Linear Feedback Control Law Research Articles

Designing of a non‐fragile robust predictive controller for uncertain systems with time‐varying delay: A delay‐range‐dependent approach

This study addresses a new delay-dependent non-fragile robust model predictive controller for a class of uncertain continuous-time systems with time-varying delay subjected to constrained input and perturbed controller gain. The uncertainties in system parameters and controller gain are considered as general additive forms. The proposed controller can provide a suitable linear feedback control law depending on delay such that robust performance is achieved to the possible existence of uncertainties. To this end, an optimisation problem is formulated to minimise the upper-bound of the cost function involving some conditions in terms of linear matrix inequalities, utilising the information of lower-and upper-bounds of time-varying delay. By including information regarding the delay range in the quadratic function, the ability to have less conservative results compared to the related works in literature is provided. The effectiveness of the proposed technique is illustrated through a comparison with recent works.

Feedback tracking control of optimal reference trajectories for spacecraft relative motion

In this paper, first the optimal trajectories are defined by a fixed end-time, continuous-thrust trajectory which minimizes a terminal cost at the end of an inter-planetary trajectory by appending the multi-body dynamic equations defining the motion by a set of Lagrange multipliers or co-states. The solution of these co-states and the optimal trajectories for a fixed end-time are obtained by solving a two-point boundary value problem along with a steering control law, which is used to provide a reference trajectory. Inspired by the general expression for the gravitation potential and the Q-law, a tracking control law is designed to track the reference trajectory. As the steering controller is not a feedback controller, a feedback tracking control law is proposed to continuously correct the spacecraft's actual relative motion trajectory so it tracks the reference relative motion trajectory. The nonlinear relative motion tracking control law is reduced to a linear feedback control law, when the spacecraft is sufficiently close to the reference relative motion trajectory. The feedback laws demonstrate the feasibility of developing practical tracking laws for continuous trajectory correction manoeuvre control of spacecraft relative motion, for implementing low-thrust inter-planetary trajectory following control in electrically propelled spacecraft, in practice.

Optimal Motion Planning in GPS-Denied Environments Using Nonlinear Model Predictive Horizon.

Navigating robotic systems autonomously through unknown, dynamic and GPS-denied environments is a challenging task. One requirement of this is a path planner which provides safe trajectories in real-world conditions such as nonlinear vehicle dynamics, real-time computation requirements, complex 3D environments, and moving obstacles. This paper presents a methodological motion planning approach which integrates a novel local path planning approach with a graph-based planner to enable an autonomous vehicle (here a drone) to navigate through GPS-denied subterranean environments. The local path planning approach is based on a recently proposed method by the authors called Nonlinear Model Predictive Horizon (NMPH). The NMPH formulation employs a copy of the plant dynamics model (here a nonlinear system model of the drone) plus a feedback linearization control law to generate feasible, optimal, smooth and collision-free paths while respecting the dynamics of the vehicle, supporting dynamic obstacles and operating in real time. This design is augmented with computationally efficient algorithms for global path planning and dynamic obstacle mapping and avoidance. The overall design is tested in several simulations and a preliminary real flight test in unexplored GPS-denied environments to demonstrate its capabilities and evaluate its performance.

Nonlinear postural control paradigm for larger perturbations in the presence of neural delays.

Maintaining balance is an essential skill regulated by the central nervous system (CNS) that helps humans to function effectively. Developing a physiologically motivated computational model of a neural controller with good performance is a central component for a large range of potential applications, such as the development of therapeutic and assistive devices, diagnosis of balance disorders, and designing robotic control systems. In this paper, we characterize the biomechanics of postural control system by considering the musculoskeletal dynamics in the sagittal plane, proprioceptive feedback, and a neural controller. The model includes several physiological structures, such as the feedforward and feedback mechanism, sensory noise, and proprioceptive feedback delays. A high-gain observer (HGO)-based feedback linearization controller represents the CNS analog in the modeling paradigm. The HGO gives an estimation of delayed states and the feedback linearization control law generates the feedback torques at joints to execute postural recovery movements. The whole scheme is simulated in MATLAB/Simulink. The simulation results show that our proposed scheme is robust against larger perturbations, sensory noises, feedback delays and retains a strong disturbance rejection and trajectory tracking capability. Overall, these results demonstrate that the nonlinear system dynamics, the feedforward and feedback mechanism, and physiological latencies play a key role in shaping the motor control process.

