Smooth Control Signal Research Articles

Energy-Aware Hierarchical Control of Joint Velocities

Nowadays, robots are applied in dynamic environments. For a robust operation, the motion planning module must consider other tasks besides reaching a specified pose: (self) collision avoidance, joint limit avoidance, keeping an advantageous configuration, etc. Each task demands different joint control commands, which may counteract each other. We present a hierarchical control that, depending on the robot and environment state, determines online a suitable priority among those tasks. Thereby, the control command of a lower-prioritized task never hinders the control command of a higher-prioritized task. We ensure smooth control signals also during priority rearrangement. Our hierarchical control computes reference joint velocities. However, the underlying concepts of hierarchical control differ when using joint accelerations or joint torques as control signals instead. So, as a further contribution, we provide a comprehensive discussion on how joint velocity control, joint acceleration control, and joint torque control differ in hierarchical task control. We validate our formulation in an experiment on hardware.

Adaptive Fuzzy Filter-based L 1 Adaptive Controller Design for Electromechanical Actuator Containing Uncertainties and Disturbances

Conventional L 1 adaptive controller utilizes high adaptation gain to quickly adapt time varying uncertainties and disturbances. However, it contaminates the control signal with high frequency components. To eliminate this high frequency signal, it uses a low pass filter with fixed structure. Yet, the main problem with this fixed structured filter is that it may cancel the estimated values of uncertainties and disturbances along with the high frequencies. To overcome this problem, in this research work, an adaptive fuzzy low pass filter is proposed in place of the fixed structured filter of the L 1 adaptive controller. In this proposed research work, the filter changes its structure according to the time varying uncertainties and disturbances. Hence, the contributory part of this work is that the proposed adaptive fuzzy filter efficiently cancels out high frequency components without nullifying the estimated values of uncertainties and disturbances from the control signal. The stability of the proposed adaptive fuzzy filter-based L 1 adaptive controller is guaranteed analytically. The proposed method is employed on an electromechanical actuator, viz., DC motor experimental setup to validate its effectiveness. Adequate cancellation of high frequency signal incurs smooth control signal which in turn provides lower control energy.

Analytical design of modified Smith predictor for second-order stable time delay plants incorporating a zero

Simplified control tuning not only enhances engineers' proficiency in control theory and its application but also contributes to their skill development. This study focuses on the control of stable second-order plus time delay (SOPTD) plants incorporating a zero, by employing a modified Smith predictor structure. A forward path PID controller and a PID controller with a lead/lag filter in the feedback path contribute to the proposed control system. The PID controller determines the set-point tracking. The load disturbance rejection is influenced by both the PID and lead/lag filter. Each controller is simply designed using pole placement, while considering a tuning parameter to make a balance between performance and robustness. Filtering of the set-point signal is implemented to enhance its response. To assess the effectiveness of the proposed technique, the study involves examining a SOPTD plant and either a negative or a positive zero. Simulation and comparison analysis show that the proposed controller is appropriate for industrial usage since it quickly tracks the set-point and efficiently rejects disturbances, resulting in a smooth control signal. Furthermore, robustness tests reveal its satisfactory degree of robustness against model parameter uncertainties. In summary, the proposed approach is straightforward and outperforms recently published design methodologies in terms of both performance and robustness.

Enhanced control of double integrating plus time delay systems using a two‐degree‐of‐freedom Smith predictor

AbstractThis article presents a novel control approach using a two‐degree‐of‐freedom (2‐DOF) Smith predictor structure for double integrating plus time delay plants. The PD and PID controllers, integral components of the Smith predictor scheme, serve distinct roles in the control process. The PD controller is responsible for set‐point tracking, while both PD and PID controllers contribute to the rejection of load disturbances. Each controller is designed using the pole placement technique, with an appropriate tuning parameter established to balance performance and robustness effectively. A low‐pass filter is incorporated to improve the response of the set‐point signal by attenuating high‐frequency noise. The proposed method's effectiveness is compared with Skogestad internal model control, a well‐known PID tuning method, to benchmark performance improvements and demonstrate the advantages of the 2‐DOF Smith predictor approach. Simulation and comparison analysis demonstrates that the proposed controller setting is suitable for industrial applications due to its quick set‐point tracking, effective load disturbance rejection, and smooth control signal. The study highlights the practical benefits of the 2‐DOF Smith predictor in enhancing industrial control system performance and suggests directions for future research, including experimental validation and robustness analysis under varying system parameters.

