Outer Loop Research Articles

Adaptive Sliding Mode Control for Trajectory Tracking of Quadrotor Unmanned Aerial Vehicles Under Input Saturation and Disturbances

This paper addresses the challenging issue of trajectory tracking for uncertain quadrotor unmanned aerial vehicles (UAVs), particularly under the constraints of input saturation and external disturbances. It introduces adaptive laws for managing uncertainties in mass and inertia moments without requiring prior knowledge, ensuring effective control even with varying system parameters. To counteract the effects of input saturation, the study incorporates an auxiliary system designed to compensate for these limitations. Additionally, a disturbance observer (DO) is utilized to manage and mitigate the impact of time-varying external disturbances. The proposed control strategy integrates a sliding mode adaptive control approach with an inner–outer loop structure, enhancing robustness and adaptability. Numerical simulations demonstrate the effectiveness of the designed control strategy.

Effects of discharge parameters on plasma acceleration and transmission characteristics of a coaxial gun operated in gas-prefilled mode

The effects of discharge parameters on the discharge process and plasma transport characteristics of a coaxial gun in the gas-prefilled mode are studied. The plasma optical intensity and ejection velocity are measured by photodiodes, the optical emission spectrum is taken by a spectroscopic system, and the plasma evolution in the transport process is captured by a high-speed camera. The plasma acceleration characteristics under different discharge parameters show that the velocity and electron density of the ejection plasma are mainly determined by the pre-filled pressure and discharge current, which is consistent with the snowplow model. The kinetic energy of ejection plasma can be significantly increased by reducing the outer loop inductance, which is conducive to increasing the energy utilization efficiency. The time-varying images of plasma radiation and the plasma density at different transport locations illuminate the transmission characteristics of coaxial gun discharge plasma. The results show that the snowplow effect continues to play a role in the plasma transport process, and the plasma accumulation is induced by the combination of shock wave compression. The current-driven magneto hydrodynamics instability occurs during the transport process, and the luminous signal of the plasma current sheet oscillates periodically. In addition, the plasma impact effect is obvious and the gas retarding effect is enhanced with the increase in the gas pressure. These results give us a more comprehensive view of the coaxial gun discharge process and plasma transport and provide a certain reference for optimizing the parameters selection and physical design of coaxial gun discharge plasma characteristics.

Hybrid trajectory tracking control of wheeled mobile robots using predictive kinematic control and dynamic robust control

AbstractTrajectory tracking control of wheeled mobile robots (WMRs) is still a remarkable problem for many applications. In the present paper, a hybrid control is presented based on dynamic and kinematic equations of motion for wheeled mobile robots in the presence of the sum of the external disturbances and parametric uncertainty. The designed control for the WMR utilizes control and guidance to reach the reference path. In many studies, a control strategy is normally employed for WMR. However, in this study, hybrid control was used for the mentioned purpose. Akin to other studies, the kinematic control scheme here was based on the predictive control, and the dynamic control scheme was designed based on the robust control. Therefore, in this article, having introduced the kinematic model, a nonlinear predictive control was proved and designed. In the next step, a finite‐time integral type terminal sliding mode control (FITSMC) was designed based on the nonlinear dynamic model in order to automatically adjust the control gain and eliminate online disturbances and destructive chattering phenomena completely. In particular, a finite‐time disturbance observer was designed to estimate the external disturbances. The proof of the new proposed control scheme was presented using Lyapunov stability theory and numerical results. The mentioned integrated scheme, including predictive control (outer loop) and nonlinear adaptive control (inner loop), ensures the convergence and optimal tracking performance of all signals, as a result of which the tracking errors can arbitrarily converge to the origin in a finite time. In the final step, the simulation results were presented to show the effectiveness of the proposed scheme using MATLAB software, and the introduced control design was compared with a similar controller quantitatively and qualitatively.

