Partial Feedback Linearization Control Research Articles

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 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.

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.

Variable-Gain Super-Twisting Sliding Mode Damping Control of Series-Compensated DFIG-Based Wind Power System for SSCI Mitigation

Subsynchronous oscillation, caused by the interaction between the rotor side converter (RSC) control of the doubly fed induction generator (DFIG) and series-compensated transmission line, is an alleged subsynchronous control interaction (SSCI). SSCI can cause DFIGs to go offline and crowbar circuit breakdown, and then deteriorate power system stability. This paper proposes a novel adaptive super-twisting sliding mode SSCI mitigation method for series-compensated DFIG-based wind power systems. Rotor currents were constrained to track the reference values which are determined by maximum power point tracking (MPPT) and reactive power demand. Super-twisting control laws were designed to generate RSC control signals. True adaptive and non-overestimated control gains were conceived with the aid of barrier function, without need of upper bound of uncertainty derivatives. Stability proof of the studied closed-loop power system was demonstrated in detail with the help of the Lyapunov method. Time-domain simulation for 100 MW aggregated DFIG wind farm was executed on MATLAB/Simulink platform. Some comparative simulation results with conventional PI control, partial feedback linearization control, and first-order sliding mode were also obtained, which verify the validity, robustness, and superiority of the proposed control strategy.

Design and Implementation of Partial Feedback Linearization Controller for Unified Power Flow Controller

Electric power transmission systems can be effectively controlled with FACTS devices. Unified Power Flow Controller (UPFC) is a multi-functional FACTS device that can control different parameters of the power system under dynamic conditions. UPFC consists of two Voltage Source Converters (VSCs), which are connected back to back to a common DC link. In this paper, a non linear state-space model of UPFC is developed by including VSC output voltage functions, the effect of source impedance and energy variation in the passive elements. The non linear model of the UPFC is controlled with a non linear controller. The paper also proposes a non linear controller Partial Feedback Linearization (PFBLC) for UPFC. PFBLC modifies the control input such that UPFC is able to behave linearly under all non linear dynamics occurs in the system. The proposed system is designed, analyzed and tested in an interconnected power system network. The hardware implementation is also carried out in a five bus test bench. It was observed that the UPFC shows satisfactory performance in all operating conditions.

Design and Experimental Validation of a 3-DOF Underactuated Pendulum-Like Robot

This article presents the design and the experimental validation of a novel 3-degree-of-freedom (DOF) pendulum-like cable-driven robot capable of executing point-to-point motions by leveraging partial feedback linearization control and on-line trajectory planning based on adaptive frequency oscillators (AFOs). Unlike most cable-suspended parallel robots, which rely on at least n actuated cables to control n DOF, the proposed robot is capable of performing 3-DOF point-to-point motions, from a starting pose to a goal one within its dynamic workspace, by means of two actuators only. Feedback linearization allows the dynamics of the variable-length pendulum to be decoupled from the orientation of the end effector, enabling the device to use parametric excitation to control the oscillations of the variable-length pendulum, akin to a playground swing. A pool of AFOs is introduced to enable smooth, lag free on-line estimations of the current phase of the pendulum oscillation to inform the on-line planner and the parametric excitation controller. Experimental results demonstrate feasibility of the proposed design and control approach.

Linear active disturbance rejection control for pressurized water reactor power based on partial feedback linearization

Due to nonlinearity and complexity of pressurized water reactor (PWR), the simple and practical controller for PWR is relatively difficult to design. This study discusses a novel compound control scheme that combines the advantages of partial feedback linearization (PFL) and linear active disturbance rejection control (LADRC). First, a second-order linearization model is derived via PFL. Then, LADRC is designed on the basis of the linearization model. Linear extended state observer is developed to estimate ‘generalized disturbance’, which includes model uncertainty and external disturbance. Finally, the controller parameters are optimized by tuning bandwidth. Simulation results show that the combined controller has faster response, fewer overshoots, and better disturbance rejection ability than PID, whereas it guarantees robustness under various reactor operating conditions.

Experimental verification of a hybrid control scheme with chaotic whale optimization algorithm for nonlinear gantry crane: A comparative study

This paper proposes an experimental verification of a hybrid partial feedback linearization (PFL) and deadbeat (DB) control scheme as in Hamdy et al. (2018) with chaotic whale optimization algorithm (CWOA) for a nonlinear gantry crane (GC) system. The PFL linearizes the nonlinear model to end up with a linear closed-loop system. The DB controller is utilized for the desirable accelerated response without any oscillation or undesirable effects on the internal dynamics stability. The CWOA is used to tune the controller parameters. A sliding-mode observer (SMO) is utilized to estimate the unmeasured states. Using this hybrid scheme, a better payload sway elimination can be obtained. Finally, the experimental results are presented to illustrate the efficiency and the effectiveness of the proposed scheme with a comparative study.

