zero dynamics. Thus, considering the general integral of motion of the zero dynamics, the orbital stabilization is reduced to stabilize a linear time-varying system. The resulting control law is a continuous signal. Therefore, the robustness to disturbances is addressed without the tarnishing effects of chattering. The closed-loop stability analysis is done using the Lyapunov theory. The feasibility of the method is illustrated experimentally in a cart-pendulum system.

A comparative study between sliding mode and fuzzy sliding mode control for pendubot

The pendubot is a classical highly non-linear system that has been widely used in many laboratories to demonstrate the responses of the system when applying control algorithms, to analyse dynamical equations, and to study the parameter identification algorithms. The objective of this paper is to design the controller to stabilize the pendubot at equilibrium points (TOP and MID) and to track the defined trajectory. Firstly, mathematical equations of the pendubot are derived by the Euler?Lagrange method. Thence, a genetic algorithm (GA) is employed to identify the parameters of the system based on the collected data of the output states of the system when applying impulse inputs. After that, sliding mode control (SMC) is designed to balance the system at the equilibrium points and track the defined trajectory. The chattering caused by SMC is reduced by fuzzy-sliding mode control (FSMC). The proposed FSMC method solves the problem induced by SMC by applying fuzzy logic. Additionally, the partial feedback linearisation (PFL) method is introduced to design the swing-up system. Finally, both simulation and experimental results are provided to show the effectiveness and robustness of the proposed methods.

Balancing and Tracking Control of Ballbot Mobile Robots Using a Novel Synchronization Controller Along With Online System Identification

Ballbots are omnidirectional self-balancing platforms that can be exploited in many applications to detect, track, or interact with objects or humans, such as a service robot. Ballbot will enable mobile robots to stand tall and move elegantly through busy environments. However, maintaining equilibrium through synchronization of motion between the ball and the body of a Ballbot is still an open research problem. This article presents a synchronization control (SC) design, with synchronization and coupling errors for Ballbots to stabilize the body and control ball transfer simultaneously. The proposed SC method is applied to the two 2-D planar models of a Ballbot robot. The dynamic model of the Ballbot is derived, and parameters are identified online using the intelligent particle swarm optimization method. The proposed controller is proven to guarantee asymptotic convergence to zero errors in tracking and synchronization. The stabilizing and transferring problems are investigated through several simulations and experiments by using an actual Ballbot platform. Moreover, the controller performance is compared with an augmented proportional derivative controller and a partial feedback linearization controller. The results and comparisons demonstrate a superior stabilization accuracy of the proposed SC method.

A new decentralized two-stage multi-objective control of secondary network driven hybrid microgrid under variable generation and load conditions

This paper proposes a new decentralized two-stage multi-objectives voltage control technique to ensure the operational stability of the hybrid MG over the variable renewable generations as well as to confirm its reliable operation against various industrial loads by minimizing the mismatch load terminal voltage. The effective operation of hybrid MG under the running of loads reclines on its dynamics which may become non-linear due to the utilization of additional inverter-oriented secondary network or electronics components in their evolution. Also, the efficacy of the secondary network-driven microgrid (SNM) is ascertained by taking the sustained transient response, however, its supremacy can be influenced by the sporadic features of renewable energy sources (RESs). This work introduces a new decentralized hybrid voltage control (DHVC) model to effectively drive the issues raised from the load’s operation and RESs. The proposed hybrid control technique integrates the linear and non-linear control scheme which works enabling a two-level control framework in MG terminal to confirm its enhanced operational stability and minimized unbalance voltage over the various operating conditions. The non-linear control framework of the proposed DHVC is made by utilizing the partial feedback linearization approach in generalized dynamics deriving from the DC–DC converters used with RESs and battery, while the linear control scheme uses a second-order damping (SOD) control framework to regulate the inverter used with load’s network. The controllability of the proposed DHVC is evaluated by measuring the response of the SNM in terms of operational stability and mismatch voltage minimization over the change of meteorological factors of the RESs and various industrial loads. Also, an external parametric uncertainty with the single-phase secondary network dynamics is studied to guarantee the robustness of the proposed DHVC. Additionally, a comparative study is studied to cover the augmented performance of the hybrid microgrid.

An Improved Distributed Nonlinear Observers for Leader-Following Consensus via Differential Geometry Approach

This article is concerned with the leader-following output consensus problem in the framework of distributed nonlinear observers. Instead of certain hypotheses on the leader system, a group of geometric conditions is put forward to develop a novel distributed observers strategy, thereby definitely improving the applicability of the existing results. To be more specific, the improved distributed observers can precisely handle consensus problems for some nonlinear leader systems, which are invalid for the traditional strategies with a certain assumption, such as elastic shaft single linkage manipulator (ESSLM) systems and most of the first-order nonlinear systems. We prove the sufficient conditions for the exponential stability of our distributed observers’ error dynamic by proposing two pioneered lemmas to show the relationship between the maximum eigenvalues of two matrices appearing in Lyapunov type matrices. Then, a partial feedback linearization method with zero dynamic proposed in differential geometry is employed to design the purely decentralized control law for the affine nonlinear multiagent system. With this advancement, the existing results can be regarded as a specific case owing to that the followers can be chosen as an arbitrary minimum phase affine smooth nonlinear system. At last, the novel distributed observers and the improved purely decentralized control law are applied in the distributed control framework to construct a closed-loop system. We also prove the stability of the closed-loop system to achieve leader-following consensus. Our method is illustrated by the ESSLM system and Van der Pol system as leaders.

