Continuous Control Law Research Articles

Fractional finite-time control for robust tracking of nonlinear systems subject to Hölder disturbances with application to UAVs

The aim of the present article is to design a robust fractional-order (FO) finite-time (FnT) control able to tackle Hölder disturbances of second-order nonlinear systems. First, a novel sliding manifold with Arc-Tangent function is suggested for second nonlinear systems. It has been proven that the system states globally converge to the origin in FnT using the proposed sliding mode variable. To ensure a FnT stability of the sliding variable, a robust control is developed. By using fractional operators, a uniformly continuous control law is designed to tackle Hölder disturbances. Furthermore, the suggested approach is shown to be resistant to matched Hölder disturbances and uncertainties that are continuous but not necessarily differentiable. Moreover, the FnT stability of quadrotors using the proposed control, that is our second result. The quadrotor simulations analysis demonstrates the practicality of the proposed FnT controller in the presence of Hölder disturbances.

A novel nonsingular fixed-time sliding mode control for morphing aircraft with actuator faults and saturation

This paper proposes a fixed-time anti-saturation adaptive sliding mode control (FxASASMC) methodology to solve the challenge of attitude tracking control in morphing aircraft under actuator faults, saturation and external disturbances. The proposed control algorithm consists of three key components: a novel nonsingular fixed-time sliding mode surface, a fixed-time anti-saturation compensator, and a continuous fixed-time adaptive control law. The novel nonsingular fixed-time sliding mode surface is developed based on the arctan function, enabling not only the confinement and independence of the sliding modes' convergence time from the initial states but also the benefit of a smaller initial value, thereby assisting in saturation avoidance. To mitigate the saturation issue, a fixed-time anti-saturation compensator is employed. Moreover, throughout the control process, the anti-saturation compensator ensures that the output is bounded. And once the actuator saturation stops, its output converges to zero in a fixed time, which effectively minimizes the impact of the anti-saturation compensator on the control system performance in the absence of system saturation. Based on the sliding mode surface and anti-saturation compensator, the continuous fixed-time adaptive control law ensures that the attitude tracking errors converge toward the neighborhood of the origin in a fixed time, even if the boundaries of the complex disturbance are not known in advance. Moreover, the convergence time boundary remains unaffected by the initial errors. In parallel, the control command remains continuous and free of chattering. Ultimately, the proposed control scheme's effectiveness and enhanced performance are demonstrated through various numerical simulations.

Robust Tracking Control of Wheeled Mobile Robot Based on Differential Flatness and Sliding Active Disturbance Rejection Control: Simulations and Experiments.

This paper proposes a robust tracking control method for wheeled mobile robot (WMR) against uncertainties, including wind disturbances and slipping. Through the application of the differential flatness methodology, the under-actuated WMR model is transformed into a linear canonical form, simplifying the design of a stabilizing feedback controller. To handle uncertainties from wheel slip and wind disturbances, the proposed feedback controller uses sliding mode control (SMC). However, increased uncertainties lead to chattering in the SMC approach due to higher control inputs. To mitigate this, a boundary layer around the switching surface is introduced, implementing a continuous control law to reduce chattering. Although increasing the boundary layer thickness reduces chattering, it may compromise the robustness achieved by SMC. To address this challenge, an active disturbance rejection control (ADRC) is integrated with boundary layer sliding mode control. ADRC estimates lumped uncertainties via an extended state observer and eliminates them within the feedback loop. This combined feedback control method aims to achieve practical control and robust tracking performance. Stability properties of the closed-loop system are established using the Lyapunov theory. Finally, simulations and experimental results are conducted to compare and evaluate the efficiency of the proposed robust tracking controller against other existing control methods.

К выбору периода дискретизации нелинейных гибридных систем управления

Hybrid systems are often used in various technical applications, such as robotics, aviation, space, energy, etc. The emergence of hybrid control systems is due to the use of computers to implement control laws, including nonlinear ones. Digital means cannot implement continuous control laws. However, the known methods of design, especially of nonlinear systems, lead precisely to continuous controls, which caused the need to discretize the continuous control with the largest possible period. Solving the problem of determining the maximum permissible sampling period of a nonlinear control system is a rather complex stage of its creation. In this article the problem of definition of the maximum allowed sample period of the nonlinear hybrid system control and its dependence on the module of the maximum eigenvalue of the functional matrix of quasilinear model of the continuous system is also considered. The nonlinear hybrid system is created by discretizing the control of the nonlinear continuous system. This continuous system is synthesized using the algebraic polynomial and matrix method of the nonlinear control systems design in which quasilinear models are used. It has been is established that the value of the maximum permissible sample period depends not only on the module of the maximum eigenvalue, but also on initial conditions and external influences. These dependences are complex and it is difficult to find them theoretically. Experimentally, based on the example of the specific nonlinear hybrid control system it is shown that eigenvalues smaller on the module lead to larger values of the maximum of the permissible sample period. The problem of choosing the sample period of control laws of the real hybrid control systems can be solved in the similar way based on a compromise between the system high-speed performance and the sample period.