Tuning of modern speed drives using IFOC: A case study for a five-phase induction machine

Electric machines have existed since the beginning of the 19th century. Although variable-speed drive technology has evolved considerably during the last years, the indirect field-oriented control technique has been in use as a standard control method since the 1960s, using an outer speed loop and an inner current loop. This paper deals with the non-trivial problem of tuning the outer speed controller of modern variable-speed drives, where experimental results are provided to show the need for new tuning methods. The influence of non-modeled effects on the performance of the drive is illustrated considering the dynamical effect of the mechanical speed sensing procedure using optical devices. This effect has not been generally considered. However, it is shown that it has a notable effect on tuning for high performance drives. This is especially true when considering some figures of merits of relevance for drives, such as the torque ripple. A Pareto analysis is proposed to reveal trade-offs between typical figures of merit to establish new tuning methods. To focus our contribution, a five-phase induction drive is considered as the case study, using a finite-state model predictive controller for the stator current control and PI regulators for the outer speed control loop.

Variable Admittance Control of High Compatibility Exoskeleton Based on Human–Robotic Interaction Force

The wearable exoskeleton system is a typical strongly coupled human–robotic system. Human–robotic is the environment for each other. The two support each other and compete with each other. Achieving high human–robotic compatibility is the most critical technology for wearable systems. Full structural compatibility can improve the intrinsic safety of the exoskeleton, and precise intention understanding and motion control can improve the comfort of the exoskeleton. This paper first designs a physiologically functional bionic lower limb exoskeleton based on the study of bone and joint functional anatomy and analyzes the drive mapping model of the dual closed-loop four-link knee joint. Secondly, an exoskeleton dual closed-loop controller composed of a position inner loop and a force outer loop is designed. The inner loop of the controller adopts the PID control algorithm, and the outer loop adopts the adaptive admittance control algorithm based on human–robot interaction force (HRI). The controller can adaptively adjust the admittance parameters according to the HRI to respond to dynamic changes in the mechanical and physical parameters of the human–robot system, thereby improving control compliance and the wearing comfort of the exoskeleton system. Finally, we built a joint simulation experiment platform based on SolidWorks/Simulink to conduct virtual prototype simulation experiments and recruited volunteers to wear rehabilitation exoskeletons to conduct related control experiments. Experimental results show that the designed physiologically functional bionic exoskeleton and adaptive admittance controller can significantly improve the accuracy of human–robotic joint motion tracking, effectively reducing human–machine interaction forces and improving the comfort and safety of the wearer. This paper proposes a dual-closed loop four-link knee joint exoskeleton and a variable admittance control method based on HRI, which provides a new method for the design and control of exoskeletons with high compatibility.

Optimized Trajectory Tracking for ROVs Using DNN + ENMPC Strategy

This study introduces an innovative double closed-loop 3D trajectory tracking approach, integrating deep neural networks (DNN) with event-triggered nonlinear model predictive control (ENMPC), specifically designed for remotely operated vehicles (ROVs) under external disturbance conditions. In contrast to single-loop model predictive control, the proposed double closed-loop control system operates in two distinct phases: (1) The outer loop controller uses a DNN controller to replace the LMPC controller, overcoming the uncertainties in the kinematic model while reducing the computational burden. (2) The inner loop velocity controller is designed using a nonlinear model predictive control (NMPC) algorithm with its closed-loop stability proven. A DNN + ENMPC 3D trajectory tracking method is proposed, integrating a velocity threshold-triggered mechanism into the inner-loop NMPC controller to reduce computational iterations while sacrificing only a small amount of tracking control performance. Finally, simulation results indicate that compared with the ENMPC algorithm, NMPC + ENMPC can better track the desired trajectory, reduce thruster oscillations, and further minimize the computational load.

A Lyapunov Theory-Based SEIG–STATCOM Voltage Regulation Control Strategy

To improve the voltage regulation of asynchronous generators during load switching, a Lyapunov-based control strategy has been proposed to stabilize the generator’s voltage by connecting a static synchronous compensator. By constructing a Lyapunov function from the mathematical model, the error tracking problem is transformed into a global asymptotic stability problem of the Lyapunov function at the equilibrium point. The outer loop linearizes the direct current (DC) voltage control process, while the inner loop replaces integral terms with differential terms. The proposed Lyapunov method achieves linearized voltage control with a quadratic outer loop structure and the inner loop differential structure exhibits a shorter transient process, outperforming traditional methods. Simulation and experimental tests were then used, where the latter was a down-scale laboratory prototype experiment. Compared to traditional (voltage-oriented control) VOC, the outer loop (Lyapunov-function-based control) LBC reduces the DC voltage transient processes by approximately 9.4 milliseconds, while the inner loop LBC reduces both alternating current (AC) and DC voltage transient processes by approximately 2.6 ms and 8.7 ms, respectively.