A hybrid partial feedback linearization and deadbeat control scheme for a nonlinear gantry crane

This paper presents the design of a hybrid partial feedback linearization and deadbeat control scheme for a nonlinear gantry crane with friction to control its position and sway angle. The partial feedback linearization is used to linearize the nonlinear model and to stabilize its internal dynamics. In many crane applications, it's necessary to accelerate the system response. As a result, this will cause oscillation in the position as well as the sway angle. So, the deadbeat controller is added to get the desirable accelerated response without any oscillation or adverse effects on the internal dynamics stability. By using Lyapunov stability method, the proposed scheme is proved to be globally stable, with converging tracking errors to the desired performance. The simulation results are accomplished to evaluate the effectiveness of the proposed scheme and to demonstrate its reliability to control crane systems with comparative results.

Improved Bernstein Optimization Based Nonlinear Model Predictive Control Scheme for Power Systems

This paper presents a improved Bernstein global optimization algorithm based model predictive control (MPC) scheme for the nonlinear systems. A new improvement in the Bernstein algorithm is the introduction of a box pruning operator, which during a branch-and-bound search, discard portions of the solution search space that do not contain global solution, thereby speeding up the algorithm. The applicability of this MPC scheme is demonstrated with a simulation studies on a nonlinear single machine infinite bus power system over a wide range of operating conditions. The simulation results show improvement in the system damping and settling time compared with the classical power system stabilizer and partial feedback linearization control schemes.

Nonlinear Controller Design for Series-Compensated DFIG-Based Wind Farms to Mitigate Subsynchronous Control Interaction

This paper proposes a nonlinear controller to mitigate subsynchronous control interaction (SSCI) in series-compensated doubly fed induction generator (DFIG)-based wind farms. The controller is designed based on partial feedback linearization (PFL) and the proposed design approach involves scrutinizing the partial feedback linearizability of the system. The stability of the internal dynamics, which is not transformed into linear autonomous subsystems by PFL, is also analyzed in the process of deriving the control laws. The frequency scanning method is used to evaluate the performance of the proposed PFL controller, and the performance is compared to that of a finely tuned conventional proportional integral controller. A grid-connected series-compensated 100-MW DFIG-based offshore wind farm is used to demonstrate the performance of the proposed scheme through the identification and mitigation of subsynchronous resonance. An analysis of the power system reveals that the resistance is negative across the entire subsynchronous frequency range, while the reactance becomes negative around 42 Hz. The proposed controller effectively mitigates SSCI, and it can be observed that it results in positive resistance and reactance values across the entire subsynchronous frequency range. Results from the eigenvalue (modal) analysis and electromagnetic transient simulation also confirm the results obtained from frequency scanning.

High performance nonlinear controller design for AC and DC machines: partial feedback linearization approach

This paper presents the design of a partial feedback linearization controller for speed control of DC and AC machines. The design of the controller is presented based on the nonlinear modeling of the plant. The model of the plant is obtained from differential dynamic equations. A stability analysis is presented to guarantee the stability of the proposed design. To validate the effectiveness of the controller, DC and AC machines systems are simulated. The performance of proposed controller is investigated with respect to different amount of load torque. Simulation studies show that the proposed controller provides the accuracy and high performance for both AC and DC machines.

Predictor-based control for an inverted pendulum subject to networked time delay

The inverted pendulum is considered as a special class of underactuated mechanical systems with two degrees of freedom and a single control input. This mechanical configuration allows to transform the underactuated system into a nonlinear system that is referred to as the normal form, whose control design techniques for stabilization are well known. In the presence of time delays, these control techniques may result in inadequate behavior and may even cause finite escape time in the controlled system. In this paper, a constructive method is presented to design a controller for an inverted pendulum characterized by a time-delayed balance control. First, the partial feedback linearization control for the inverted pendulum is modified and coupled with a state predictor to compensate for the delay. Several coordinate transformations are processed to transform the estimated partial linearized system into an upper-triangular form. Second, nested saturation and backstepping techniques are combined to derive the control law of the transformed system that would complete the design of the whole control input. The effectiveness of the proposed technique is illustrated by numerical simulations.

Partial feedback linearization control for 3-D underactuated overhead crane systems

In this paper, a novel anti-swing control method is proposed for 3-dimensional (3-D) underactuated overhead crane systems, which guarantees fast transportation and efficient swing suppression. Specifically, to increase the performance of the payload swing suppression, a swing-suppressing element is introduced, based on which a novel positioning error signal is constructed. Then, a new control method is developed, and the overall system is divided into two subsystems. The stability analysis of the two subsystems and the overall system is given. In addition, the convergence of the system states is proved. Simulation results are provided to demonstrate the superior performance of the proposed controller over the existing controllers. Meanwhile, the practical performance of the proposed controller is experimentally validated on a portable overhead crane test-bed.

