Full State Feedback Research Articles

Output-feedback asymptotic tracking control for rigid-body attitude via adaptive neural backstepping

In this note, a novel neural adaptive output-feedback control (NAOC) with asymptotic tracking performance for rigid-body attitude is investigated subject to inertia uncertainty, unavailability of the angular velocity and unknown external disturbance. First, by virtue of the combination of the first-order filter and the coordinate transformation, the original output feedback system with immeasurable angular velocity and unknown dynamics is converted into the full-state strict feedback system with mismatched disturbance. Second, aided by infinitely integrable inequality with saturation function, an innovative neural network (NN) based adaptive control scheme is proposed via backstepping technique. By adopting the model transformation and proposed algorithm, the asymptotic tracking performance of the transformed system and the attitude tracking system without angular velocity can be achieved simultaneously. Finally, comparative numerical simulations illustrate the efficacy of the developed algorithm.

Single Grid-Current Sensor-Controlled Weak-Grid-Following Inverters: A State-and-Disturbance-Observer-Based Robust Control Scheme Achieving Grid-Synchronization and Disturbance Rejection

With the aim of reducing the number of sensors, this article investigates the single-sensor grid-following control for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -filtered inverter system, and proposes an intuitive robust stability analysis method in the linear framework to handle power control and grid voltage variations in engineering practice. Specifically, through the use of a state-and-disturbance observer, the lumped-disturbance compensated suppression and nominal system full-state feedback technologies are equivalently realized. And the lumped-disturbance estimation carrying voltage phase information at the point of common coupling is further used as synchronization target of the phase-locked loop (PLL) to achieve grid-following control, and the resulting phase-shift is further corrected by accurate phase compensation. In addition, due to the nonlinear nature of the PLL and the power control and grid voltage variations, the system analysis is faced with the dilemma of complex nonlinear analysis or small-signal analysis without a fixed equilibrium point. In this case, a PLL small-signal model with bounded parameter perturbation characterizing power control and grid voltage variations is developed, and further incorporated into the output impedance modeling of the single-sensor grid-following controlled inverter. According to the edge theorem, the system stability in the studied uncertain region is analyzed via four edge output impedances, and appropriate control parameters are selected accordingly. Finally, the experimental results from a downscaled prototype are provided to verify the effectiveness of the proposed single-sensor grid-following control scheme.

Modeling and Nonlinear Control of a Quadcopter for Stabilization and Trajectory Tracking

This paper presents an adequate mathematical representation of a quadcopter’s system dynamics and effective control techniques. A quadcopter is an unmanned aerial vehicle (UAV) that is able to do vertical take-off and landing. This study presents a nonlinear quadcopter system’s mathematical modeling and control for stabilization and trajectory tracking. The mathematical model of the system dynamics of the quadcopter is derived using Newton and Euler equations with proper references to the appropriate frame or coordinate system. A PD control algorithm is developed for the nonlinear system for stabilization. Another nonlinear control technique called full state feedback linearization (FBL) using nonlinear dynamic inversion (NDI) is developed and implemented on the quadcopter system. However, there is a problem with the normal approach of the complete derivation of the full state FBL system using NDI as gathered from the literature review. In such an approach, the PD controller that was used for attitude stabilization was able to stabilize the angles to zero states, but the position variables cannot be stabilized because the state variables are not observable. Thus, a new approach where the position variables are mapped to the angle variables which are controllable so as to drive all states to zero stability was proposed in this study. The aim of the study was achieved but the downside is that it takes a longer time to achieve this stability so it is not efficient and should only be considered when absolute zero stability is the aim without considering time efficiency. The study further investigates the problem of nonlinear quadcopter system’s mathematical modelling and control for stabilization and trajectory tracking using the feedback linearization (FBL) technique combined with the PD controller. The proposed control algorithms are implemented on the quadcopter model using MATLAB and analyzed in terms of system stabilization and trajectory tracking. The PD controller produces satisfactory results for system stabilization, but the FBL system combined with the PD controller performs better for trajectory tracking of the quadcopter system.