Networked Control of a Small Drone Resilient to Cyber Attacks

With increasing advances in networked systems and networked control systems in everyday life, the problem of cybersecurity becomes crucial. Moreover, in some applications like small UAVs, the safety and integrity of the system and its surroundings are highly susceptible to cyberattacks. In this context, the current paper proposes a resilient networked control approach. The control structure is split into an inner and an outer loop. The outer position control loop uses measurements from motion cameras connected to a remote computer, while the commands are sent through the network. We consider the resilience problem for two types of cyberattacks: denial of service (DoS), emulated as an increase in the network transmission delay, and man in the middle (MitM), emulated as additive input disturbances. The mitigation for the DoS attack is performed through the help of a reference governor (RG), which uses the delay estimates and the system’s model to predict future safety violations and adapts the reference accordingly. The MitM attack is mitigated by an unknown input disturbance observer (UIDO) together with a RG. Experimental results on a Parrot Mambo drone show that both types of attacks are rejected successfully, ensuring a safe and stable flight.

Modulation and control scheme for DC-link current minimization of an improved current source inverter

The traditional three-phase current source inverter (CSI) cannot maintain a constant DC-link current, the charging and discharging process under different operating modes will lead to the DC-link current being discontinuous or continuously increasing. To address this issue, the topology of CSI is improved, and a modulation scheme without additional losses is proposed in this paper to control the DC-link current. Then, based on the analysis of the DC-link ripple under all switching states, the calculation expression for the optimal reference of the DC-link current is derived, under the premise of meeting the current demand for the AC load, the minimum loss and harmonic distortion can be obtained by reducing the DC-link current. Finally, the math model of the AC-side is established, and the closed-loop control system including the voltage outer loop and the current inner loop is designed. The feasibility and correctness of the proposed modulation strategy and control method are validated by the simulation and experimental results, the minimum and stable DC-link current with the ripple below ± 1 A is obtained, and the high steady-state and dynamic control performances are achieved. The total harmonic distortion of the load current is less than 4 %, and the dynamic response time is 0.3 s.

An enhanced proportional topology optimization method with new density filtering weight function for the minimum compliance problem

This article proposes an enhanced proportional topology optimization (EPTO) method to solve the structural topology optimization problem of minimizing compliance under material volume constraints. In the proposed method, a new filtering weight function based on the improved Heaviside threshold function is adopted to filter element density during the optimization process. The optimization process of the EPTO method consists of an inner loop and an outer loop. In the inner loop, density distribution is modified in combination with a new filtering weight function. By locally averaging the weighted element compliance, an improved density distribution function in the inner loop is put forward to make the topology configuration of the optimized structure more reasonable. In addition, the projection method is used to reduce the number of intermediate density elements, thereby obtaining optimization results with clear boundaries. In the outer loop, a new termination criterion is adopted, which terminates the optimization process by determining that the relative error of the objective function in several consecutive iterations is less than the specified value. The effectiveness and efficiency of the proposed method are demonstrated through several numerical examples involving two-dimensional (2D) and three-dimensional (3D) topology optimization problems. The results of numerical examples show that the proposed method can not only accelerate the convergence of optimization iterations, but also obtain optimized structures with smaller objective function values and better topology configurations. HIGHLIGHTS A new density filtering weight function is proposed based on an improved Heaviside threshold function. An improved inner loop density distribution formula is proposed by combining a new filtering weight function. Using projection based methods to suppress the appearance of intermediate density elements. Verify the effectiveness of the proposed algorithm by comparing the optimization results with existing algorithms such as top88 and PTO.