A nonlinear disturbance observer for sliding mode control of surge in centrifugal compressors via TCV actuator

Surge is a form of dynamic instability created as an unstable pattern in the flow of fluid and can severely affect centrifugal compressor performance by causing fluctuations in flow and pressure parameters. Due to the heavy and costly damage that the surge may cause in various industrial processes such as petrochemical plants, it is necessary to design an appropriate control system to reduce the effect of this phenomenon. The problem of active surge control of a centrifugal compressor using the throttle control valve (TCV) in the presence of compressor parametric uncertainties as well as large demands on upstream and downstream loads is investigated in this work. The control objective was to design a robust control system that can stabilize the compressor over a wide operating range without knowing the upper bound for the uncertainties and load demand. The controller should also react quickly by generating a smooth control signal without saturating the control input. These objectives are achieved by designing a sliding mode controller along with a nonlinear disturbance observer. The performance of the proposed disturbance observer-based controller is evaluated under various operational and load conditions and the results are compared against fuzzy type 1, conventional sliding mode, and wavelet-based neural network robust adaptive controllers. The results show that the proposed method can tolerate large disturbances without any knowledge on the upper bound of the incident disturbance, both on the downstream pressure and upstream mass flow which is highly desirable in practice. The comparative study proves the efficacy of the proposed method using various performance measures. The study also confirms the superior robust performance and stability of the proposed method in front of matched and mismatched disturbances as well as model uncertainties especially close to the instability boundary. Although choosing a TCV actuator has made the control system design easier, the sensitivity of the control valve to flow coefficient and zero calibration under different operating ranges of the compression system is studied carefully and some recommendations for the users are provided.

Tillage depth regulation system via depth measurement feedback and composite sliding mode control: A field comparison validation study

The existing methodologies employed for the quantification and regulation of tractor’s tillage depth present considerable shortcomings, primarily characterized by their low accuracy and poor disturbance rejection proficiency in complex agricultural terrains. In this study, we present a sophisticated feedback control strategy designed to mitigate these challenges. Our innovative approach hinges on calculating tillage depth from the alignment of the tractor’s hydraulic lifting arm, achieved by employing a mechanical angle sensor. This sensor adeptly gages the angle of the lifting arm, aligning it with the tillage angle of the pull rod and the implement’s angle, resulting in a robust relational model correlating the lifting arm angle with the tillage depth. This pioneering method amalgamates the accuracy inherent in the static model, derived from the tillage angle-based depth measurement, with the dynamic stability afforded by the mechanical ascertainment of the lifting arm angle. In conjunction, we introduce a Hybrid Extended State Observer-Based Backstepping Sliding Mode Controller (HESO-BacksteppingSMC). The HESO is instrumental in estimating unmeasured state variables and lumped disturbances, utilizing the system’s output feedback signal. Our control frame component capitalizes on the fast power-reaching law to yield a continuously smooth control signal, effectively eradicating the conventional chattering phenomenon inherent in controllers and amplifying its functional applicability. Theoretical evaluations affirm the uniformly and ultimately bounded stability of the errors associated with our proposed observer and controller, underscoring their robustness. The superior performance of our proposed tillage depth measurement and control methodology has been corroborated through a series of comprehensive simulation and field plowing trials, attesting to its precision and reliability in complex agricultural settings.

Command-Filter-Based Region-Tracking Control for Autonomous Underwater Vehicles with Measurement Noise

This paper investigates the AUV region-tracking control problem with measurement noise and transient and steady-state constraints. To achieve the fluctuation of AUV tracking error within an expected region while satisfying the transient and steady-state performance constraints, this paper proposes an improved nonlinear tracking error transformation method. This method converts the tracking error into a new virtual error variable through nonlinear conversion, thus transforming the above performance requirements for the tracking error into boundedness requirements for the new virtual error variable. In addition, aiming at the problem of measurement noise causing strong fluctuation of the control signal, this paper proposes a finite-time AUV control method based on a two-stage command filter. This method utilizes a finite-time sliding mode differentiator to filter the virtual control signal during the derivation of the control law using the backstepping technique. In light of the signal loss incurred by two-stage filtering and its potential impact on system stability, a finite-time compensator is designed to compensate the signal loss and achieve finite-time stability of the closed-loop system. Finally, simulations conducted using ODIN AUV demonstrate that the proposed method exhibits smooth control signal and low energy consumption characteristics. Furthermore, the tracking error meets the requirements for both transient and steady-state performance, as well as regional tracking.