Nonlinear Model Predictive Horizon for Optimal Trajectory Generation

This paper presents a trajectory generation method for a nonlinear system under closed-loop control (here a quadrotor drone) motivated by the Nonlinear Model Predictive Control (NMPC) method. Unlike NMPC, the proposed method employs a closed-loop system dynamics model within the optimization problem to efficiently generate reference trajectories in real time. We call this approach the Nonlinear Model Predictive Horizon (NMPH). The closed-loop model used within NMPH employs a feedback linearization control law design to decrease the nonconvexity of the optimization problem and thus achieve faster convergence. For robust trajectory planning in a dynamically changing environment, static and dynamic obstacle constraints are supported within the NMPH algorithm. Our algorithm is applied to a quadrotor system to generate optimal reference trajectories in 3D, and several simulation scenarios are provided to validate the features and evaluate the performance of the proposed methodology.

Constrained regulation problem for continuous-time stochastic systems under state and control constraints

Constrained regulation problem (CRP) for continuous-time stochastic systems is investigated in this article. New existence conditions of linear feedback control law for continuous-time stochastic systems under constraints are proposed. The computation method for solving constrained regulation problem of stochastic systems considered in this article is also presented. Continuous-time stochastic linear systems and stochastic nonlinear systems are focused on, respectively. First, the condition of polyhedral invariance for stochastic systems is established by using the theory of positive invariant set and the principle of comparison. Second, the asymptotic stability conditions in the sense of expectation for two types of stochastic systems are established. Finally, finding the linear feedback controller model and corresponding algorithm of constrained regulation problem for two types of stochastic systems are also proposed by using the obtained condition. The presented model of the stochastic constrained regulation problem in this article is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Our approach establishes a connection between the stochastic constrained regulation problem and positively invariant set theory, as well as provides the possibility of using optimization methodology to find the solution of stochastic constrained regulation problem, which differs from other methods. Numerical examples illustrate the proposed method.

Stabilization of switched linear systems using an improved event-triggered control scheme

This paper is concerned with the event-triggered control of switched linear systems. The coupling of system switching and event-triggered communication raises two phenomena: (1) the update of controller cannot always catch up with the active subsystem; (2) the switching may lead to additional triggers. The first phenomenon is called the asynchronous switching induced by network communication and the second one brings great difficulty to avoid the Zeno behavior of event-triggered mechanism (ETM). To address the above problem, we propose a new ETM which contains the switching signal of models and controllers and the discontinuity of triggering error at switching time instants. A relative threshold strategy, combined with a jump function, is designed as a new threshold function. By introducing a compensation term, the linear feedback control law is extended to avoid the Zeno behavior of ETM and improve the solvability of control algorithm. Based on the proposed event-triggered control scheme, the exponential stabilization of switched systems is achieved with relaxed constraints on the triggering and switching conditions. The obtained results are validated by a numerical example.

Active disturbance rejection adaptive control for uncertain nonlinear systems with unknown time‐varying dead‐zone input

AbstractThis paper rigorously investigates the problem of active disturbance rejection control for nonlinear systems subject to uncertainties and dead‐zone input. One of the features of the considered systems is that the dead‐zone parameters are allowed to be time varying and asymmetrical. The main idea of this paper is to utilize an extended state observer (ESO) to estimate all the external disturbance, the uncertain nonlinearity, the unknown dead‐zone model, and the unmeasurable states. A switched dynamic parameter estimation law is established to separate the dead‐zone model from the total uncertainty and estimate the parameters of dead‐zone online. Based on the proposed estimation law and the ESO, an output feedback linearization control law is designed to cancel the total disturbance and compensate the dead zone. The theoretical analysis of stability shows that the closed‐loop system has multi‐time scale convergence properties. Finally, simulation results are provided to illustrate the efficiency of the proposed method.