Dynamic modeling and adaptive finite-time control of cable-driven parallel robots for ship cleaning

ABSTRACT Ship cleaning, often manually performed by numerous workers, is crucial in the shipping industry. This study introduces a marine cable-driven parallel cleaning robot (MCDPCR) to enhance cleaning security and efficiency. To investigate trajectory tracking under the moving base, the dynamic model of MCDPCR is established, and the optimisation of cable forces is considered. Then, an adaptive terminal sliding mode controller is designed, integrating the discontinuous sign function term to obtain a continuous actual control law and thus a chattering-free response. Meanwhile, the uncertainty is compensated by an adaptive method. The stability of the control strategy is analyzed using the Lyapunov stability theory. Finally, the effectiveness of the proposed control strategy is verified by several simulation scenarios. The results show that the controller has a fast global convergence speed, high tracking accuracy, and strong robustness. The method can provide a valuable reference for developing automated marine cleaning equipment.

Attitude tracking of rigid bodies using exponential coordinates and a disturbance observer

In this paper, we study the problem of attitude trajectory tracking of rigid bodies subject to external disturbances. The attitude control problem has been studied in the last decades and novel solutions have been proposed. Nevertheless, most of the proposed controllers only achieve local or almost global asymptotic stability without considering external disturbances. Contrary to other works, we focus on the problem of achieving almost global exponential stability of the attitude tracking errors in the presence of external disturbances using continuous control laws. We propose an attitude trajectory tracking controller based on the exponential coordinates of rotation in combination with a disturbance observer that estimates the exogenous signals. To solve this problem, we adopt a hierarchical approach, where the proposed control law is divided into a kinematic controller (outer control loop) and a velocity tracking controller (inner control loop). To design the disturbance observer, it is assumed that exogenous signals can be generated by a linear exosystem, i.e. the magnitude and phase of the disturbance are unknown. The almost global exponential stability of the closed-loop dynamics' equilibrium point was proved by a strict Lyapunov function. The performance of the proposed approach is assessed by numerical simulations and experimental tests on a low-cost quadrotor.

Continuous and Periodic Event-Triggered Sliding-Mode Control for Path Following of Underactuated Surface Vehicles.

This article develops continuous and periodic event-triggered sliding-mode control (SMC) algorithms for path following of underactuated surface vehicles (USVs). Based on the SMC technology, a continuous path-following control law is designed. The upper bounds of quasi-sliding modes for path following of USVs are established for the first time. Subsequently, both continuous and periodic event-triggered mechanisms are considered and added into the proposed continuous SMC scheme. It is demonstrated that with appropriate selecting of control parameters, the use of hyperbolic tangent functions does not affect the boundary layer of quasi-sliding mode caused by event-triggered mechanisms. The proposed continuous and periodic event-triggered SMC strategies can make the sliding variables reach the quasi-sliding modes and stay in there. Moreover, energy consumption can be reduced. Stability analysis shows that the USV can follow a reference path by using the designed method. The simulation results show the effectiveness of the proposed control methods.

Practical fixed-time output feedback trajectory tracking control for marine surface vessels with unknown disturbances

This paper proposes a fixed-time output feedback trajectory tracking control scheme based on an extended state observer for marine surface vehicles (MSVs) with uncertain dynamics and unknown disturbances. The scheme utilizes a high-gain fixed-time extended state observer (HGFxESO) to estimate the reconstructed unmeasured velocities and lumped disturbances. The upper bound of the settling time of the HGFxESO is only determined by the design parameters, and the estimation errors can converge to a bounded set within a fixed time. Moreover, a novel fixed-time control law is proposed based on the backstepping technique and “adding a power integrator” (API) technique. The designed continuous control law ensures the trajectory tracking errors of MSVs converge to a neighborhood around the origin within a fixed time. The fixed-time stability of the MSVs trajectory tracking control system is proved using Lyapunov theory. Finally, simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

Sliding mode controller design for unstable processes with dead time with a case study on continuous stirred tank reactor