Time-optimal trajectory planning for a rigid formation of nonholonomic mobile platforms

AbstractThis paper presents a method for planning time-optimal trajectories for a formation of multiple nonholonomic (heavy duty) platforms (HDPs) to cooperatively transport an object to a specified pose. The first part addresses the mobile platforms themselves while the second part provides a trajectory planning approach derived from the well-known virtual leader approach. In order to ensure proper transport of the shared payload, the vehicles are modeled individually, resulting in a formation control problem. The goal of the optimization process is to minimize a cost function that balances time optimality, smooth control signals, and formation rigidity. The optimal control problem (OCP) takes into account the kinematics of the vehicles as well as their physical limitations. It is solved by using a multiple shooting method, which yields the desired trajectories for all vehicles while ensuring smooth control signals. The paper includes optimization results for several scenarios involving two and three HDPs together with various target poses, demonstrating the effectiveness of the proposed method.

Distributed adaptive fault tolerant formation control for multiple underwater vehicles: Free-will arbitrary time approach

This note examines the distributed free-will arbitrary time (FwAT) fault-tolerant formation control for heterogeneous multiple autonomous underwater vehicles (AUVs) operating under actuator faults, uncertainties, and exogenous disturbances. The established formation control protocol is free from initial conditions and provides higher tracking accuracy, singularity-free and smooth control signal, while the convergence time of the system is non-conservative. An adaptive nonsingular sliding mode is then developed in which the bound of lumped uncertainty is not necessary to know in advance. Due to the need for a rapid and immediate response in fixed-time control, the actuators are prone to saturation as a result of the high control torque required and to overcome this issue, an input saturation compensator is designed and incorporated into the control framework. Stability analysis under the developed control law is thoroughly performed using the Lyapunov stability theory. Finally, simulations and comparisons are demonstrated in order to verify the effectiveness of the proposed distributed formation control algorithm for a group of AUVs.

Reactive Symbolic Planning and Control in Dynamic Adversarial Environments

Satisfying both safety and reachability requirements in dynamic adversarial environments is very challenging, particularly when little or no information about the dynamics and intentions of the adversarial objects is available. Therefore, this paper addresses the problem of path planning and control of autonomous vehicles in a dynamic adversarial reach-avoid scenario with two non-cooperative vehicles and their competitive objectives: &#x201C;reaching a target and avoiding the other vehicle&#x201D; for one of them, called attacker, and &#x201C;protecting the target and capturing the opponent vehicle&#x201D; for the other one, called defender. In the proposed solution, first, a discrete version of the problem is formulated and solved using Linear Temporal Logic, temporal games, and <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>-calculus to construct winning discrete strategies that guarantee safety and reachability. A comprehensive discussion on the existence, correctness, and complexity analysis of the solution is also provided. Finally, a novel correct-by-design hybrid controller is designed to generate smooth control signals that preserve the satisfaction of safety and reachability.

Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation. The considered system can depict the behavior of a large class of engineering systems, such as vehicular systems, robot manipulators and satellites. All these systems are often characterized by highly nonlinear characteristics, heavy modeling uncertainties and unknown perturbations, therefore, accurate-model-based nonlinear control approaches become unavailable. Motivated by the challenge, a reinforcement learning (RL) adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics. The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error (RISE) control approach. Different from a classical RISE control law, a tanh(·) function is utilized instead of a sign(·) function to acquire a more smooth control signal. The developed controller requires very little prior knowledge of the dynamic model, is robust to unknown dynamics and exogenous disturbances, and can achieve asymptotic output tracking. Eventually, co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom (3-DOF) manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

Integral Backstepping Control Algorithm for a Quadrotor Positioning Flight Task: A Design Issue Discussion

