Proportional Feedback Research Articles

Data-driven set-point control for nonlinear nonaffine systems

Optimal set-point control is important in maintaining good control performance of practical industrial processes. Considering the challenges when modeling a complex process, this work presents a data-driven optimal set-point control (DDOSC) scheme for nonlinear nonaffine systems bypassing modeling steps. The outer loop of the proposed DDOSC adopts an ideal nonlinear set-point control function which is theoretically achievable to obtain a perfect tracking. Then, a dynamic linearization (DL) is used to transfer the ideal nonlinear set-point control law into a linear parametric one such that it is implementable through a parameter updating law. To address the nonlinear nonaffine system within a data-driven framework, the DL method is again used to obtain its linear data model which is further updated by a parameter-adaptive law. With a proportional feedback controller in the inner loop, the convergence of the DDOSC method is shown. In addition, the results are further extended by considering a proportional-integral-derivative feedback controller in the inner loop. The simulation results on a numerical example and a car suspension system verify the effectiveness of the proposed DDOSC in improving the performance of the local feedback controller.

Control of resistive wall modes in the spherical tokamak

In this work, the MARS-F/K codes (Liu et al 2000 Phys. Plasmas 7 3681; Liu et al 2008 Phys. Plasmas 15 112503) are utilized to model the passive and active control of the n= 1 (n is the toroidal mode number) resistive wall mode (RWM) in a spherical tokamak (aspect ratio A = 1.66). It is found that passive stabilization of the RWM gives a relatively small increase in normalized beta above the no-wall limit, relying on toroidal plasma flow and drift kinetic resonance damping from both thermal and energetic particles. Results of active control show that with the flux-to-voltage control scheme, which is the basic choice, a proportional controller alone does not yield complete stabilization of the mode. Adding a modest derivative action, and assuming an ideal situation without any noise in the closed-loop, the RWM can be fully stabilized with the axial plasma flow at 5% of the Alfvén speed. In the presence of sensor signal noise, success rates exceeding 90% are achieved, and generally increase with the proportional feedback gain. On the other hand, the required control coil voltage also increases with feedback gain and with the sensor signal noise.

Impulse Eliminations for Rectangular Descriptor Systems: A Unified Approach

Descriptor systems, in general, have impulses in their solutions and do not admit arbitrary initial conditions. In this letter, we design a unified proportional state feedback controller for rectangular descriptor systems such that the closed-loop system has no-impulsive modes if the system is impulsive-mode controllable. Further, the closed-loop system will have no-impulsive modes and admits arbitrary initial conditions provided that the system is impulse controllable. Additionally, some other equivalent algebraic criteria for impulse controllability are also deduced. Real-life models from robotics and electrical systems are given to illustrate the theory.

A dual-mode finite-time extremum seeking controller design technique

This manuscript proposes a finite-time extremum-seeking control system for a class of unknown nonlinear dynamical systems. A dual-mode approach is considered. The dual-mode control action combines a proportional feedback operating in the time-scale of the system and a slow perturbation-based extremum-seeking gradient descent. The resulting two time-scale extremum seeking control formulation is shown to achieve practical finite-time stability of the system to the optimum equilibrium conditions for the state variables and the input variables. A brief simulation study is presented to demonstrate the effectiveness of the proposed technique.

Aeroelastic analysis and active control of one-dimensional acoustic black hole structures in supersonic airflow

In this paper, the aeroelastic characteristic and active control of one-dimensional acoustic black hole structures in supersonic airflow are analyzed. Utilizing Hamilton's principle, the equation of motion of the one-dimensional acoustic black hole (ABH) structures in supersonic airflow with attached piezoelectric elements is established. The first-order piston theory is used to simulate the aerodynamic pressure of the composites, and the controller is designed based on speed feedback and proportional feedback algorithms. Through numerical simulations, the variation of the natural frequency concerning the aerodynamic pressure is carried out studies to determine the flutter point of the system. Besides, the influences of piezoelectric actuators and sensors on the aeroelastic flutters of one-dimensional ABH structures are analyzed. Results show that the velocity negative feedback can improve the critical pneumatic pressure of the system, thereby increasing the aerodynamic elastic stability of the composite structure. The kinetic and strain energies of the proposed system varied with the different feedback gains are also investigated. We found that the application of velocity negative feedback can effectively suppress the vibration of the proposed system, whereas, there are no apparent effects on the dynamics for varying the proportional feedback.

