Proportional-differential Research Articles

Reinforcement Learning-Based Satellite Attitude Stabilization Method for Non-Cooperative Target Capturing.

When a satellite performs complex tasks such as discarding a payload or capturing a non-cooperative target, it will encounter sudden changes in the attitude and mass parameters, causing unstable flying and rolling of the satellite. In such circumstances, the change of the movement and mass characteristics are unpredictable. Thus, the traditional attitude control methods are unable to stabilize the satellite since they are dependent on the mass parameters of the controlled object. In this paper, we proposed a reinforcement learning method to re-stabilize the attitude of a satellite under such circumstances. Specifically, we discretize the continuous control torque, and build a neural network model that can output the discretized control torque to control the satellite. A dynamics simulation environment of the satellite is built, and the deep Q Network algorithm is then performed to train the neural network in this simulation environment. The reward of the training is the stabilization of the satellite. Simulation experiments illustrate that, with the iteration of training progresses, the neural network model gradually learned to re-stabilize the attitude of a satellite after unknown disturbance. As a contrast, the traditional PD (Proportion Differential) controller was unable to re-stabilize the satellite due to its dependence on the mass parameters. The proposed method adopts self-learning to control satellite attitudes, shows considerable intelligence and certain universality, and has a strong application potential for future intelligent control of satellites performing complex space tasks.

Uniform switched control strategy of valve‐controlled asymmetric hydraulic system

Model set of a valve-controlled asymmetric hydraulic system was built, and uniform switched control (USC) strategy was proposed for multi-model set hydraulic system. Aiming at each subsystem model, the uniform feedback linearisation control (FLC) structure was put forward based on the FLC method, and switch control strategy was used by adjusting switch gain between different sub-models. The boundary layer function was designed in order to enhance the system robustness and to reduce oscillation which is caused by discontinuous item. Furthermore, the switch control gain was further revised according to different load condition. At last, the USC, FLC control, and proportional differential (PD) control strategy was carried out by experiment, and the results show that the maximum speed tracking error of PD and FLC control was 1.1 and 1 mm/s, respectively. The USC strategy speed error is <0.25 mm/s. Compared with the PD and the FLC, the USC was found to be more speed accuracy in multiple state hydraulic system control.

Control Schemes for Autonomous Car‐following Systems with two Classical Compensators

AbstractIn this paper, we improve the dynamics of an autonomous car‐following system with two classical compensation methods: proportional‐differential (PD) and velocity feedback (VF) control methods. Based on an optimal velocity model, the system transfer function was derived and control block diagram was given with an open‐loop transfer function. Three theorems were proposed and proven with the use of small gain theorem. The analytical results show that two compensation factors play important roles in stabilizing the car‐following system. In the simulation, three dynamical models were derived in reverse from the closed‐loop transfer function and the numerical results show that, with increasing factors, the stability of car‐following was enhanced and traffic jams were eliminated. The analytical results are supported by the numerical results.

Disturbance Rejection Attitude Controller Design for Launch Vehicle based on Orthogonal Function Neural Network

A disturbance rejection attitude controller of launch vehicle based on chebyshev orthogonal function (COF) neural network and proportional-differential (PD) control is proposed to attenuate effect of parameter variation and disturbances of launch vehicle on attitude control accuracy and stability. The chebyshev orthogonal function (COF) neural network is used to estimate and compensate impact of parametric uncertainties and disturbances by taking full advantage of information of gyros and attitude sensors. The designed controller applies proportional-differential control to realize attitude control. Simulation results show that the controller exhibits good dynamic performance, high ability and strong robustness against external disturbance and parameter uncertainty.

Analysis on Control Stability of STATCOM Applied on Weak Power System

Control stability when Multi-level STATCOM is applied on weak power system is discussed in this paper. In order to research the stability of weak system quantitatively, the current inner open-loop transfer function with system impedance is presented. Nyquist curve is used to demonstrate the relationship between the system impedance and the system control performance. Then a new control strategy - adding the current’s proportion-differential (PD) to the feed forward voltage, is proposed. This control strategy can eliminate the positive feedback action caused by system impedance. Finally, test result proves that the above theoretical analysis is correct.