For quadrotor control applications, it is necessary to rely on attitude angle changes to indirectly achieve the position trajectory tracking purpose. Several existing literature studies omit the non-negligible attitude transients in the position controller design for this kind of cascade system. The result leads to the position tracking performance not being as good as expected. In fact, the transient behavior of the attitude tracking response cannot be ignored. Therefore, the closed-loop stability of the attitude loop as well as the position tracking should be considered simultaneously. In this study, the flight controller design of the position and attitude control loops is presented based on an integral backstepping control algorithm. This control algorithm relies on the derivatives of the associated virtual control laws for implementation. Examining existing literature, the derivatives of the virtual control law are realized approximated by numerical differentiations. Nevertheless, in practical scenarios, the numerical differentiations will cause the chattering phenomenon of control signals in the presence of unavoidable measurement noise. The noise-induced control signals may further cause damage to the actuators or even diverge the system response. To address this issue, the analytic form for the derivative of the virtual control law is derived. The time derivative virtual control law is analyzed and split into the disturbance-independent compensable and disturbance-dependent non-compensable terms. By utilizing the compensable term, the control chattering due to the differentiation of the noise can be avoided significantly. The simulation results reveal that the proposed control algorithm has a better position tracking performance than the traditional dual-loop control scheme. Meanwhile, a relatively smooth control signal can be obtained for a realistic control algorithm realization. Simulations are provided to illustrate the position tracking issue of a quadrotor and to demonstrate the effectiveness of the proposed compromised control scheme.

An integral sliding‐mode parallel control approach for general nonlinear systems via piecewise affine linear models

AbstractThe fundamental problem of stabilizing a general nonaffine continuous‐time nonlinear system is investigated via piecewise affine linear models (PALMs) in this article. A novel integral sliding‐mode parallel control (ISMPC) approach is developed, where an uncertain piecewise affine system (PWA) is constructed to model a nonaffine continuous‐time nonlinear system equivalently on a compact region containing the origin. A piecewise sliding‐mode parallel controller is designed to globally stabilize the PALM and, consequently, to semiglobally stabilize the original nonlinear system. The proposed scheme enjoys three favorable features: (i) some restrictions on the system input channel are eliminated, thus the developed method is more relaxed compared with the published approaches; (ii) it is convenient to be used to deal with both matched and unmatched uncertainties of the system; and (iii) the proposed piecewise parallel controller generates smooth control signals even around the boundaries between different subspaces, which makes the developed control strategy more implementable and reliable. Moreover, we provide discussions about the universality analysis of the developed control strategy for two kinds of typical nonlinear systems. Simulation results from two numerical examples further demonstrate the performance of the developed control approach.

An Adaptive Control Methodology for Spacecraft Attitude Tracking Under Model and Environmental Uncertainties

This study investigates the attitude tracking problem for rigid spacecraft under model and environmental uncertainties. Two different control laws are separately developed and combined. First, based on a nominal attitude dynamic model assuming no uncertainty, the first controller is developed that exactly tracks a prespecified attitude reference trajectory with minimized control cost. The designer can generate this reference to prescribe desired performance specifications such as the maximum convergence time and overshoot. Next, an uncertain attitude dynamic system is considered, and the second controller is designed and added so that the controlled system can successfully track the predesigned reference trajectory with a user-specified tolerance even subject to uncertainty whose bounds are unknown. Compared to existing adaptive control schemes, the proposed approach possesses a very simple structure with a small number of control parameters and is not computationally intensive, making it more attractive for practical implementation. The proposed control laws generate smooth control signals and any information about the uncertainty bound is not needed in its design. Simulation results are provided to demonstrate the practical feasibility of the proposed approach, where reorientation/slew maneuvers of a large spacecraft are considered. The effects of limitations on the control torques are also investigated to show the effectiveness of the control methodology developed herein.

Dynamic Sliding Mode Control of DC-DC Converter to Extract the Maximum Power of Photovoltaic System Using Dual Sliding Observer

This paper concerns the maximum power extraction of a photovoltaic generator system (PGS). The PGS consists of single photovoltaic (PV) cells. To improve the efficiency of a PGS, it is necessary to work within its maximum power point (MPP). In a PGS, output power is dependent on solar irradiance and the operating temperature and, therefore, MPP would be varied. To address this problem, a converter should be placed after the PGS and a smooth control signal should be used to adjust its duty cycle. The other challenge of a total system, i.e., PGS and converter, is the uncertainty involved. To overcome this uncertainty, a dynamic sliding mode control (SMC) can be used to regulate the smooth duty cycle. The low-pass integrator before the system can remove the chattering in dynamic SMC. However, due to the integrator, the states of the system increase and, hence, we propose a dual sliding observer (DSO) to estimate this added state. For a reliable comparison with the conventional SMC, the same proposed DSO can be applied in both dynamic and conventional SMC. The provided comparison shows the effectiveness of dynamic SMC in chattering suppression and real implementation with respect to conventional SMC.