DC-Link Voltage Research of Photovoltaic Grid-Connected Inverter Using Improved Active Disturbance Rejection Control

In this paper, a robust DC-link voltage control scheme is proposed to improve the tolerance of photovoltaic (PV) grid-connected inverter to disturbances. The sensitive characteristic of the DC-link voltage complicates the dynamics of the inverter control system and limits its overall performance, especially when uncertain disturbances are considered. To cope with this issue, a voltage controller based on the linear active disturbance rejection control (LADRC) is designed. By exploring the principle of deviation regulation, an improved linear extended state observer (LESO) is established to ensure that the total disturbance can be estimated in a relatively timely manner. The linear state error feedback (LSEF) control law is generated to compensate for the total disturbance, which reduces the plant to approximate the canonical cascaded double integrator. The stability and disturbance rejection capability of the improved LADRC are further analyzed in frequency domain. Finally, theoretical analysis and experimental results confirm the feasibility of the proposed control scheme.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

Abstract This paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

Analytical guidance for circular orbit transfers with staging of space propulsion systems

This paper considers the combination of an analytical reference trajectory with linear state feedback control to allow for autonomous guidance and control of a spacecraft for coplanar circle-to-circle transfers with a stage-based propulsion system. Staging of electric propulsion components, such as tanks and thrusters, could allow small spacecraft to achieve high-ΔV capabilities with current propulsion technology. In order to utilize these propulsion systems, further developments in guidance and control of such spacecraft are required due to limitations in computational power and communications. Analytical approximations for low-thrust trajectories could allow for computationally simple guidance and control of autonomous spacecraft for circle-to-circle transfers around large central bodies. Many trajectories have been developed for conventional propulsion systems, based either on their shape or input thrust, and applied for preliminary mission design. A previously developed analytical trajectory is extended to account for the effects of staging propulsion system components. In order to stabilize the trajectory in the presence of disturbances, a linear state feedback control law is designed with linear quadratic regulator methods. Finally, a methodology for determining the correct phasing between the spacecraft and a target object is developed and is practical to implement on power-limited computers. The use of the analytical reference trajectory is simulated on an orbit transfer from low-Earth orbit to geostationary orbit.

Fuzzy active disturbance rejection control design for autonomous underwater vehicle manipulators system

AbstractIn this article, a fuzzy active disturbance rejection controller (FADRC) is proposed for autonomous underwater vehicle manipulator system (AUVMS). First, the AUVMS is separated into nine subsystems. Then, for each subsystem, dynamic uncertainties, hydrodynamic forces, unknown disturbance, and nonlinear coupling effects are lumped into a total disturbance. Next, a linear extended state observer (LESO) and linear feedback control law are designed to estimate and compensate the total disturbance. The convergence and estimation error of the LESO are analyzed here to validate its performance. Then considering the control output in real industry are always limited, a saturated proportional‐derivative (PD) controller is proposed, and close‐loop stability of the controller can be ensured. Given the fact that there are many parameters to be scheduled in practical industrial applications, an FADRC is proposed to determine the parameters of the proposed LESO and saturated PD controller. The given fuzzy rules of the parameters' change of the saturated PD controller and bandwidths of LESO can be used in other FADRCs. In order to verify the effectiveness of the proposed method, two tasks are chosen to test the performance of trajectory tracking and the capability of rejecting and attenuating the total disturbance. Simulation shows that the proposed FADRC can achieve better performance and consume less energy than classic fuzzy logic controllers and linear active disturbance rejection controllers.