Force Sensorless Compliance Control of a Lower-limb Exoskeleton Robot

Lower limb rehabilitation machines are widely used to enhance the mobility function of elderly people and patients suffering from spinal cord injury and stroke. In this paper, a four degrees of freedom (DOF) lower body exoskeleton with a model-based compensation control framework is proposed to support hip-knee rehabilitation. The exoskeleton control movement is realized by designing a trajectory for each leg movement. A function approximation technique (FAT) based adaptive control is applied to each two DOF legs during a rehabilitation task. Using the FAT based adaptive control, the natural system dynamic is adaptively compensated for without knowing the acceleration feedback and system dynamics. Simulation results show the disturbance observer successfully estimated the user’s applied leg force. The leg force is given as the input to compliance control applied in 2 DOF motors when performing a walking sequence on a treadmill. Moreover, the FAT-based adaptive control outperformed the standard proportional-differential (PD) control and could accommodate different subjects without any changes to control parameters.

Active vibration control of a flexible link robot with the use of piezoelectric actuators

Within robot systems the use of flexible links could solve many issues raised by their rigid counterparts. However, when these flexible links are integrated within systems which include moving parts their main issue lies in the vibrations experienced along their length due to disturbances. Much research effort has been made to solve this issue, with particular attention being paid to the application of piezoelectric patches as actuators within active vibration control (AVC). The study will consist of accurate models of a flexible link and two surface bonded piezoelectric patches, where the link and the piezoelectric patches will be modelled through the use of Euler-Bernoulli beam theory (EBT). The link will be subject to an initial displacement at its free end, and the resulting displacement of this end of the beam is to be controlled using a classic proportional-differential (PD) controller. The voltages to be applied across each of the actuators is to be controlled in accordance with the displacement of the free end of the beam, the actuators will then induce a strain upon the link opposing the movement of the tip. This research outlines this general method, obtains the best location of the piezoelectric patches and the control gains to be used, and proves that the method can be used to attenuate the vibrations experienced by a flexible link.

Dynamic modeling and hierarchical compound control of a novel 2-DOF flexible parallel manipulator with multiple actuation modes

Abstract This paper addresses the problem of rigid-flexible coupling dynamic modeling and active control of a novel flexible parallel manipulator (PM) with multiple actuation modes. Firstly, based on the flexible multi-body dynamics theory, the rigid-flexible coupling dynamic model (RFDM) of system is developed by virtue of the augmented Lagrangian multipliers approach. For completeness, the mathematical models of permanent magnet synchronous motor (PMSM) and piezoelectric transducer (PZT) are further established and integrated with the RFDM of mechanical system to formulate the electromechanical coupling dynamic model (ECDM). To achieve the trajectory tracking and vibration suppression, a hierarchical compound control strategy is presented. Within this control strategy, the proportional-differential (PD) feedback controller is employed to realize the trajectory tracking of end-effector, while the strain and strain rate feedback (SSRF) controller is developed to restrain the vibration of the flexible links using PZT. Furthermore, the stability of the control algorithm is demonstrated based on the Lyapunov stability theory. Finally, two simulation case studies are performed to illustrate the effectiveness of the proposed approach. The results indicate that, under the redundant actuation mode, the hierarchical compound control strategy can guarantee the flexible PM achieves singularity-free motion and vibration attenuation within task workspace simultaneously. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and efficient controller design of other flexible PMs, especially the emerging ones with multiple actuation modes.

