Continuous Control Law Research Articles

Optimal Control of a Grid Assisted Photovoltaic-Hydrogen Production System

Abstract This paper deals with the optimal control of a H2 production system supplied by a photovoltaic solar energy and assisted by the grid. For that, we propose a simple dynamic model accounting for the main features of the system, where the electrolizer current is used as the control variable, and we obtain the control law that optimizes the grid energy consumption despites the solar energy variability An important constraint on the obtained solution is the physical limits of the hydrogen storage tank, which results in a nonsmooth and noncontinuous problem. The Pontryagin’s maximum principle is used to solve the boundary value problem and an explicit piecewise continuous control law is found. Simulation results are presented to illustrate the effectiveness of the proposed control design.

Design of Control Law for Ejection Seat under Adverse Attitudes

The escape performance of ejection seat under adverse attitudes is the key technology for the 4th generation ejection seat, and the design of control law algorithm is the core problem for attitude and trajectory adjustment. A new control law design method was presented. Firstly, a simulation model for the entire ejecting process was established and a control parameter optimization model was designed, through which an optimum parameter set was obtained as the discrete control law. Then, by utilizing multilayer feedback of the error back propagation (BP) algorithm based neural network model, the ultimate continuous control law can be acquired under the whole ejecting conditions. The roll attitude ejecting condition was exampled to design and validate the approached method. The results indicate that the performance of ejection seat by adopting the control law designed by the proposed method is higher than the multi-mode control law and the K3JI-3.5 ejection.

Interval Type-2 FNN-Based Quantized Tracking Control for Hypersonic Flight Vehicles With Prescribed Performance

This paper presents a tracking control scheme with quantization mechanism for hypersonic flight vehicles (HFVs) with prescribed performance using an interval type-2 fuzzy neural network (IT2FNN). A parameterized tracking error model of the HFV is derived with some considered uncertainties, which are approximated by an IT2FNN. The tracking control of the velocity and altitude of the HFV is designed by using a prescribed performance control technique. It allows that transient characteristics of the tracking errors can be improved and adjusted by some prescribed performance functions. According to an adaptive backstepping control design procedure, novel continuous control laws of the fuel equivalency ratio, canard deflection, and elevator deflection are designed with logarithmic quantization mechanism, for the sake of avoiding inadvertently increasing the effective gains of continuous controllers as well as reducing loads of the communication from controller unit to actuator unit. Besides, the limited tracking errors of the flight path angle and angle-of-attack can be achieved by applying the designed controllers. Finally, the presented tracking controllers with quantization mechanism are validated by comparative simulations.

An Adaptive Neural Non-Singular Fast-Terminal Sliding-Mode Control for Industrial Robotic Manipulators

In this study, a robust control strategy is suggested for industrial robotic manipulators. First, to minimize the effects of disturbances and dynamic uncertainties, while achieving faster response times and removing the singularity problem, a nonsingular fast terminal sliding function is proposed. Second, to achieve the proposed tracking trajectory and chattering phenomenon elimination, a robust control strategy is designed for the robotic manipulator based on the proposed sliding function and a continuous adaptive control law. Furthermore, the dynamical model of the robotic system is estimated by applying a radial basis function neural network. Thanks to those techniques, the proposed system can operate free of an exact robotic model. The suggested system provides high tracking accuracy, robustness, and fast response with minimal positional errors compared to other control strategies. Proof of the robustness and stability of the suggested system has been verified by the Lyapunov theory. In simulation analyses, the simulated results present the effectiveness of the suggested strategy for the joint position tracking control of a 3-degree of freedom (3-DOF) PUMA560 robot.

Implementation of model-free motion control for active suspension systems

Abstract This paper focuses on the implementation of motion control for active suspension systems using a novel scheme of model-free finite-time tracking control method. The proposed strategy facilitates the realization since the system plant modeling is not needed. Correspondingly, the suspension vertical dynamics including external disturbances are estimated by the time-delay estimation, and its estimated error is compensated by the integral sliding mode control scheme. Theoretical analysis proves that the sliding mode and desired system dynamics can achieve a finite time convergence performance with continuous control law. In active suspension control, the continuous control law contributes to preventing the unexpected chattering in practical implementation. The advantage of the presented control algorithm is verified via comparative investigation, especially the comparison of the existing extended state observer-based feedback control scheme, which requires a high-gain observer to realize the desired dynamics. Comparative experimental studies are presented to confirm the effectiveness and superiority of the proposed control strategy over the traditional methods.