Structure Design and Stable-balancing Control of a Kind of Wire-moving Robot

Wire-moving robots are mechanical systems that can maintain their balance and move on tightropes. Their name comes from the manner in which tightrope walkers maintain their balance by rolling or moving a pole from left to right. In order to investigate the internal laws of these systems and to apply a mechanism of self-balance control to them, a new mechanical structure for wire-moving robots is presented here. This structure consists of a rotational pole and a translational pole coupled with each other in a parallelogram. The robot is an underactuated system. A dynamic model of the robot is established here based on the Lagrange method, and the controller of the system was designed using a partial feedback linearization control algorithm. Finally, the efficiency of the algorithm and the stabilization were verified by computer simulation and experimentation using a prototype.

Partial feedback linearization control of a three-dimensional overhead crane

Based on partial feedback linearization, an improved nonlinear controller is analyzed and designed for the three-dimensional motion of an overhead crane. Three control inputs composed of bridge moving, trolley travelling, and cargo hoisting forces are used to drive five state variables consisting of bridge motion, trolley movement, cargo hoisting displacement, and two cargo swing angles. The control scheme is constituted by linearly combining two components that are separately obtained from the nonlinear feedback of actuated and un-actuated states. To verify the quality of the control process, both numerical simulation and experimental study are carried out. The proposed controller asymptotically stabilizes all system states.

NONLINEAR CONTROL FOR GAL REGULATORY NETWORK IN S. CEREVISIAE

Recently, applying control theory to regulate the intracellular mRNA level was introduced as a new direction for gene regulation. However, the high nonlinearity in the gene regulatory networks imposes significant challenges in control design. As a well understood benchmark example, the GAL regulatory network in S. cerevisiae was recently proposed as a test-bed system for validating theoretical control algorithms in cellular systems. A simple proportional feedback control approach was previously proposed for regulating the intracellular mRNA level in the GAL network, however, there were still limitations with its use to control the nonlinear GAL network. To improve the performance and effectiveness, this paper proposes an advanced nonlinear control strategy. The reduced mathematical model for the GAL network is reorganized into a nonlinear affine system. Then, a partial feedback linearization control approach was employed to regulate the concentration of a protein at a desired level. For validating the control approach in experimental studies, we choose Gal1p as a measurable output, instead of GAL1 mRNA used in the previous study. Simulation results demonstrate that this control approach can shorten the convergence time between states comparing with the proportional feedback control.

Partial feedback linearization control of overhead cranes with varying cable lengths

Overhead cranes are under-actuated mechanical systems with three degrees-of-freedom (trolley displacement, cable length, and cargo swing angle) and only two actuators: one for cargo hoisting and another for trolley driving. An overhead crane transfers the trolley to a desired position, hoists the cargo up and down until the desired cable length is achieved while keeping the cargo swing angle small during the transfer process. The rope should no longer have a swing angle at the load destination. In this research, a nonlinear controller is proposed for an overhead crane system, in which partial feedback linearization technique is used. To show the effectiveness of the proposed controller, we perform both simulation and experimental study. The simulation and experimental results show that the crane system with the proposed controller is asymptotically stable. Furthermore, all state trajectories of the system reach a steady state within a considerably short time even if the inherent structure of the system is changed.

Determining maximum load carrying capacity of planar flexible-link robot: closed-loop approach

SUMMARYMaximum load carrying capacity (MLCC) of flexible robot manipulators is computed based on closed-loop approach. In open-loop approach, controller is not considered, so the end effector deviation from the predefined path is significant and the accuracy constraint restrains the maximum payload before actuators go into saturation mode. In order to improve the MLCC, a method based on closed-loop strategy is presented. Since in this case the accuracy is improved the actuators constraint is not a major concern and full power of actuators can be used. Since controller can play an important role in improving the maximum payload, a sliding mode based partial feedback linearization controller is designed. Furthermore, a fuzzy variable layer is used in sliding mode design to boost the performance of the controller. However, the control strategy required measurements of elastic variables velocity that are not conveniently measurable. So a nonlinear observer is designed to estimate these variables. Stability analysis of the proposed controller and state observer are performed on the basis of Lyapunov's direct method. In order to verify the effectiveness of the presented method, simulation is done for a two-link flexible manipulator. The obtained maximum payload in open-loop and closed-loop cases is compared and the superiority of the method is illustrated and the results are discussed.

Control algorithms for stabilizing underactuated robots

Three control algorithms are developed to stabilize an underactuated two-link robot at its unstable inverted position. The well-known linear quadratic regulator is described first. Next, a stabilization control law using partial feedback linearization is developed where the reference trajectories for the linearized degrees of freedom are designed by analyzing the zero dynamics. The linear quadratic regulator and partial feedback linearization control algorithms both assume an exact dynamic model. To deal with modeling inaccuracies, a robust controller using sliding mode concepts is supplied. Numerical simulations are presented. © 1998 John Wiley & Sons, Inc.