Dynamic state feedback controller and observer design for dynamic artificial neural network models

Artificial neural networks are black-box models that can be used to model nonlinear dynamical systems. This article presents a synthesis method for full dynamic state feedback controllers and state and output observers that have guaranteed properties for systems approximated by dynamic artificial neural networks. The resulting control designs are applicable to the practical situation in which the steady-state values for the control input are not known. Dynamic artificial neural networks are written in the standard nonlinear operator form, also known in the literature as the Luré formulation. A generalized form of the Luré formulation is adopted to allow for the representation of deep ℓ-layer networks, ℓ≥1. Sufficient conditions for controller synthesis and observer design are derived in the form of linear matrix inequalities, using a quadratic Lyapunov function. The synthesis method is demonstrated for the control of pH in two tanks in series and a numerical example.

A New Stability Framework for Trajectory Tracking Control of Biped Walking Robots

This article proposes a new stability criterion for biped walking systems on the linear inverted pendulum model, in which the dynamic relationship between the center of mass (CoM) and the zero moment point (ZMP) is dealt with. More precisely, based on the fact that a biped walking robot is stable if its ZMP is always located in the supporting region, we consider whether the ZMP error between its reference and real values stays inside a certain area to guarantee the stability condition. To this end, a norm-based new stability criterion is introduced, in which the temporal supremum of the ZMP error is concerned. Regarding the applicability of the stability criterion, we propose two control approaches to biped walking systems with the consideration of the norm-based stability criterion. In other words, full-state and observer-based feedback control approaches are analyzed in this article, and the initial CoM conditions with respect to the stability criterion are obtained for the two control approaches. We call the sets derived by such conditions the stability regions. Toward a more practical significance, we also deal with the effect of unknown disturbances and sensor noises on the stability of biped walking systems. More importantly, even though computing stability regions intrinsically involves an infinite number of linear inequalities, all the stability regions are shown to be explicitly obtained through only finite numbers of computations in this article. Finally, some simulation results are provided to demonstrate the validity as well as the practical applicability of the developed computation methods.

Dynamics compensation approach to stabilization and observation for abstract linear systems

This paper considers the problem of actuator dynamics and sensor dynamics compensation for linear systems. The dynamics compensations are described by stabilizing or observing cascade systems which can be decoupled by the upper-block-triangle transform. A full state feedback is designed to stabilize the cascade system exponentially and a state observer is proposed to estimate the system state in the abstract framework. It is shown that the error based observer design for output regulation can be converted into a sensor dynamics compensation problem by the well-known regulator equations. As applications, an unstable heat equation with ODE actuator dynamics and an ODE with an unstable heat equation sensor dynamics are investigated to validate the theoretical results. The numerical simulations for both of them are carried out to validate the proposed approach visually.

Convolution/Volterra Reduced-Order Modeling for Nonlinear Aeroelastic Limit Cycle Oscillation Analysis and Control

A methodology for leveraging a combination of linear (through convolution integrals) and nonlinear (through Volterra series) reduced-order modeling (ROM) development was demonstrated on both a two- and three-degree-of-freedom (2-DOF and 3-DOF, respectively) aeroelastic system. The linear/nonlinear ROM approach was demonstrated against previous work in the field for a 2-DOF system and subsequently extended to a 3-DOF (flapped airfoil) system. Excellent agreement was demonstrated at limit cycle oscillation (LCO) onset (flutter) prediction between computational fluid dynamics, linear ROMs, and nonlinear ROMs. Although linear ROMs were sufficient to predict LCO onset, the nonlinear Volterra correction was required to estimate the amplitude of post-LCOs. Corrections that accounted for more coupling between degrees of freedom predicted the amplitudes more accurately. A study was undertaken to determine the minimal training set required to produce reasonable LCO amplitude estimates of the 3-DOF airfoil. A controller was also implemented in an effort to mitigate LCO onset and flutter divergence and to demonstrate the usefulness and power of leveraging the ROM for control design. A full-state feedback controller, tuned via a linear quadratic regulator (LQR), was shown to be effective in controlling the system below LCO onset. However, beyond LCO onset, this specific linear controller structure was observed to be ineffective in controlling the system. Future work will evaluate nonlinear control methods in which the ROM can be deployed as a part of the control system to update the LQR gains in a fully coupled approach.