Real-time hybrid testing using iterative control for periodic oscillations

Real-time hybrid testing is a method in which a substructure of the system is realized experimentally and the rest numerically. The two parts interact in real time to emulate the dynamics of the full system. Such experiments, however, are often difficult to realize as the actuators and sensors, needed to ensure compatibility and force–equilibrium conditions at the interface, can seriously affect the predicted dynamics of the system and result in stability and fidelity issues. The traditional approach of using feedback control to overcome the additional unwanted dynamics is challenging due to the presence of an outer feedback loop, passing interface displacements or forces to the numerical substructure. We, therefore, advocate for an alternative approach, removing the problematic interface dynamics with an iterative scheme to minimize interface errors, thus, capturing the response of the true assembly. The technique is examined by hybrid testing of a bench-top four-storey building with different interface configurations, where using conventional hybrid measurement techniques is very challenging. A case where the physical part exhibits nonlinear restoring force characteristics is also considered. These tests show that the iterative approach is capable of handling even scenarios which are theoretically infeasible with feedback control.

Fault-tolerant model predictive sliding mode control for trajectory replanning of multi-UAV formation flight

To tackle the trajectory-following problem of multiple unmanned aerial vehicles (UAVs) characterized by high non-linearity and strong coupling, this paper methodologically separates the dynamics of fixed-wing UAVs into two subsystems and designs appropriate controllers for each loop. Unlike previous works, the proposed multi-purpose method simultaneously accounts for constraints, computational time, external disturbances, and actuator faults. The inclusive structure of the proposed strategy is as follows: Firstly, in the outer loop, by employing the high precision and constraint-handling attributes of nonlinear model predictive control (NMPC), the trajectories of the agents are guided to their reference positions while considering spatial limitations, including no-fly zone evasion and inter-vehicle collision evasion. Then, the optimal states of the inner loop are designed. Secondly, in the inner loop, a fault-tolerant sliding mode predictive control (SMPC) is reconfigured to accommodate identified actuator faults and follow the optimal states produced by NMPC. The effectiveness of the suggested algorithm is verified through a series of simulation results. Comparison simulation results substantiate the ascendancy of the suggested dual-loop method over the NMPC trajectory replanning algorithm.

Super Twisting Sliding Mode Control of Four-Phase Interleaved Boost Converter

This paper presents a novel control method that integrates super-twisting sliding mode (STSM) voltage control with proportional-integral (PI) current control for a four-phase interleaved boost converter (IBC) in fuel cell applications. The STSM control, employed in the outer voltage loop, provides robust voltage regulation by generating precise reference currents for each phase. The conventional PI control in the inner current loop utilizes these reference currents to generate pulse width modulation (PWM) signals for each phase. The effectiveness of the proposed control strategy is evaluated through comprehensive simulation studies in MATLAB/Simulink, demonstrating an improvement in dynamic performance and enhanced robustness compared to conventional methods. Quantitative analysis shows that the output voltage quickly rises to the reference voltage within approximately 0.25 seconds in the proposed STSM-PI control method and improves transient response by 16 times compared to the conventional PI-PI method. This integrated STSM-PI control strategy offers significant advancements in reliability and efficiency making it a promising solution for high-performance fuel cell power systems.

Analysis of Influence of Grid-Following and Grid-Forming Static Var Generators on High-Frequency Resonance in Doubly Fed Induction Generator-Based Wind Farms

In Doubly Fed Induction Generator (DFIG)-based wind farms with Static Var Generators (SVGs), high-frequency resonance will be more like to occur when an unloaded cable is put into operation, which will threaten the stable operation of the wind farm. To address this issue, the influence of power outer loops on the impedance of grid-connected inverters is considered. Based on harmonic linearization, theoretical models for the sequence impedances of DFIGs, Grid-following (GFL) SVGs, and Grid-forming (GFM) SVGs are established. The correctness of the three models is verified by impedance scanning using the frequency sweep method. Through a comparative analysis of these sequence impedances, it is found that unlike the GFM SVG (which exhibits inductive impedance), the GFL SVG exhibits capacitive impedance in the high-frequency band, which leads to negative damping characteristics in the high-frequency band for the wind farm system with the grid-following SVG; thereby, the risk of high-frequency resonance also increases accordingly. On the contrary, GFM control adopted by SVGs can effectively eliminate the negative damping region in the high-frequency band for wind farms to suppress high-frequency resonance. Meanwhile, for grid-forming SVGs, the parameter variations in power synchronous loops have no significant impact on the suppressing effect of high-frequency resonance for wind farms. Finally, an electromagnetic simulation model for a DFIG-based wind farm system with an SVG is established using the StarSim-HIL (hardware-in-the-loop) experiment platform, and the simulation results validate the correctness of the theoretical analysis.