Planar rigid-flexible coupling spacecraft modeling and control considering solar array deployment and joint clearance

Based on Nodal Coordinate Formulation (NCF) and Absolute Nodal Coordinate Formulation (ANCF), this paper establishes rigid-flexible coupling dynamic model of the spacecraft with large deployable solar arrays and multiple clearance joints to analyze and control the satellite attitude under deployment disturbance. Considering torque spring, close cable loop (CCL) configuration and latch mechanisms, a typical spacecraft composed of a rigid main-body described by NCF and two flexible panels described by ANCF is used as a demonstration case. Nonlinear contact force model and modified Coulomb friction model are selected to establish normal contact force and tangential friction model, respectively. Generalized elastic force are derived and all generalized forces are defined in the NCF-ANCF frame. The Newmark-β method is used to solve system equations of motion. The availability and superiority of the proposed model is verified through comparing with numerical co-simulations of Patran and ADAMS software. The numerical results reveal the effects of panel flexibility, joint clearance and their coupling on satellite attitude. The effects of clearance number, clearance size and clearance stiffness on satellite attitude are investigated. Furthermore, a proportional-differential (PD) attitude controller of spacecraft is designed to discuss the effect of attitude control on the dynamic responses of the whole system.

Control circuit design and chaos analysis in an ultrasonic machining system

PurposeThis study aims to investigate the dynamic motion of an ultrasonic machining system comprising two Duffing oscillators, each with a single degree of freedom. After derivation of the differential equations of the system using the Lagrange equations and dimensionless time, numerical analysis was used to observe changes in the system caused by differences in excitation frequency.Design/methodology/approachTo suppress this effect and improve performance, proportional differential (PD) control was used. The integral absolute error was used as the fitness function, and particle swarm optimization was used to find the best value for the gain constant of the PD controller.FindingsThe results showed that with specific changes of excitation frequency, the dynamic motion of the system became nonlinear and chaotic behavior resulted. This made the system unstable and affected performance.Originality/valueA range of methods, including fuzzy control, was used to analyze the results, and exhaustive laboratory work was carried out. Means of control were found that were effective in suppressing the chaotic behavior, and differences in response to control were investigated and verified. The findings of this study can be used as a basis for system parameter settings or control circuit design.

Model-free adaptive control law for nuclear superheated-steam supply systems

Nuclear steam supply system (NSSS), which provides saturated or superheated steam to the secondary loop system for electricity or cogeneration, is central in a nuclear plant. The control of NSSS is important for the safe, stable and efficient plant operation. Nuclear superheated-steam supply system (Su-NSSS), which is equipped with an under moderated fission reactor and a once-through steam generator (OTSG) for producing superheated steam flow, is an important type of NSSS that widely applied in the nuclear plants based on the common large pressurized water reactors (PWR) and small modular reactors (SMRs) such as integral PWR (iPWR) and modular high temperature gas-cooled reactor (MHTGR). There is still very limited results for the control of Su-NSSS. Motivated by the gap between the importance and the lack of results in the field of Su-NSSS control, a model-free adaptive power-level control law is developed for Su-NSSSs with forced primary circulation in this paper. This new control law is free from physical and thermal-hydraulic parameters, is in the simple proportional-integral (PI) or proportional-differential (PD) form. To verify the feasibility of the newly-built Su-NSSS controller, it is applied to the NSSS control of a two modular high temperature gas-cooled nuclear plant with comparison to a specific MHTGR-based NSSS control law. Numerical simulation results show that this new control law can improve the transient performance of neutron flux and steam temperature in normal operation case, and can realize system resilience in some abnormal cases.

A nonlinear control approach for a hypersonic vehicle

PurposeThe purpose of the paper is to design a robust control system for a generic hypersonic vehicle which includes dynamic nonlinear, open loop unstable and parametric uncertainties.Design/methodology/approachFor a complex longitudinal model of a generic hypersonic vehicle which includes dynamic nonlinear, open loop unstable and parametric uncertainties, a nonlinear dynamic inverse (NDI) approach combined with proportional differential (PD) control is used to design a strong robust control system to deal with the sensitivity to changes of atmosphere condition. In this way, a simple genetic algorithm is used to search a group of parameters of the control system to satisfy the specific performance indices. Then parametric uncertainties are considered to verify the robustness of the control system.FindingsThe PD hypersonic vehicle control system using NDI approach can satisfy the specific flight performance. And it has strong robustness under the parametric uncertainties.Originality/valueThe paper fulfills a complete process of the nonlinear control system design for a generic hypersonic vehicle. And, the simulation results show the efficiency and robustness of the control system.