Adaptive optimal output tracking of continuous-time systems via output-feedback-based reinforcement learning

Reinforcement learning provides a powerful tool for designing a satisfactory controller through interactions with the environment. Although off-policy learning algorithms were recently designed for tracking problems, most of these results either are full-state feedback or have bounded control errors, which may not be flexible or desirable for engineering problems in the real world. To address these problems, we propose an output-feedback-based reinforcement learning approach that allows us to find the optimal control solution using input–output data and ensure the asymptotic tracking control of continuous-time systems. More specifically, we first propose a dynamical controller revised from the standard output regulation theory and use it to formulate an optimal output tracking problem. Then, a state observer is used to re-express the system state. Consequently, we address the rank issue of the parameterization matrix and analyze the state re-expression error that are crucial for transforming the off-policy learning into an output-feedback form. A comprehensive simulation study is given to demonstrate the effectiveness of the proposed approach.

Full State Feedback H-Infinity Controller Design for Nonlinear Systems

Real world systems are inherently nonlinear in nature. Over the last few decades, nonlinear systems are regarded as the most significant issue in control theory. In this work, a nonlinear full state feedback H-infinity controller is proposed for nonlinear systems. The black hole optimization method (BHO) is used as an effective optimization technique to find the optimal parameters for the proposed controller based on the proposed cost function. The suggested controller gain matrix is computed by solving the H-infinity algebraic Riccati equation. As case studies, two types of nonlinear systems are demonstrated to demonstrate the utility of the proposed controller. Finally, simulation findings show that the suggested nonlinear controller improves the stability and performance of nonlinear systems by compensating them and compelling their states to track the reference input asymptotically with a workable and feasible control action.

Ensemble of long short-term memory recurrent neural network for semi-active control of tuned liquid wall damper

A critical challenge in structural control is the design of controllers capable of rapid adaptation to uncertainties, including changes in local dynamics and unknown parameters. A solution is the use of data-based controllers, but these typically require pre-training and may be computationally expensive to utilize. In this paper, the authors proposed a fast neuro-controller capable of pure online learning. The controller is built using an ensemble of recurrent neural networks (ERNNs) based on long short-term memory (LSTM) cells running in parallel. A multi-rate sampler is used to sequentially construct the individual RNN input vectors using local measurements at sampling rates pre-determined from the structure’s natural frequencies. Each RNN performs an individual estimation with the associated sampling rate, and these estimations are assembled into an attention and a dense layer to produce an estimated control force. Critical advantages of the proposed architecture are (1) rapid online adaptation and processing; (2) capability to adapt to local dynamics and non-stationarities; and (3) pure online learning architecture minimizing reliance on pre-training. First, the performance of the ERNNs control algorithm is validated on an actively controlled single-degree-of-freedom system, and stability of the controller is demonstrated. Second, the ERNNs is simulated on a full-scale 20-story building equipped with a semi-active tuned liquid wall damper (TLWD) system that consisted of distributed semi-active tuned liquid multiple column dampers. The ERNNs controller effectively improved the passive performance of the control strategy and performed similarly to that of a full state-feedback sliding mode controller under multi-hazard scenario. The evolution of attention weights under both the wind and seismic hazards demonstrated that the importance of each RNN follows the importance of the structural frequency responses, showing that the controller was capable of capturing and adapting fast-changing dynamics.

Active disturbance rejection adaptive control of multi‐degrees of freedom hydraulic manipulators

SummaryThis article investigates the precise motion control of multi‐degrees of freedom (DoF) hydraulic manipulators, and proposes an active disturbance rejection adaptive control (ADRAC) architecture based on full state feedback with consideration of both unmatched and matched uncertainties, that is, parametric uncertainties and uncertain nonlinearities. The new control strategy integrates adaptive control with extended state observer (ESO) via the backstepping method. Parametric uncertainties are handled by the synthesized adaptive law, and ESO is designed to estimate the remaining uncertainties before being compensated in a feedforward way. In particular, the unmatched and matched uncertainties can be observed in real‐time by constructing an ESO for each channel of the hydraulic manipulator system. The burden on ESO should be greatly reduced since parameter adaptation offsets most parametric uncertainties. Accordingly, high‐gain feedback is avoided in the resulting controller, and improved servo performance can thus be expected. In theory, the suggested ADRAC controller can attain asymptotic tracking performance under the influence of not only parametric uncertainties derived from various hydraulic parameters but also invariant disturbances. Furthermore, when uncertain nonlinearities become time‐variant, prescribed transient tracking performance and final tracking accuracy can also be ensured. Comparative simulations concerning both matched and unmatched uncertainties are obtained to illustrate the high tracking performance nature of the developed control algorithm.