Energy shaping nonlinear control of underactuated needle insertion

This work investigates the position control of an underactuated mechatronic system for straight needle insertions in soft tissues. The system consists of a pneumatic cylinder pushing a slender needle supported at the base and subject to external forces at the tip due to interactions with soft tissues. The system dynamics is described by a rigid-link underactuated model for controller design purposes. The main contribution of this work is a new energy shaping control law that: (i) does not rely on the analytical solution of partial differential equations, which is a major hurdle in energy shaping techniques, and does not require partial feedback linearization, which is known to be sensitive to model uncertainties; (ii) accounts for the work of the friction forces on the pneumatic cylinder and of the lateral forces acting on the needle tip, which are estimated adaptively with nonlinear observers. For comparison purposes, an alternative controller that employs feedback linearization is also presented. Simulations and experiments on silicone rubber phantoms using a needle with axial-symmetric tip indicate that the proposed controller can reduce the needle tip rotation and the corresponding deflection compared to a PID algorithm. In case of larger insertion forces, the controller can limit the insertion depth to prevent large needle deflections: this behavior can be influenced by acting on a specific tuning parameter, thus providing additional flexibility compared to previous implementations. Finally, the proposed solution is less sensitive to parameter uncertainties than the alternative controller.

A two‐level hybrid control strategy to augment transient stability and tracking accuracy of hybrid microgrid coupled with industrial loads

AbstractThe hybrid microgrid (HMG) is an arrangement for empowering the society by using the renewable energy sources (RESs) connected with common DC bus terminal. The effective operation of the HMG relies on the transient response of the DC bus as well as the stability of the system state that may change due to the stochastic behavior of RESs and industrial loads. This work is motivated to develop a two‐level decentralized control strategy consisting of a non‐linear and linear control scheme to augment the transient stability and tracking performance of an HMG. Firstly, a non‐linear partial feedback linearization control framework combined with a PI regulator (PFLC‐PI) is designed for the transient stability enhancement of the common bus. Secondly, a linear unified controller (UC) is developed to guarantee the constant load voltages over the industrial loads through the control of the load‐side inverter. The UC effectiveness is measured by varying the load parameters associated with single‐ and three‐phase load networks. The obtained results are then compared with the existing controllers to guarantee the augmented performance of proposed two‐level controller. Additionally, an external parametric uncertainty is intentionally added to the single‐phase load network dynamics and studied to ensure the robustness of the controller.

Robust Nonlinear Controller Design for DC–AC Converter in Grid-Connected Fuel Cell System

This article presents a robust nonlinear controller for distributed fuel cell in the three-phase grid-connected system. A partial feedback linearization scheme is applied to linearize the grid-connected fuel cell system. The mismatches between the actual system and the dynamical model are considered uncertainties. The noise decoupling capability of the feedback linearized control scheme is also demonstrated. A loop-shaping-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{H}_\infty$</tex-math></inline-formula> mixed-sensitivity controller is designed for the partially linearized plant of the grid-connected fuel cell system. Performance of the designed controller is investigated under power factor changes, three-phase short-circuit fault, parameter variation, and measurement noise in a hardware-in-loop simulation platform with OP 4510.

Backstepping control for a class of underactuated nonlinear mechanical systems with a novel coordinate transformation in the discrete-time setting

In this technical note, a combined discrete-time controller, consisting of a partial feedback linearization controller and a backstepping controller, is proposed to manage the stabilization for a class of underactuated nonlinear mechanical systems. The traditional backstepping control method is impracticable to directly apply it to underactuated systems since they are generally not in the lower triangular form. First, a feedback controller that partially linearizes the underactuated mechanical systems is derived to facilitate the backstepping controller design. In the design, discrete-time system dynamics obtained utilizing the Euler approximation are considered. Afterward, a novel coordinate transformation is introduced for a class of underactuated systems that transform the mathematical model of the partially linearized underactuated mechanical systems into the strict-feedback form. After these steps, the conventional backstepping approach is structured in discrete-time setting. The stability of the closed-loop system dynamics with the proposed combined discrete-time controller is shown utilizing Lyapunov theory. Several computer-based simulations are executed to depict the performance and the applicability of the proposed method on the Cart–Pole system and the Inertia Wheel Pendulum. Moreover, the effectiveness of the proposed nonlinear controller is verified by numerical simulation results in comparison with a discrete-time chattering-free sliding-mode controller.