Unstable processes are difficult to control because one or more poles lie on the right-hand side of the s-plane. Control becomes further complicated by the presence of dead time in such systems. In this study, a sliding mode control (SMC) design is proposed for the control of unstable processes with dead time. To apply the SMC, a second order plus dead time (SOPDT) model of the unstable process is used, and a proportional-integral-derivative-acceleration type sliding surface is considered. The parameters of continuous and discontinuous control laws are obtained using the differential evolution optimization technique. The optimal control problem is solved by satisfying a new weighted bi-objective function constituting the performance index integral absolute error and control input total variation. The proposed control scheme has been satisfactorily extended to control unstable integrating and higher-order unstable processes with dead time by approximating them into the unstable SOPDT model. The efficacy of the suggested scheme has been evaluated on several benchmark unstable industrial chemical processes, including the continuous stirred tank reactor (CSTR). Further, this scheme has been compared with recently reported work, and the obtained results clearly demonstrate the effectiveness of the suggested controller.

Recurrent-Neural-Network-Based Fractional Order Sliding Mode Control for Harmonic Suppression of Power Grid

A continuous fractional order sliding mode controller (CFOSMC) based on a developed output feedback feature selection neural network (OFFSNN) for an active power filter (APF) is studied in this paper to effectively compensate grid harmonic current and improve power quality. A fractional order sliding mode manifold is introduced firstly. Then a continuous fractional order sliding mode controller is adopted to resolve the shortcoming of chattering phenomenon in the conventional one by designing a continuous control law. Furthermore, considering the unknown part of APF system, a new neural structure called OFFSNN is established to estimate the unknown dynamic characteristic with high precision and low computational burden. Compared with general neural network, the proposed OFFSNN is adept at adjusting neural structure and parameters by selecting beneficial nodes as well as deleting useless ones. To demonstrate the effectiveness and superiority of the presented scheme, experiments in various cases on the APF platform are given.

A Robust Control for Five-level Inverter Based on Integral Sliding Mode Control

The limitations of classical carrier wave-based pulse width modulation (PWM) techniques prevent themfromensuringgoodoutputqualityformulti-levelinverters.Thispaperproposesanewslidingmodecontrol(NSMC)method for controlling cascaded H-bridge multi-level inverters (CHB-MLIs) to improve the output quality of theinverter, reduce the common-mode (CM) voltage with high-order harmonics, and achieve stable and robustnesscontrolfortheCHB-MLIs.TheNSMCmethodmodulatesthePWMpulsesforthemulti-levelinverterbycomparingthecontrolsignalu(t)andthecomparatorlevelswithoutusingcarrierwavetechniques.Thisapproachfacilitatestheformation of a control signal u(t) which can be flexibly adjusted to optimize the generation of PWM pulses. Toreducethechatteringproblemaroundthesliding-modesurfaceathighfrequenciesandtoincreasespeedconvergence, the integral sliding-mode surface integrated with a continuous control law is used to design thecontroller. Additionally, a first-order low-pass filter (LPF) with a variable cut-off frequency is added to the controllawtoimprovestabilityandreduceoscillationcausedbyrapidandlargechangesintheloadcurrentamplitude.ThestabilityofthecontrolsystemisvalidatedbytheLyapunovtheory.Simulationandexperimentaltestswereperformedon the same cascaded H-bridge five-level inverter (CHB-5LI) with an R-L load. The results show that the proposedNSMC method is robust and performs better efficiently for multi-level inverter control systems. Furthermore, theoutput quality of the inverter is significantly improved compared to classical carrier wave-based PWM techniques,with a reduced CM voltage and fewer high-order harmonics, resulting in reduced losses and switching frequency. Therefore, the stability and strong robustness of the CHB-MLIs can b eachieved by the proposed NSMC method.

Practical Predefined-Time Output-Feedback Consensus Tracking Control for Multiagent Systems.

This article addresses the issue of output-feedback consensus control of multiagent systems under the directed topology and subject to bounded external disturbances. By employing a smooth time-varying function, a distributed practical predefined-time (PPT) observer is developed to estimate the reference trajectory for the entire team (i.e., the leader's state) and a practical preset-time extended-state observer is also proposed to estimate bounded disturbances and unmeasurable system states. Next, a novel continuous and nonsingular PPT consensus control law is designed on the basis of the observers. Furthermore, the designed control protocol can achieve PPT stability, that is, consensus tracking errors are enforced to a neighborhood around zero within a predetermined time, which can be specified a priori, independent of initial states of agents and/or any other design parameters. Finally, illustrative numerical examples, including a comparative one, are provided to demonstrate the performance of the present predefined-time control approach.