Discussion: “Selective-Compliance-Based Lagrange Model and Multilevel Noncollocated Feedback Control of a Humanoid Robot” (Spyrakos-Papastavridis, E., Dai, J. S., Childs, P. R. N., and Tsagarakis, N. G., 2018, ASME J. Mech. Rob., 10(3), p. 031009)

Abstract The present comment concerns the above paper. [DOI: 10.1115/1.4039394]

Modeling and Optimal Control for Rotary Unmanned Aerial Vehicles in Northern Ireland Climate

Rotary Unmanned Aerial Vehicles (RUAVs) suffer in average Northern Irish winters due to heavy wind preventing vital tasks from being performed in the economy, such as search and rescue or civil engineering observations. This work provides enhanced stability of RUAVs under wind disturbances by using metaheuristic algorithms to select optimal controller gains. Previous work demonstrated how Particle Swarm Optimization can be used to tune optimal controllers; this work uses a machine learning algorithm (Genetic Algorithm) to tune the controller. Simulations carried out on Full State Feedback, Full State Compensator and Linear Quadratic Gaussian controllers tuned by a variety of techniques revealed that the Genetic Algorithm outperformed conventional manual tuning by 20% and Particle Swarm Optimization by 17% in performance measured in settling time. The proposed method tunes the feedback gains and Kalman filter by Genetic Algorithm, which outperforms the manually tuned conventional schemes and “GA-Hybrid” approach. The conditions required to employ Reinforcement Learning as an alternative method for RUAV stabilization in future scope is also explored.

Dynamics and Computed-Muscle-Force Control of a Planar Muscle-Driven Snake Robot

This paper presents the dynamic formulation of an artificial-muscle-driven and computed-muscle–force control for the planar locomotion of a snake robot. The snake robot uses a series of antagonistic pneumatic artificial muscles, assembled at the joints, to generate the locomotion. Kinematics of the artificial-muscle-driven robot in the joint and Cartesian spaces was derived with respect to the muscles’ motion. The Lagrangian mechanics was employed for the formulation of the dynamic model of the robot and deriving the equations of motion. A model-based computed-muscle-force control was designed to track the desired paths/trajectories in Cartesian space. The feedback linearization method based on a change of coordinate was utilized to determine an equivalent linear (input-to-state) system. Then, a full state feedback control law was designed, which satisfies the stability and tracking problems. The performance of the dynamic model and the controller were successfully demonstrated in simulation studies for tracking a circle-shape path and a square-shape path with a constant linear velocity while generating the lateral undulation gait. The results indicate a low magnitude of tracking errors where the controlled muscle force are bounded to the actual pneumatic artificial muscle’s limitations.

Development of Machine Learning Based Control System for Vehicle Active Suspension System

In this paper, Gaussian process (GP) algorithm, which is one of the machine learning methods, is designed to control the vehicle active suspension system (VASS). Experimental data were trained by supervised learning method (regression method). The data were obtained from an optimal linear quadratic controller tuned based on a full state feedback optimal control approach. The results demonstrated that the proposed machine learning (ML) based ground-penetrating radar (GPR) controller outperforms the optimal controller under uncertainties in terms of reducing the oscillation in sprung mass position with a 15% and 21.64% reduction for square and random road conditions, respectively.