How Training Data Impacts Performance in Learning-Based Control

When first principle models cannot be derived due to the complexity of the real system, data-driven methods allow us to build models from system observations. As these models are employed in learning-based control, the quality of the data plays a crucial role for the performance of the resulting control law. Nevertheless, there hardly exist measures for assessing training data sets, and the impact of the spatial distribution of the data on the closed-loop system properties is largely unknown. This letter derives - based on Gaussian process models - an analytical relationship between the density of the training data and the control performance. We formulate a quality measure for the data set, which we refer to as ρ-gap, and derive the ultimate bound for the tracking error under consideration of the model uncertainty. We show how the ρ-gap can be applied to a feedback linearizing control law and provide numerical illustrations for our approach.

Control Design, Stability Analysis, and Traffic Flow Implications for Cooperative Adaptive Cruise Control Systems with Compensation of Communication Delay

Communication delay is detrimental to the performance of cooperative adaptive cruise control (CACC) systems. In this paper, we incorporate communication delay explicitly into control design and propose a delay-compensating CACC. In this new CACC system, the semi-constant time gap (Semi-CTG) policy, which is modified on the basis of the widely-used CTG policy, is employed by a linear feedback control law to regulate the spacing error. The semi-CTG policy uses historical information of the predecessor instead of its current information. By doing so, communication delay is fully compensated, which leads to better stability performance. Three stability properties—local stability, string stability, and traffic flow stability—are analyzed. The local stability and string stability of the proposed CACC system are guaranteed with the desired time gap as small as the communication delay. Both theoretical analysis and simulation results show that the delay-compensating CACC has better string stability and traffic flow stability than the widely-used CACC system. Furthermore, the proposed CACC system also shows the potential for improving traffic throughput and fuel efficiency. Robustness of the proposed system against uncertainties of sensor delay and vehicle dynamics is also verified with simulation.

Model-free active input–output feedback linearization of a single-link flexible joint manipulator: An improved active disturbance rejection control approach

Traditional input–output feedback linearization requires full knowledge of system dynamics and assumes no disturbance at the input channel and no system’s uncertainties. In this paper, a model-free active input–output feedback linearization technique based on an improved active disturbance rejection control paradigm is proposed to design feedback linearization control law for a generalized nonlinear system with a known relative degree. The linearization control law is composed of a scaled generalized disturbance estimated by an improved nonlinear extended state observer with saturation-like behavior and the nominal control signal produced by an improved nonlinear state error feedback. The proposed active input–output feedback linearization cancels in real-time fashion the generalized disturbances which represent all the unwanted dynamics, exogenous disturbances, and system uncertainties and transforms the system into a chain of integrators up to the relative degree of the system, which is the only information required about the nonlinear system. Stability analysis has been conducted based on the Lyapunov functions and revealed the convergence of the improved nonlinear extended state observer and the asymptotic stability of the closed-loop system. Verification of the outcomes has been achieved by applying the proposed active input–output feedback linearization technique on the single-link flexible joint manipulator. The simulations results validated the effectiveness of the proposed active input–output feedback linearization tool based on improved active disturbance rejection control as compared to the conventional active disturbance rejection control–based active input–output feedback linearization and the traditional input–output feedback linearization techniques.

Handling Torque Input Constraints Under Robust Nonlinear Regulation Control of Robotic Systems with Parametric Uncertainties

This paper proposes a methodology of handling torque input constraints under robust nonlinear regulation control synthesis for robotic systems with parametric uncertainties. The proposed method is composed of: (i) an inner loop controller design applying a nonlinear geometric control via feedback linearization to transform uncertain robotic systems into worst-case uncertain linear system, (ii) a new method of torque input constraint mapping the constraints on the input torques into a constraint on new control inputs of the uncertain linear system through the feedback linearizing control law, and (iii) a new approach of outer loop controller design using robust H( static state feedback controller to handle the remaining uncertain nonlinear parts and to satisfy the mapped input constraints. In order to verify the correctness and the performance of the proposed method, it is demonstrated via simulation of position control problem for a two-link robotic system.