Adaptive barrier function‐based fractional‐order chattering‐free finite‐time control for uncertain chaotic systems

This study proposes the adaptive continuous barrier function as the fractional‐order control system using the terminal sliding mode control technique with chattering‐free property to stabilize chaotic systems that have unknown uncertainties. The important reason for using the fractional‐order controller is its greater flexibility than the integer‐order controller. Using adaptive approach and Lyapunov's stability theory, an adaptive continuous barrier fractional‐order chattering‐free finite‐time controller for a category of chaotic systems with the unknown uncertainties and external disturbances is presented. The suggested controller can stabilize the chaotic system excellently with a continuous and smooth control law even without knowing the boundaries and in the presence of unknown disturbances due to the model uncertainties. According to MATLAB simulation results, the high efficiency of the suggested control technique to control the chaotic systems in the attendance of unknown perturbations is obviously confirmed.

Design of Continuous Finite-Time Controller Based on Adaptive Tuning Approach for Disturbed Boost Converters

This research study proposes a continuous finite-time controller based on the adaptive tuning approach for the boost converters with unknown disturbances. A Lyapunov candidate function which contains an absolute function based on the fractional power of the sliding surface is employed to attain a smooth continuous control input. The recommended technique can eliminate the chattering phenomenon made by the sliding mode control signal and improve the control performance. Furthermore, the continuous adaptive-tuning control law is given to estimate the unknown bounds of exterior disturbances. The performance of the adaptive-tuned terminal sliding mode control law to the load variations and parametric uncertainties, and the input voltage, are studied in the MATLAB-Simulink environment. The obtained simulation results confirm the effectiveness of the suggested technique.

Chattering Free Sliding Mode Control and State Dependent Kalman Filter Design for Underground Gasification Energy Conversion Process

The fluctuations in the heating value of an underground coal gasification (UCG) process limit its application in electricity generation, where a desired composition of the combustible gases is required to operate gas turbines efficiently. This shortcoming can be addressed by designing a robust control scheme for the process. In the current research work, a model-based, chattering-free sliding mode control (CFSMC) algorithm is developed to maintain a desired heating value trajectory of the syngas mixture. Besides robustness, CFSMC yields reduced chattering due to continuous control law, and the tracking error also converges in finite time. To estimate the unmeasurable states required for the controller synthesis, a state-dependent Kalman filter (SDKF) based on the quasi-linear decomposition of the nonlinear model is employed. The simulation results demonstrate that despite the external disturbance and measurement noise, the control methodology yields good tracking performance. A comparative analysis is also made between CFSMC, a conventional SMC, and an already designed dynamic integral SMC (DISMC), which shows that CFSMC yields 71.2% and 69.9% improvement in the root mean squared tracking error with respect to SMC and DISMC, respectively. Moreover, CFSMC consumes 97% and 23.2% less control energy as compared to SMC and DISMC, respectively.

Velocity-free finite-time relative 6-DOF control for rigid spacecraft

This paper addresses the problem of spacecraft’s finite-time six-degree-of-freedom(6-DOF) tracking control without velocity measurements. To estimate the unavailable incorporating angular and translational velocities (called the dual angular velocity), a novel observer with a simple structure and finite-time stability is presented in the dual quaternion frame. Then, combining with the estimated dual angular velocity, a continuous velocity-free 6-DOF control law based on the terminal sliding mode theory is presented to achieve the relative pose tracking objective within finite time, where the specially designed parameter ensures its non-singularity. In addition, by designing the desired reference frame, the proposed control law can be employed to various missions. With consideration of the observation errors, a rigorous proof is provided to demonstrate the finite-time stability of the observer-alone and the observer-based control law. Two typical numerical simulations, hovering and circumnavigation, are carried out to verify the effectiveness of the proposed method.

Grammatical-Evolution-based parameterized Model Predictive Control for urban traffic networks

While Model Predictive Control (MPC) is a promising approach for network-wide control of urban traffic, the computational complexity of the, often nonlinear, online optimization procedure is too high for real-time implementations. In order to make MPC computationally efficient, this paper introduces a parameterized MPC (PMPC) approach for urban traffic networks that uses Grammatical Evolution to construct continuous parameterized control laws using an effective simulation-based training framework. Furthermore, a projection-based method is proposed to remove the nonlinear constraints that are imposed on the parameters of the parameterized control laws and to guarantee the feasibility of the solution of the MPC optimization problem. The performance and computational efficiency of the constructed parameterized control laws are compared to those of a conventional MPC controller in an extensive simulation-based case study. The results show that the parameterized control laws, which are automatically constructed using Grammatical Evolution, decrease the computational complexity of the online optimization problem by more than 80% with a decrease in performance by less than 10%.