On-Line Learning for Planning and Control of Underactuated Robots With Uncertain Dynamics

We present an iterative approach for planning and controlling motions of underactuated robots with uncertain dynamics. At its core, there is a learning process which estimates the perturbations induced by the model uncertainty on the active and passive degrees of freedom. The generic iteration of the algorithm makes use of the learned data in both the planning phase, which is based on optimization, and the control phase, where partial feedback linearization of the active dofs is performed on the model updated on-line. The performance of the proposed approach is shown by comparative simulations and experiments on a Pendubot executing various types of swing-up maneuvers. Very few iterations are typically needed to generate dynamically feasible trajectories and the tracking control that guarantees their accurate execution, even in the presence of large model uncertainties.

Frequency-Modulation Input-Shaping Strategy for Double-Pendulum Overhead Cranes Undergoing Simultaneous Hoist and Travel Maneuvers

Large payloads hoisted by overhead cranes exhibit the same behavior as that of a double pendulum. Changes in the hoisting cable length during payload transfer maneuvers gives rise to time-dependent system frequencies rendering input-shaped commands ineffective. In this paper, a frequency-modulation input-shaping strategy that enables simultaneous hoist and travel maneuvers using single-mode input-shaping is presented. This strategy utilizes model-based feedback and partial feedback linearization techniques. Simulations are carried out using arbitrary travel and hoist commands combined with the common single-mode zero-vibration (ZV) and zero-vibration-derivative (ZVD) input-shapers. Sensitivity analysis reveals robust performance in the presence of high system uncertainties.

PID passivity-based control laws for joint position regulation of a self-balancing robot

The problem of joint position regulation of a self-balancing robot moving on a slope via a PID passivity-based controller is addressed in the present paper. It is assumed that the angle of the slope is known, and the robot can move up or down. The contributions are the original presentation of the design and practical implementation for comparison purposes of two PID passivity-based control laws for position regulation of a self-balancing robot, and the original proposal of the respective asymptotic stability analysis. Experimental results illustrate the performance of the proposed controllers in a self-balancing robot, which were evaluated together with a different passivity-based controller, reported in the control literature, and a linear control law to test its superiority. Finally, the experiments were extended to deal with disturbance rejection, where one of the PID passivity-based control laws, the one that does not use partial feedback linearization, showed to be better than the other three controllers used for comparison.

Evaluation of Linearization Methods for Control of the Pendubot

The aim of this paper is to test the usefulness of a new approach based on partial feedback linearization to control the Pendubot. The control problem stated in the article is to stabilize the Pendubot in the upright position. In particular, properties of the closed-loop system and the zero dynamics are investigated and illustrated by results of simulations. Next, the performance of a hybrid-like controller in the case of input saturation is evaluated by conduction extensive simulation trails. The experimental results suggest that the considered control methodology can be successfully applied for a real system.

Nonlinear Control Strategies for an Autonomous Wing-In-Ground-Effect Vehicle.

Autonomous vehicles are nowadays one of the most important technologies that will be incorporated to every day life in the next few years. One of the most promising kind of vehicles in terms of efficiency and sustainability are those known as Wing-in-Ground crafts, or WIG crafts, a family of vehicles that seize the proximity of ground to achieve a flight with low drag and high lift. However, this kind of crafts lacks of a sound theory of flight that can lead to robust control solutions that guarantees safe autonomous operation in all the cruising phases.In this paper we address the problem of controlling a WIG craft in different scenarios and using different control strategies in order to compare their performance. The tested scenarios include obstacle avoidance by fly over and recovering from a random disturbance in vehicle attitude. MPC (Model Predictive Control) is tested on the complete nonlinear model, while PID, used as baseline controller, LQR (Linear Quadratic Regulator) and adaptive LQR are tested on top of a partial feedback linearization. Results show that LQR has got the best overall performance, although it is seen that different design specifications could lead to the selection of one controller or another.

Torsional Vibrations Control of Double‐Ended Driving and Dual‐Excited Turbo‐Generator Shafts Based on Multi‐Index Nonlinear Control

The problem of shafting torsional vibrations has been increasingly emerging due to the increasing capacity of turbo‐generator and the complexity of power grid. Therefore, how to reduce the torsional vibration of the turbo‐generator shaft and improve the stability of the power system has become the focus of our research. First, in order to solve the problem and alleviate the torsional vibrations of turbo‐generator shafts, this paper proposed a new shafting structure model of Double‐ended Driving and Dual‐Excited Turbo‐Generator set (DDDETG). A static excitation mode is used for the excitation of the DDDETG and the mechanical power is supplied symmetrically and synchronously from both ends of the generator rotor. Then, in order to improve the output characteristic of the generator and further suppress the torsional vibrations of the turbo‐generator shafts, combined with the nonlinear control design method of partial feedback linearization, a Multi‐Index Nonlinear Coordinated Control (MINCC) strategy for the double‐ended driving and dual‐excited turbo‐generator is proposed to ensure good dynamic and static state performances of each state in the system. Finally, the simulation results on a single‐machine infinite bus system demonstrate the effectiveness of the proposed control strategy. In addition, this paper compares the performance of DDDETG and the traditional Single‐ended Drive and Single‐Excited Turbo Generator (SDSETG), the simulation results show that the restraint effect of the DDDETG structure on shafting torsional vibrations is more obvious under the proposed control strategy. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.