A Finite-Time Disturbance Observer Based Full-Order Terminal Sliding-Mode Controller for Manned Submersible with Disturbances

A novel full-order terminal sliding-mode controller (FOTSMC) based on the finite-time disturbance observer (FTDO) is proposed for the “JIAOLONG” manned submersible with lumped disturbances. First, a finite-time disturbance observer (FTDO) is developed to estimate the lumped disturbances including the external disturbances and model uncertainties. Second, a full-order terminal sliding-mode surface is designed for the manned submersible, whose sliding-mode motion behaves as full-order dynamics rather than reduced-order dynamics in conventional sliding-mode control systems. Then, a continuous sliding-mode control law is developed to avoid chattering phenomenon, as well as to drive the system outputs to the desired reference trajectory in finite time. Furthermore, the closed-loop system stability analysis is given by Lyapunov theory. Finally, the simulation results demonstrate the satisfactory tracking performance and excellent disturbance rejection capability of the proposed finite-time disturbance observer based full-order terminal sliding-mode control (FTDO-FOTSMC) method.

Finite-time sliding mode and super-twisting control of fighter aircraft

The development of two nonlinear robust higher-order flight control systems for roll-coupled maneuvers of fighter aircraft with uncertain parameters is discussed in this article. The objective is to independently control the output variables (roll angle, pitch angle and sideslip angle) using aileron, elevator and rudder control surfaces. For a nominal model of aircraft, first a finite time stabilizing (FTS) control law, based on the notion of geometric homogeneity, is designed. Then for robust control in the presence of parameter uncertainties, (i) a discontinuous sliding mode (DSM) control law and (ii) a super-twisting (STW) continuous control law is designed. It is shown that in the composite closed-loop system consisting of either (a) the FTS and DSM control laws or (b) the FTS and STW control systems, the output trajectory tracking error and its first-order derivative converge to the origin in finite time. Digital simulation results for a swept-wing fighter aircraft, including the two composite control systems, are obtained. These results show that each of the designed flight controllers accomplishes precise simultaneous large longitudinal and lateral maneuvers, despite uncertainties in the aerodynamic and inertia parameters, turbulence, and partial loss of control surface effectiveness.

Fixed-time stabilization of high-order integrator systems with mismatched disturbances

The fixed-time stabilization of high-order integrator systems with both matched and mismatched disturbances is investigated. A continuous non-switching control law is designed based on the bi-limit homogeneous technique for arbitrary-order integrator systems. Combining with fixed-time disturbance observer, the proposed continuous control law for the system with matched and mismatched disturbances guarantees that the convergence time is uniformly bounded with respect to any initial states. Finally, the numerical results are provided to verify the efficiency of the developed method.

Sequential distributed predictive control of a 3D tower crane

An asymptotically stabilizing sequential distributed model predictive control (MPC) of a 3D tower crane is proposed. Stability is ensured by employing three locally stabilizing MPC control laws. In the case of Lipschitz continuous local MPC control laws, a terminal cost and a terminal set constraint are used as stabilizing ingredients while robust control invariant feasible set is used as an additional constraint to guarantee recursive feasibility. On the other hand, in the case of an arbitrary cost function, switching to a robust dual-mode local control law is used inside of the terminal set to guarantee asymptotic stability.

Robust stochastic stabilization of attitude motion

This study proposes robust stochastic stabilization of rigid body attitude motion within the framework of geometric mechanics, which can globally represent the attitude dynamics model. The system is subject to a stochastic input torque with an unknown variance parameter and an unknown nonlinear diffusion coefficient matrix. Our development starts with introducing a general notion of the stochastic stability in probability within the framework of geometric mechanics. Then, the Morse–Lyapunov (M–L) technique is employed to design a nonlinear continuous stochastic feedback control law. Finally, the asymptotic stability of the system is guaranteed in probability and the control gain parameters are obtained via solving a linear matrix inequality feasibility problem. An estimate of the region of attraction of the system is calculated to provide a better insight for tuning the control gain parameters. Two illustrative examples are performed based on the discretized model of the closed-loop system to demonstrate the effectiveness of the proposed control scheme.