Indirect adaptive fuzzy finite time synergetic control for power systems

Introduction. Budget constraints in a world ravenous for electrical power have led utility companies to operate generating stations with full power and sometimes at the limit of stability. In such drastic conditions the occurrence of any contingency or disturbance may lead to a critical situation starting with poorly damped oscillations followed by loss of synchronism and power system instability. In the past decades, the utilization of supplementary excitation control signals for improving power system stability has received much attention. Power system stabilizers (PSS) are used to generate supplementary control signals for the excitation system in order to damp low-frequency oscillations caused by load disturbances or short-circuit faults. Problem. Adaptive power system stabilizers have been proposed to adequately deal with a wide range of operating conditions, but they suffer from the major drawback of requiring parameter model identification, state observation and on-line feedback gain computation. Power systems are nonlinear systems, with configurations and parameters that fluctuate with time that which require a fully nonlinear model and an adaptive control scheme for a practical operating environment. A new nonlinear adaptive fuzzy approach based on synergetic control theory which has been developed for nonlinear power system stabilizers to overcome above mentioned problems. Aim. Synergetic control theory has been successfully applied in the design of power system stabilizers is a most promising robust control technique relying on the same principle of invariance found in sliding mode control, but without its chattering drawback. In most of its applications, synergetic control law was designed based on an asymptotic stability analysis and the system trajectories evolve to a specified attractor reaching the equilibrium in an infinite time. In this paper an indirect finite time adaptive fuzzy synergetic power system stabilizer for damping local and inter-area modes of oscillations for power systems is presented. Methodology. The proposed controller design is based on an adaptive fuzzy control combining a synergetic control theory with a finite-time attractor and Lyapunov synthesis. Enhancing existing adaptive fuzzy synergetic power system stabilizer, where fuzzy systems are used to approximate unknown system dynamics and robust synergetic control for only providing asymptotic stability of the closed-loop system, the proposed technique procures finite time convergence property in the derivation of the continuous synergetic control law. Analytical proofs for finite time convergence are presented confirming that the proposed adaptive scheme can guarantee that system signals are bounded and finite time stability obtained. Results. The performance of the proposed stabilizer is evaluated for a single machine infinite bus system and for a multi machine power system under different type of disturbances. Simulation results are compared to those obtained with a conventional adaptive fuzzy synergetic controller.

Optimal Safety for Constrained Differential Inclusions Using Nonsmooth Control Barrier Functions

For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs. Through the use of nonsmooth analysis tools, we show that a continuous optimal control law can be selected from a set-valued constraint capturing the system constraints and conditions guaranteeing safety using control barrier functions. Our results guarantee optimality and safety via a continuous state-feedback law designed using nonsmooth control barrier functions. An example pertaining to obstacle avoidance with a target illustrates our results and the associated benefits of using nonsmooth control barrier functions.

Design and Xilinx Virtex-field-programmable gate array for hardware in the loop of sensorless second-order sliding mode control and model reference adaptive system–sliding mode observer for direct torque control of induction motor drive

This article aims first to propose an improved space vector modulation–direct torque control in order to enhance the induction motor performance using: (1) a super-twisting controller and (2) a novel model reference adaptive system based on a sliding mode observer. Second, due to the complexity of the suggested control algorithm, this article deals also with a hardware implementation on a field-programmable gate array board. Indeed, the field-programmable gate array is mainly chosen to reduce the execution time, thanks to its parallel processing which significantly improves the quality of the control system by reducing the sampling period, and consequently the delays in the control loop. Besides, the super-twisting controller is proposed to enhance the speed regulation loop which is a second-order sliding mode control technique that uses a continuous control law to prevent the chattering phenomenon induced by the first-order sliding mode control technique. Moreover, the high performance control requires information about the rotor speed which can be obtained by a sensor. Generally, the use of the speed sensor increases the system cost and size, and reduces its system reliability. Therefore, a combination between a model reference adaptive system observer and a sliding mode observer is suggested for speed estimation and overcoming the sensitivity of the classical model reference adaptive system observer against uncertainties and stator resistance variations. The performance of the proposed space vector modulation--direct torque control--super-twisting controller with the model reference adaptive system--sliding mode observer algorithm of an induction motor is verified through simulation, hardware co-simulation and experimental validation utilizing a field-programmable gate array Virtex-5-ML507 board. The performance of the suggested sensorless control method is compared also with other recent published schemes.