Frequency-response-based multivariable controller tuning for &lt;i&gt;H&lt;/i&gt;&lt;SUB align="right"&gt;&amp;infin; loop shaping method

Robust control is applied to systems with uncertainties and disturbances. Above all, the H∞ loop shaping method is known to achieve good control performance and robustness. However, this method takes much time to build the mathematical model of an actual plant and its uncertainty. This paper proposes a controller tuning method which only uses frequency responses of the plant. In this method, the controller is designed by iterative linear-matrix-inequality (LMI) optimisation using frequency responses of the plant. Since the controller is designed without the modelling, identification cost is expected to be saved compared with the model-based approach. Moreover, a fixed structural controller such as a proportional-differential (PD) or a proportional-integral-differential (PID) controller is readily designed. The effectiveness of the proposed method is verified through the experiment for a tension-and-velocity control apparatus, and comparison with the other method is given in the last of this paper.

Frequency-response-based multivariable controller tuning for &lt;i&gt;H&lt;/i&gt;&lt;SUB align="right"&gt;&amp;infin; loop shaping method

Robust control is applied to systems with uncertainties and disturbances. Above all, the H∞ loop shaping method is known to achieve good control performance and robustness. However, this method takes much time to build the mathematical model of an actual plant and its uncertainty. This paper proposes a controller tuning method which only uses frequency responses of the plant. In this method, the controller is designed by iterative linear-matrix-inequality (LMI) optimisation using frequency responses of the plant. Since the controller is designed without the modelling, identification cost is expected to be saved compared with the model-based approach. Moreover, a fixed structural controller such as a proportional-differential (PD) or a proportional-integral-differential (PID) controller is readily designed. The effectiveness of the proposed method is verified through the experiment for a tension-and-velocity control apparatus, and comparison with the other method is given in the last of this paper.

Quantised consensus by using the PD-like protocols in directed networks

ABSTRACTThis paper studies the distributed consensus problem in sampled-data multi-agent systems with directed network topologies subject to a quantisation constraint. Different from the widely used consensus protocol which exploits current information, we adopt a distributed proportional-differential (PD)-like protocol. First, we provide a necessary and sufficient condition of control gains which guarantee the consensus with the assumption that real-valued communication information can be obtained. Next, we analyse the quantisation effects in system performances under the proposed protocol; it is proved that the quantised consensus can be achieved. Finally, by providing numerical examples, we show that with appropriate parameters, the consensus can be achieved and the quantisation noises can be attenuated effectively.

Switched Fuzzy-PD Control of Contact Forces in Robotic Microbiomanipulation.

Force sensing and control are of paramount importance in robotic micromanipulation. A contact force regulator capable of accurately applying mechanical stimuli to a live Drosophila larva could greatly facilitate mechanobiology research on Drosophila and may eventually lead to novel discoveries in mechanotransduction mechanisms of neuronal circuitries. In this paper, we present a novel contact force control scheme implemented in an automated Drosophila larvae micromanipulation system, featuring a switched fuzzy to proportional-differential (PD) controller and a noise-insensitive extended high gain observer (EHGO). The switched fuzzy-PD control law inherits the fast convergence of fuzzy control and overcomes its drawbacks such as large overshoot and steady-state oscillation. The noise-insensitive EHGO can reliably estimate system modeling errors and is robust to force measurement noises, which is advantageous over conventional high gain observers (sensitive to signal noises). Force control experiments show that, compared to a proportional-integral-differential (PID) controller, this new force control scheme significantly enhances the system dynamic performance in terms of rising time, overshoot, and oscillation. The developed robotic system and the force control scheme will be applied to mechanical stimulation and fluorescence imaging of Drosophila larvae for identifying new mechanotransduction mechanisms.