Saturated Output Feedback Control for Robot Manipulators With Joints of Arbitrary Flexibility

Abstract This paper proposes a saturated output feedback controller for flexible-joint robot manipulators with joints of arbitrary flexibility. First, under the framework of singular perturbation theory, a saturated flexible compensator is introduced in the dynamics model to enlarge the joint stiffness and achieve a united control for the robot with joints of arbitrary flexibility. Meanwhile, the saturation problem of torque control is also addressed. Second, an extended Kalman filter (EKF) with adaptive high gain that combines the noise filter of EKF with global convergence of high-gain observer is presented to enable the output feedback tracking control without the velocity of the link side or the motor side. Third, explicit but strict stability analyses of the whole system in both full-state feedback and output feedback are given. Finally, simulation comparisons are provided to verify the effectiveness of the proposed approach.

Performance analysis of State-Estimator Implementation on Hardware-In-The-Loop of Ball and Beam System

Ball and beam system (BBS) is a commonly used model to represent several complex and unstable systems. BBS is underactuated system. It is an ideal model to implement kind of control theory. Most of control design are done using simulation method. This method is not realistic because it is conducted on the ideal situation which implies that the result cannot be directly used to control the real system. Hardware in the loop (HIL) simulation is a method that can be used to solve these problems. The use of real controller makes the design experience more realistic and ready to implement. This paper proposes a design of full state feedback for BBS stabilization using HIL simulator. The contribution of this work is to design state estimator on the BBS setup to estimate position and velocity. The result shows that the proposed control and estimator are successfully implemented. The estimator can estimate the output position with time convergent about 1,32 second. The performance of the system is similar with simulation and real plant implementation. It shows that this method can represent the dynamic response of the system on full state feedback control.

Brake Current Control System Modeling Using Linear Quadratic Regulator (LQR) and Proportional integral derivative (PID)

This paper provides a comparative analysis between PID control as a classical control technique and modern control technique in the dinamometer Eddy current brakes system. Eddy current brakes is a modern braking system that requires a control system to support the braking performance. PID control is often used to be implemented but in some conditions it is less optimal. Therefore, it is necessary to develop a modern and optimal control, such as a full state feedback Linear Quadratic Regulator (LQR). The comparison of the braking time responses were simulated using Matlab/Simulink. The simulation results show that the response of LQR control is better than the PID, with Ts = 2.12 seconds, Tr = 1.18 seconds, and without overshoot. On the other side, PID control, although having Ts = 0.27 seconds and Tr = 0.18 seconds, there is still an overshoot about 0.7%.

Prescribed performance tracking for a class of uncertain nonlinear systems with actuator failures

AbstractIn this article, we consider the design of a tracking controller for a class of uncertain nonlinear systems with external disturbances and actuator failures and achieve predesignated performance results on the tracking error. First, since the existing prescribed performance strategies are unable to specify performance bounds in an arbitrary way, we propose a new tool to address the prescribed performance issue by constructing chained first‐order filters and an input switching method. With the aid of the new and flexible prescribed performance tool, any predesignated continuous bounds can be formed by setting the reference coordinate values, sufficiently small coordinate value intervals and the gain parameters of the filters. Second, a full state feedback controller design scheme based on the prescribed performance bounds, which describe the convergence rate and maximum overshoot of the tracking error, is proposed. It is proven that the tracking error always satisfies the prescribed performance bounds. Finally, simulation studies are used to illustrate the effectiveness of the proposed tool and the correctness of the established theoretical results.

Inter-relationship between approximate dynamic inversion and MRAC augmented with proportional-integral controller

Approximate Dynamic Inversion (ADI) is basically an approximation of exact dynamic inversion or feedback linearisation, which converts a nonlinear system to an equivalent linear structure. This method can be widely applied for controlling minimum phase, nonaffine-in-control systems. For applying the ADI method, a fast dynamic subsystem for deriving explicit inversion of the nonaffine equation is required. With full state feedback, ADI may be expressed in the same way as a Proportional Integral (PI) controller with only knowledge of the sign of control effectiveness and also without any approximation. The Model Reference Adaptive Controller (MRAC) augmented with the PI method is an adaptive control technique where the PI parameters are updated/tuned as per the control methodology based on the MRAC-Massachusetts Institute of Technology (MIT) rule so that the plant is capable to follow the reference model. The main objective of this paper is to find the relationship between ADI and MRAC augmented with a PI controller.