Active tuning of the vibration and wave propagation properties in electromechanical metamaterial beam

Locally resonant metamaterial beams made from flexible substrates with piezoelectric layers can exhibit bandgap and vibration attenuation properties. However, the bandgap properties of the electromechanical metamaterials are limited by the electromechanical coupling coefficient. In order to effectively overcome this limitation of the locally resonant bandgaps, a locally resonant electromechanical metamaterial beam with piezoelectric actuators and sensors is presented, and the piezoelectric shunting technique and negative proportional feedback control strategy are combined. In this design, both negative capacitance (NC) and inductance (L) are incorporated into the shunt circuits. Then, the classical root locus method is employed to obtain single/multiple bandgaps and particular structural response by arranging the poles and zeros. Finally, the influences of the feedback control gain, the shunt circuit type, and the damping ratio on the bandgap properties and wave propagation behaviors are analyzed. Numerical results demonstrate that the single/multiple bandgaps can be obviously broadened by properly increasing the control gain. Specifically, adding negative capacitance in series to pure inductive circuit can generate wider absolute bandgaps at lower frequencies. The comparison of the frequency response and the bandgap characteristics reveals a very good agreement. Summarily speaking, combining the piezoelectric shunting technique and negative proportional feedback control strategy can effectively tune the vibration and wave propagation behavior.

The exponential stabilization of a heat-wave coupled system and its approximation

In this paper, we consider exponential stabilization for a heat-wave coupled system under boundary control and collocated observation. It is known that the system is polynomially stable without control. Two kinds of feedback strategies namely static negative proportional feedback and dynamic feedback are designed. By the Lyapunov function direct method, the exponential stabilities of the closed-loop systems under different two feedbacks are firstly verified. Secondly, the H∞ robustness is further analyzed and the related sufficient conditions are developed. Furthermore, the closed-loop systems are discretized into semi-discrete systems by a new finite difference method, and the uniform exponential stabilities of the discrete systems are established by the approach paralleling to the continuous counterpart.

Reliable induced [formula omitted] control for polytopic uncertain continuous-time singular systems with dynamic quantization

This paper considers the problem of state feedback control for a class of polytopic uncertain continuous-time singular systems with input quantization and actuator faults. The aim of this paper is to design the reliable controller and dynamic quantizer that ensure the considered closed-loop system is asymptotically stable and satisfies the prescribed induced L∞ performance constraint. The introduced proportional plus derivative state feedback controller can eliminate the structural restrictions of the system matrices, thus a more general sufficient condition is obtained for the problem. Finally, the four-mesh circuit is provided to demonstrate the effectiveness of the proposed induced L∞ control approach.

Inverse dynamics modelling and tracking control of conical dielectric elastomer actuator based on GRU neural network

This paper presents intelligent modelling and tracking control methods for a conical dielectric elastomer actuator (CDEA) utilized in soft robots. Firstly, an inverse dynamics model (IDM) of the CDEA is established based on a gated recurrent unit neural network. Then, the IDM is directly taken as a feed-forward compensation controller to compensate the complex “memory” characteristic (mainly including the hysteresis nonlinearity and the creep nonlinearity) of the CDEA in its tracking control. Next, a proportional integral feedback controller is devised to cooperate with the compensating controller to enhance the tracking control performance. Lastly, some tracking control experiments with various target trajectories are implemented to demonstrate the validity of the presented methods. Different from traditional methods, using the proposed method can directly construct the compensating controller, thereby avoiding the complicated calculation of the analytical inverse of the dynamics model. Moreover, the fitness values of the results of tracking control experiments are higher than 93.6%, and the root-mean-square errors are lower than 1.3%. Therefore, the proposed intelligent modelling and tracking control methods are superior.