Nonlinear ellipsoid based attitude control for aggressive trajectories in a quadrotor: Closed-loop multi-flips implementation

In this paper a model-free continuous nonlinear control law for the attitude of a quadrotor, based on the Attractive Ellipsoid Method and a saturation term, is proposed. This control law allows the vehicle to track aggressive maneuvers, such as multiple flips about the y axis of the body frame, with high angular velocities. The controller is designed through a singularity-free attitude representation based on a unit quaternion and its gains are computed by solving an optimization problem with LMIs. The proposed controller preserves the advantageous characteristics of the Attractive Ellipsoid Method and increases its robustness properties with the fast response of the nonlinear saturation term, minimizing as much as possible the attitude tracking error and assuring its convergence to a small neighborhood around the origin. A numerical study based on simulations is presented to analyze the advantages of the proposed approach, and experiments are presented to show the performance of the closed-loop system for tracking aggressive multiple flips, even in outdoors.

Terminal Synergetic Control for Blood Glucose Regulation in Diabetes Patients

In this paper, a new robust terminal synergetic control scheme is proposed to regulate blood glucose level in diabetic patients (type I diabetes), based on recently developed synergetic control and a terminal attractor technique. The technique presented has the advantage of using a continuous control law. Moreover, the proposed control scheme, besides being chattering free, has the characteristics of finite time convergence. Lyapunov synthesis is adopted to ensure controlled system stability. Simulation results of terminal synergetic control are compared to classic synergetic and second-order sliding mode control (SMC) performance, demonstrating that the proposed control method allows for rapidly achieving normoglycemia in type I diabetes patients.

Globally rigid formation of [formula omitted]-link doubly nonholonomic mobile manipulators

This paper provides a new framework for the collective motion control of a team of n-link doubly nonholonomic mobile manipulators in a constrained environment. A continuous decentralized motion planner is proposed. It guarantees the establishment and strict maintenance of a team formation using the Lyapunov-based control scheme (LbCS), which takes into account all the practical limitations, and the constraints due to fixed obstacles, nonholonomy and globally rigid formation requirements. The control scheme inherently utilizes artificial potential fields within an overarching leader–follower framework to mobilize the prescribed globally rigid formation. The designated leader of the team is modeled as a moving reference point, referred to as the virtual leader. With its protective polygonal region, it directs the motion of the team and manipulate the geometry of the formation. It is the authors’ belief that this navigation and globally rigid formation control problem of n-link doubly nonholonomic mobile manipulators is treated for the first time with the use of continuous time-invariant control laws within the framework of LbCS and a variant of the leader–follower scheme. The effectiveness of the motion planner and the resulting acceleration-based control laws are demonstrated via computer simulations.

Distributed Coordination of Multiple Unknown Euler-Lagrange Systems

A robust consensus tracking problem is addressed for multiple unknown Euler-Lagrange systems where only a subset of the agents is informed of the desired time-varying trajectory. Challenging unstructured uncertainties, including unknown nonlinear dynamics and disturbances, are considered in the agent dynamics. A model-free, identifier-based, continuous, distributed robust control method is designed to solve this problem under both undirected and directed graphs. The control inputs and coupling gains depend only on local information and the consensus tracking errors are proven to converge to zero asymptotically. Under an undirected graph, a distributed nonlinear identifier is developed for each agent to compensate for the unknown nonlinear dynamics and disturbances. Based on this identifier, a continuous distributed control law is designed to enable asymptotic robust consensus tracking. By selecting the gains of the designed controller according to the derived conditions, closed-loop stability is proven using graph theory and Lyapunov analysis. Furthermore, the directed graph case is investigated via a distributed two-layer coordination scheme in which a model-free continuous distributed controller is designed by using information obtained from a distributed leader estimator. Numerical simulation results are given to illustrate the effectiveness of the proposed methods.

Multivariable Finite Time Attitude Control for Quadrotor UAV: Theory and Experimentation

The attitude control of quadrotor unmanned aerial vehicle (UAV) is investigated. The aim of this paper is to develop a continuous multivariable attitude control law, which drives the attitude tracking errors of quadrotor UAV to zero in finite time. First, a multivariable super-twisting-like algorithm (STLA) is proposed for arbitrary order integrator systems subject to matched disturbances. A discontinuous integral term is incorporated in the control law in order to compensate the disturbances. A rigorous proof of the finite time stability of the close-loop system is derived by utilizing the Lyapunov method and the homogeneous technique. Then, the implementation of the developed method in an indoor quadrotor UAV is performed. The remarkable features of the developed algorithm includes the finite time convergence, the chattering suppression and the nominal performance recovery. Finally, the efficiency of the proposed method is illustrated by numerical simulations and experimental verification.