Research on Heave Compensation System Based on Switched Reluctance Motor

Aiming at the requirements of the marine work platform for real-time control, time-varying speed and the time-varying torque control of the motor-driven active heave compensation device, this paper introduces a composite control strategy based on the switched reluctance motor (SRM)-driven active heave compensation device. As for the compensation error caused by the time lag in the real-time system, the model prediction trajectory algorithm is used to predict the compensation displacement obtained using the dynamic model. The next time, the control parameters are then provided for the SRM control system in advance to reduce the compensation error. The SRM control strategy selects a double closed-loop compound control strategy of Back Propagation (BP) fuzzy neural network Proportion Integration Differentiation (PID) control. Its outer speed loop uses a fuzzy controller to quickly track a wide range of speed changes. The torque inner loop uses BP neural network adaptive PID control. This helps to reduce torque ripple and to ensure that the electromagnetic torque output of the SRM remains stable. Finally, the system feasibility is verified by setting different wave parameters. The simulation results show that the simulation conditions can reach 97.5% and 96.4% under the 3 and 4 wave levels, respectively. The simulation effect is satisfying, which verifies the feasibility of the proposed scheme.

Performance evaluation and analysis for hydraulic active suspension using the collaborative control method

Hydraulic active suspension has the coupling characteristics of integrated mechanical-hydraulic-control system, and its performance is also affected by external interference, noise interference, and other factors. Therefore, a novel controller is presented to achieve system-level optimal performances by using the collaborative control method. The proposed collaborative method is provided an implementation framework, and includes outer loop control of Linear Quadratic Regulator (LQR), inside loop control of modified linearized active disturbance rejection control (M-LADRC) and Kalman filter, and so on. In addition, the semi-physical simulation method is used to the simulation and test, and the force tracking control test for hydraulic servo system and Kalman filter test are carried out. Finally, the performance of semi-physical active suspension is compared with that of the ideal active suspension and passive suspension under the different road profile excitation. The superiority and effectiveness are verified for the collaborative control method. The collaborative controller has improved the suspension system performance and is more practical, which is beneficial for the application of the achievements.

Active Disturbance Rejection Control Combined with Improved Model Predictive Control for Large-Capacity Hybrid Energy Storage Systems in DC Microgrids

In DC microgrids, a large-capacity hybrid energy storage system (HESS) is introduced to eliminate variable fluctuations of distributed source powers and load powers. Aiming at improving disturbance immunity and decreasing adjustment time, this paper proposes active disturbance rejection control (ADRC) combined with improved MPC for n + 1 parallel converters of large-capacity hybrid energy storage systems. ADRC is utilized in outer voltage control loops, and improved MPC is employed in inner current control loops of n battery converters. Droop control is adopted to obtain power distribution between n battery converters, and a DC bus voltage compensator is used to compensate voltage deviations and maintain constant DC bus voltage. The low-pass filter (LPF) is adopted to obtain high-frequency power as the reference for the supercapacitor converter, ADRC is also utilized in the outer power control loop, and MPC is employed in the inner current control loop. Compared with traditional observers, the voltage expansion state observer of the proposed ADRC control is independent of the system model and parameters and consequently has strong disturbance immunity, and significantly reduces voltage overshoots during power fluctuations. The MPC-based inner current control loops of n + 1 converters accelerate current response speed and significantly decrease switching losses. Simulation and experimental results indicate that utilizing the proposed control strategies, large-capacity HESS has stronger anti-interference ability, shorter regulation time, smaller switching loss, and simultaneously maintains the stability of the DC bus voltage.