A Control Strategy of LCL-Type Grid-Connected Inverters for Improving the Stability and Harmonic Suppression Capability

The conventional inverter-side current single-loop feedback control scheme is weak in suppressing the grid-side current harmonics, posing a challenge for an inverter to inject high-quality current under distorted grid voltage. With capacitor current compensation added, the control scheme achieves controllability of the grid-side current harmonics so that it can effectively suppress some specific harmonic components. However, due to the stability requirements, only a few low-order harmonic resonance controllers can be applied, which limits the mitigation of high-order harmonics. To tackle this problem, the grid-side current feedback control with inductor–capacitor–inductor (LCL) resonance damping is proposed in this paper. In this case, a higher LCL resonance frequency can be set compared to the inverter-side current single-loop feedback control scheme. Thereby, more resonance controllers can be applied to suppress high-order grid-side current harmonics. The active damping method of capacitor current proportional feedback plus capacitor voltage proportional feedback is adopted because of its high robustness to grid impedance variations. Furthermore, this paper reveals that the applied active damping method has a limitation in that it only considers a single inverter under inductive grid impedance, which cannot eliminate the risk of resonance caused by the interaction of multiple inverters and the grid. To address this issue, a phase lead compensator (PLC) is proposed, eliminating the resonance risk by removing the non-passive region of the inverter output admittance. To retain the advantage of the inverter-side current single-loop feedback control scheme, i.e., only a few measuring devices are required, a digital differentiator is used to calculate the capacitor current from the capacitor voltage. The difference between the measured inverter-side current and the calculated capacitor current is taken to approximate the grid-side current for the feedback control. The control performance is comparable to using the grid-side current for feedback. Simulation and experimental results demonstrate that the proposed control scheme endows the inverter with good stability and current quality without extra measurement devices.

Compact and efficient radio frequency digital feedback control system for accelerator applications

The digital feedback (DFB) setup employed in a low-level radio frequency (LLRF) control system is crucial to ensure RF field stability in accelerating cavities, thus guaranteeing successful operation. To this end, a novel in-house and multi-purpose prototype DFB setup was developed for multiple applications at the Japan Proton Accelerator Research Complex (J-PARC). Being efficient, low-cost, and compact is key to achieving a cost-effective system that fulfills the performance specifications. It also reduces the production and maintenance costs of future DFB setups. A field-programmable gate array (FPGA)-based design with a digital signal processing (DSP) function uses an analog in-phase/quadrature-phase (I/Q) demodulator for RF-to-baseband signal conversion and an I/Q modulator to generate RF power. This arrangement compensates for RF phase fluctuations and amplitude modulations by employing a proportional and integral (PI) feedback controller. In addition, systematic errors are minimized by applying a hardware-error-compensation process. The system was utilized to conduct high-power tests on the interdigital H-mode drift-tube linac (IH-DTL) cavity of a muon linac for short RF pulses. The setup was also tested on a buncher cavity (Buncher-2) in the J-PARC linac, achieving efficient performance for longer RF pulses. The stability of the RF accelerating field in the IH-DTL was achieved at ±0.25% peak-to-peak (pp) in amplitude and ±0.36 degree pp in phase. For the Buncher-2, the amplitude stability of ±0.18% pp and phase stability of ±0.13 degree pp were obtained. Therefore, this DFB setup can be used to conduct high-power tests of RF cavities and klystrons. This study discusses the design aspects of a cost-effective DFB system and reports high-power measurements.