Implementation of Linear Controllers via Active Disturbance Rejection Control Structure

Linear active disturbance rejection control (LADRC) takes the controlled plant as a cascaded integral model and treats all other plant information and external disturbances as a generalized disturbance, and uses an linear extended state observer (ESO) to estimate the generalized disturbance and incorporates it in a linear state feedback control law to reject it quickly. This ESO-based LADRC controller is a fixed-structure controller as long as the (relative) order of the controlled system is specified. This article shows that any linear finite-dimensional controller can be implemented via the LADRC structure; thus, it is a general-purposed control structure in that it can be applied to any control system where linear control is sufficient. Case study shows that the implementation not only retains the disturbance rejection performance of the original linear controller but also improves its tracking performance due to the two-freedom-of-degree property of LADRC.

Linear Active Disturbance Rejection Control of a Two-Degrees-of-Freedom Manipulator

This paper presents linear active disturbance rejection control (LADRC) for a two-degrees-of-freedom (2-DOF) manipulator system to achieve trajectory tracking. The system is widely used in engineering applications and exhibits the characteristics of high nonlinearity, strong coupling, and large uncertainty with two inputs and two outputs. First, the problem of dynamic coupling in the model of the 2-DOF manipulator is addressed by considering the dynamic coupling, model uncertainties, and external disturbances as total disturbances. Second, a linear extended state observer is designed to estimate the total disturbances, while a linear state error feedback control law is designed to compensate these disturbances. The main contribution is that the stability of the closed-loop system with two inputs and two outputs is analyzed, and the relationship between the performance of the closed-loop system and the controller parameters is established. The joint simulation of SolidWorks and Matlab/Simulink is conducted. The simulation and experimental results clearly indicate the superiority of LADRC over the PID for trajectory tracking and dynamic performance.

Non-linear Control of Inverted Pendulum

Presented is a study of non-linear control for an inverted pendulum system. The inverted pendulum system is a great example of an underactuated, non-minimum phase, and highly unstable system. The objective of this research paper is to derive non-linear control laws for an inverted pendulum system. First, dynamic equations of the inverted pendulum are derived by utilizing the Lagrange's equations and then it is linearized around an unstable upright position. Secondly, the corresponding analysis uses the standard linear stability arguments and the traditional Lyapunov method. The non-linear sliding mode control and feedback linearization control laws are then derived The feedback linearization control law is used to transform the non-linear system into an equivalent linear system such that a suitable feedback control law can be proposed. The stabilization of the initial condition and reference tracking is studied in this paper. I demonstrate the effectiveness of the proposed non-linear control strategies using MATLAB/Simulink software.

Second-Order Linear Active Disturbance Rejection Control and Stability Analysis of Energy Storage Grid-Connected Inverter

At present, which has gradually become a technical development trend that the energy storage grid-connected inverter system is connected to the grid to ensure the stable operation of the whole system. However, the stability of the energy storage system itself is also very important for the safe operation of the power grid. Therefore, improving the stability of grid-connected energy storage system is still the key technology of current research. Aiming at the strong coupling and low-voltage ride-through fault of grid-connected system, a second-order mathematical model of grid-connected control system is established. Based on its state space model, a linear extended state observer (LESO) for state observation and a linear state error feedback (LSEF) control law for disturbance estimation are designed. The second-order linear active disturbance rejection control (LADRC) is introduced into the voltage loop, the stability of the second-order LADRC controller is proved by the Lyapunov stability theory, and the stability conditions are given. Finally, the simulation model of the grid-connected energy storage system is built on the MATLAB/Simulink digital platform, and the low-voltage ride-through fault is designed on the grid-side. The simulation results show that the effect of the second-order LADRC control is better than that of the traditional PI control obviously, which reflects the superiority of the second-order LADRC in controlling the grid-side low-voltage ride-through fault.