Analysis of a Simplified Predictive Function Control Formulation Using First Order Transfer Function for Adaptive Cruise Control

This paper presents a formulation and analysis of a low computation Predictive Functional Control (PFC), which is a simplified version of the more advanced Model Predictive Control (MPC) for an Adaptive Cruise Control (ACC) system by using a representation of first order closed-loop transfer function. In this work, a non-linear mathematical model of vehicle longitudinal dynamics is considered as a control plant. Then, a simple Proportional Integral (PI) controller is employed as an inner loop to identify the first-order relationship between its actual and desired trajectory speed according to the reasonable time constant based on the logical response of pedals pressing. To directly control the whole plant, the PFC is formulated as an outer loop to track the desired speed together with the convergence rate based on a user preference while satisfying constraints related to acceleration and safe distancing. Since PFC is formulated based on the first-order transfer function, the prediction and tuning processes are straightforward and specific to this system. The simulation results confirm that the proposed controller managed to track the desired speed while maintaining a comfortable driving response. Besides, the controller also can retain safe distancing during the car following application, even in the presence of unmeasured disturbance. In summary, this framework can avoid the need to formulate an inverse non-linear model that is typically used when deploying a hierarchical control structure to compute the throttle and brake pedals pressing as it has been replaced with an inner loop PI controller. The performance also is comparable yet more conservative due to the simplification. These findings can become a good reference for designing and improving the ACC controller, as the framework can be easily generalized for any type of vehicle for future work.

Enhanced Multi-UAV Formation Control and Obstacle Avoidance Using IAAPF-SMC

In response to safety concerns pertaining to multi-UAV formation flights, a novel obstacle avoidance method based on an Improved Adaptive Artificial Potential field (IAAPF) is presented. This approach enhances UAV obstacle avoidance capabilities by utilizing segmented attraction potential fields refined with adaptive factors and augmented with virtual forces for inter-UAV collision avoidance. To further enhance the control and stability of multi-UAV formations, a Sliding Mode Control (SMC) method is integrated into the IAAPF-based obstacle avoidance framework. Renowned for its robustness and ability to handle system uncertainties and disturbances, the SMC method is combined with a feedback control system that utilizes inner and outer loops. The outer loop generates the desired path based on the leader’s state and control commands, while the inner loop tracks these trajectories and adjusts the follower UAVs’ motions. This design ensures that obstacle feedback is accounted for before the desired state information is received, enabling effective obstacle avoidance while maintaining formation integrity. Integrating leader-follower formation control techniques with SMC-based multi-UAV obstacle avoidance strategies ensures the effective convergence of the formation velocity and spacing to predetermined values, meeting the cooperative obstacle avoidance requirements of multi-UAV formations. Simulation results validate the efficacy of the proposed method in reaching otherwise unreachable destinations within obstacle-rich environments, while ensuring robust collision avoidance among UAVs.

Hazard-consistent scenario selection for long-term storm surge risk assessment over extended coastal regions

The recent destructive hurricane seasons and concerns related to the future influence of climate change have increased the relevance of coastal storm hazards and, in particular, of storm surge hazard estimation when discussing the resilience of coastal communities. This hazard is generally represented as surge inundation probabilities over a large number of individual locations in the geographic domain of interest, and is typically assessed utilizing an ensemble of storm scenarios (i.e., storm events) that are representative of the regional climatology. This paper investigates the storm ensemble selection within this setting, with the objective of identifying a small number of storm scenarios that are consistent with some chosen hazard descriptions over a large geographic region. Beyond the storm events, the occurrence rates (i.e., weights) are also updated. Following past works, a two-stage optimization is adopted for the storm selection. The inner-loop identifies the occurrence rates for a given storm subset, formulating the problem as a linear programming optimization for the sum of absolute deviation for the predicted hazard. The outer-loop searches for the best subset with the desired number of storms, adopting a genetic algorithm integer optimization for minimizing the aforementioned deviation. This work extends this implementation to extended coastal regions, with many locations of interest. In this case, it is computationally intractable to consider all the locations in the domain within the linear programming formulation, and for this reason, a subset of representative locations is chosen through cluster analysis. The hazard description for only these locations is used in the storm ensemble selection. For clustering, different strategies using correlation between locations based on geospatial information, surge response, or a combination of both are examined. Additionally, the correlation in the hazard description is better integrated into the storm selection by establishing a modification of the objective function adopted for the outer optimization loop. Applications to different North Atlantic coastal domains are presented as case studies.