Automatic calibration with robust control of a six DoF mechatronic system

This paper presents a robust control methodology incorporating an automatic calibration step to compensate dynamic variations in a 6 DoF mechatronic system. The application used to illustrate the efficacy of the proposed approach is the ball and plate system based on the Stewart platform. To emulate dynamic changes in the system, we make use of various types of balls, varying in mass, diameter and surface. An automatic calibration step is introduced to obtain a model based on the type of ball which is placed on the plate. Using a model-based tuning technique, an optimal proportional-differential (PD) controller is designed based on the previous calibration. The resulting controller is tested for robustness by changing the ball without changing the controller parameters. The results indicate that our setup is robust and performs well in the presence of significant changes.

High-Precision Dual-Loop Position Control of an Asymmetric Bilateral Linear Hybrid Switched Reluctance Motor

In this paper, to enhance the machine performance and realize a high-precision position control performance, a dual-loop position controller is employed for the asymmetric bilateral linear hybrid switched reluctance motor (ABLHSRM). Machine characteristics are investigated by finite-element method. The dual-loop controller is constructed by employing a tradition proportional–integral differential velocity controller as the inner loop and a fuzzy proportional differential (PD) controller for the outer loop. Experimental results demonstrate that both the position control performance and the velocity control performance under the dual-loop control algorithm are superior to the single-loop PD position control strategy. An absolute steady-state error of 4 $\mu \text{m}$ can be achieved under the dual-loop control strategy. Performance comparison from the ABLHSRM and its asymmetric bilateral linear switched reluctance counterpart with the same dimensions are carried out. Position tracking results show that the rise time is improved for the proposed ABLHSRM under the proposed control scheme.

Adaptive position tracking control of electro-hydraulic six-degree-of-freedom driving simulator subject to perturbation

In this paper, a new Lyapunov-based adaptive control scheme for the position tracking of an electro-hydraulic Stewart–Gough platform type six-degree-of-freedom (DOF) driving simulator is proposed. The kinematics and the dynamics of both the moving platform and the hydraulic actuator are first derived, and the linearized dynamic equation of the moving platform is developed for the controller design. Two control loops are employed, in which the platform controller is in the outer loop and the actuator controllers are in the inner loop. In the platform controller, the compound proportional-differential (PD) feedback and adaptive compensation controller is designed. The PD part is used to create the principal control signal, and the adaptive part is used to compensate for the parameter uncertainty and external disturbance. To suppose that the upper bound of the perturbation is known, a gradient descent method-based adaptive law is developed for parameter estimation. For each actuator controller a servo force control scheme is designed to ensure the actuator to accurately track the desired force output by the platform controller. All the controllers are designed together based on the Lyapunov method to guarantee the stability of the whole system. Numerical simulation on a six-DOF simulator shows that the proposed control scheme has better tracking performance than its non-adaptive counterpart.

Experimental Application of Hybrid Fractional-Order Adaptive Cruise Control at Low Speed

This brief deals with the design and experimental application of a hybrid fractional adaptive cruise control (ACC) at low speeds. First, an improved fractional-order cruise control (CC) is presented for a commercial Citroen C3 prototype-which has automatic driving capabilities-at low speeds, which considers a hybrid model of the vehicle. The quadratic stability of the system is proved using a frequency domain method. Second, ACC maneuvers are implemented with two different distance policies using two cooperating vehicles-one manual, the leader, and the other, automatic-also at very low speeds. In these maneuvers, the objective is to maintain a desired interdistance between the leader and follower vehicles, i.e., to perform a distance control-with a proportional differential (PD) controller in this case-in which the previously designed fractional-order CC is used for the speed control. Simulation and experimental results, obtained in a real circuit, are given to demonstrate the effectiveness of the proposed control strategies.