Continuous fixed-time convergent regulator for dynamic systems with unbounded disturbances

This paper presents a novel continuous fixed-time convergent control law for dynamic systems in the presence of unbounded disturbances. A continuous fixed-time convergent control is designed to drive all states of a multi-dimensional integrator chain at the origin for a finite pre-established (fixed) time, using a scalar input. The fixed-time convergence is established and the uniform upper bound of the settling time is computed. The designed control algorithm is applied to fixed-time stabilization of two mechatronic systems, a cart inverted pendulum and a single machine infinite bus turbo generator with main steam valve control.

Synthesis of intelligent fuzzy control in the space of bounded piecewise-continuous functions based on the combined maximum principle

It is shown that the solution of the problem of control synthesis using the Hamilton-Ostrogradskii principle leads to a variational inequality, from which the conditions for the maximum of the the generalized power function in the space of bounded piecewise continuous functions follow. It allows to find a feedback structure up to a synthesis function. Using the methods of the structure construction the nonlinear structures of the relay and continuous control laws are obtained. The proposed control method allows to avoid the mode with frequented switching. It consists of the following two stages. At the first stage, the control object is brought into the vicinity of the terminal state using the relay control law. In the second stage, the quasi-optimal continuous control is used. The uncertainty of the transition area size is resolved using fuzzy logic. The efficiency of the intelligent controls is demonstrated by the example of mathematical modeling of the system dynamics.

Distributed Control for Spatial Self-Organization of Multi-agent Swarms

In this work, we design distributed control laws for spatial self-organization of multi-agent swarms in 1D and 2D spatial domains. The objective is to achieve a desired density distribution over a simply connected spatial domain. Since individual agents in a swarm are not themselves of interest and we are concerned only with the macroscopic objective, we view the network of agents in the swarm as a discrete approximation of a continuous medium and design control laws to shape the density distribution of the continuous medium. The key feature of this work is that the agents in the swarm do not have access to position information. Each individual agent is capable of measuring the current local density of agents and can communicate with its spatial neighbors. The network of agents implement a Laplacian-based distributed algorithm, which we call pseudo-localization, to localize themselves in a new coordinate frame, and a distributed control law to converge to the desired spatial density distribution. We start by studying self-organization in one dimension, which is then followed by the 2D case.

Discrete-time sliding mode control of a class of linear uncertain saturated systems

This paper proposes a new design approach of discrete-time sliding mode control of a class of linear uncertain systems in presence of saturation constraint. The saturation constraint is reported on inputs vector and it is subject to constant limitations in amplitude. The uncertainty is being norm bounded reported on both dynamic and control matrices. In general, sliding mode control strategy consists on two essential phases. The design of the quasi-sliding surface is the first phase which is formulated as a pole assignment of linear uncertain and saturated system in a specific region through convex optimisation. The solution to this problem is therefore numerically tractable via linear matrix inequalities optimisation. The controller design is the second phase of the sliding mode control design, which leads to the development of a continuous and nonlinear control law. An approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behaviour is proposed to provide robustness of the nonlinear control. Finally, the validity and the applicability of this approach are illustrated by a multivariable numerical example of a robot pick and place.

Discrete-time sliding mode control of a class of linear uncertain saturated systems

This paper proposes a new design approach of discrete-time sliding mode control of a class of linear uncertain systems in presence of saturation constraint. The saturation constraint is reported on inputs vector and it is subject to constant limitations in amplitude. The uncertainty is being norm bounded reported on both dynamic and control matrices. In general, sliding mode control strategy consists on two essential phases. The design of the quasi-sliding surface is the first phase which is formulated as a pole assignment of linear uncertain and saturated system in a specific region through convex optimisation. The solution to this problem is therefore numerically tractable via linear matrix inequalities optimisation. The controller design is the second phase of the sliding mode control design, which leads to the development of a continuous and nonlinear control law. An approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behaviour is proposed to provide robustness of the nonlinear control. Finally, the validity and the applicability of this approach are illustrated by a multivariable numerical example of a robot pick and place.