Development of autonomous vehicle lateral control using time-varying asymmetric barrier Lyapunov function via ADRC approach

In a surface vehicle ride, the passenger’s comfort is desirable, ensuring safety under various tight constraints. To consider this requirement, this article has proposed a lateral control for autonomous vehicle considering the lateral offset error constraints. A reduced-order dynamics of the vehicle has been considered for improving and easy implementation of backstepping. A nonlinear control has been developed by utilizing the Time-varying Asymmetric Barrier Lyapunov Function via the Active Disturbance Rejection Control (ADRC) approach. The Extended State Observer, a component of applied ADRC, estimates all unknown system states as well as the unknown disturbance. The desired trajectories (smooth and non-smooth) based on the yaw rate profile have been synthesized to test the performance of the vehicle. Simulation results are presented to show the effectiveness of the proposed closed-loop control strategy. The vehicle performance has been compared using the proposed method, the conventional Quadratic Lyapunov Function and Symmetric Barrier Lyapunov Function based control. The proposed control provides a smoother control signal, small tracking error and robustness in presence of hard road constraints for smooth/non-smooth vehicle motion.

A Robust Backstepping Sliding Mode Controller with Chattering-Free Strategy for a Swarm of Drones

This paper presents a robust controller for a swarm of drones that are subjected to external disturbances. Integrating a fuzzy-based system in the sliding mode control technique, a chattering-free controller is proposed for the trajectory tracking of a drone. Furthermore, the formation controller for a group of drones is developed using the Backstepping control design technique. The integration of a fuzzy rule-based system in the sliding mode tracking controller enables overcoming the inherent chattering problem due to discontinuous switching function in the sliding mode control technique and provides smooth and chattering-free control signals. The asymptotic stability of the overall system is shown using the Lyapunov stability theory. Finally, the control design performance is evaluated using numerical simulations.

Pitch actuator fault-tolerant control of wind turbines based on time delay control and disturbance observer

This paper addresses an Active Fault-tolerant Control (AFTC) based on Time Delay Control (TDC) and nonlinear disturbance observer for wind turbines, exposed to pitch system sensor and actuator faults, uncertainties and exogenous disturbances. The developed adaptive TDC uses Time Delay Estimation (TDE) to estimate parametric uncertainties and provides an appealing model-free structure. TDE is also applied as an online fault estimation algorithm. Then, an adaptive robust control is designed for TDC using a combination of adaptive sliding mode with novel adaptation laws and a nonlinear disturbance observer (NDO). Through estimating the exogenous disturbances, the control gain of discontinuous term of sliding mode control law is kept small which in turn results in reduced chattering. Thus, the proposed structure provides smooth control signals and can isolate and accommodate the effect of faults. Stability analysis is conducted based on Lyapunov Theory. To verify the validity of the proposed structure, the controller is implemented in FAST environment. Simulation results reveal the effectiveness of the proposed controller in the presence of different faults, as well as uncertainties and turbulent wind field, compared to two existing methods, gain schedule PI (GSPI) and nonlinear PI (N-PI) control schemes.

RISE-based backstepping control design for an electro-hydraulic arm system with parametric uncertainties

In this paper, a self-tuning Robust Integral of Sign of Error (RISE)-based backstepping controller is designed for an electro-hydraulic arm system with a fourth-order system model. The RISE controller, which constitutes the robust part of the control rule, is fused with a backstepping control strategy to cope with model-based and parametric uncertainties. Different from a classical RISE control rule, a function is used instead of a function to obtain a more smooth control signal. All the gains in the RISE controller are tuned by using continuous update rules. The efficiency of the controller is demonstrated by conducting numerical simulations.

Backstepping-Based Adaptive Control of a Class of Uncertain Incommensurate Fractional-Order Nonlinear Systems With External Disturbance

Normally, achieving asymptotic convergence in the presence of unknown arbitrarily bounded external disturbance requires noncontinuous control signals. In this article, an adaptive backstepping controller for a class of incommensurate fractional-order nonlinear systems with parametric uncertainties and external time-varying disturbance is proposed to realize asymptotic perfect output tracking. Appropriate adaptive laws are designed to deal with the uncertainties and unknown bounded disturbance. In the designed adaptive backstepping control scheme, an auxiliary function is adopted to obtain a smooth control signal. It is theoretically shown that asymptotic output tracking to a given reference signal is achieved while ensuring global system stability in the sense that all the closed-loop signals are bounded. Simulation and experimental studies demonstrate the effectiveness of the proposed backstepping control scheme.