Role of Integral Control for Enlarging Second-Order Delay Consensus Margin Under PID Protocols: None.

Proportional, integral, and derivative (PID) feedback control, as a popular control law, plays a central role in industrial processes and traditional control applications. In the context of multiagent systems, one may also wonder what the fundamental capability and limitation of PID control may be. This article attempts to provide an answer from the viewpoint of consensus robustness against uncertain delay. We consider robust consensus of second-order unstable agents under PID feedback protocols, subject to a constant but unknown time delay over an undirected graph. The issue concerns the so-called delay consensus margin (DCM), which is the largest delay range within which robust consensus can be achieved. The specific problem under study investigates the role of integral control on the robust consensus, seeking to understand whether integral control can be employed to enhance consensus robustness. Our result shows that there is none; that is, in a PID protocol, the integral control action has no improving effect on the DCM, and that PID and proportional-derivative (PD) protocols achieve the same DCM. As a byproduct of this finding, the DCM under PID and PD protocols is found to be computable by solving a quasiconcave, albeit nonsmooth, unimodal optimization problem.

Power Flow Management With Q-Learning for a Grid Integrated Photovoltaic and Energy Storage System

This article develops a fuzzy Q-learning (FQL) approach-based power flow management algorithm for a single-phase grid-connected (GC) photovoltaic (PV) system with an energy storage unit (ESU). The FQL coordinates the PV power generation, which is based on the mission profile, the state of charge (SOC) of ESU, and the load profile such that a power balance is achieved in the network. Furthermore, the transition between standalone (SA) and GC modes during the power flow management is achieved using a proportional capacitor current feedback. While operating in the SA mode, the control action for the load voltage is achieved by an outer current loop. This combination of coordinated and transition control achieves power balance and smooth transition between the SA and GC modes. To verify the effectiveness of the proposed control strategy, a 4 – kWp PV system is operated along with an ESU in both SA and GC modes for a varying mission and load profile. The simulation and experimental results validated the multifunctional features of the proposed method.

Static feedback stabilization of a rotating disk–cable system with measurements from each boundary

In this paper, we consider the stabilization of a unitized rotating disk–cable system, which consists of a uniform cable attached to a disk rotating at an angular velocity about an axis through the center of the disk and perpendicular to the disk. When the angular velocity is greater than π2, the system always has at least one positive eigenvalue, which makes the system cannot be stabilized only with the collocated static feedback control. This is why the existing literature usually considers the case where the admissible angular velocity is always less than π2. To overcome this obstacle, we design a static proportional feedback control with both collocated and anti-collocated measurements from each boundary to stabilize the system, where the admissible angular velocity is improved from less than π2 to less than π while ensuring that the system is minimum-phase. Through a detailed spectral analysis, the spectrum of the closed-loop system is proved to be in the left-half complex plane, and the asymptotic expressions of both eigenvalues and eigenfunctions are obtained. By the Riesz basis approach, the stability of the closed-loop system is proved. The effectiveness of the feedback control is verified by numerical simulation.

Active proportional feedback control of turbulent flow over a circular cylinder with averaged velocity sensor

In the present study, we perform an active proportional (P) feedback control of laminar and turbulent flows over a circular cylinder with an averaged velocity sensor to reduce its drag and lift fluctuations. As a sensor for the feedback control, we adopt an averaged transverse velocity on the centerline of the wake. For the averaging of the transverse sensing velocity, we consider both temporal averaging over a finite period and spatial averaging in the spanwise direction. As a control input, the blowing/suction actuation is provided on the cylinder surface near the flow separation, and its magnitude is linearly proportional to the averaged transverse sensing velocity. With the control, the fluctuations of the transverse sensing velocity are significantly reduced and the vortices right after the cylinder and the Kármán vortex shedding in the wake are weakened, resulting in substantial reductions of the mean drag and lift fluctuations. Furthermore, it is shown that the adoption of the averaged sensing velocity makes the P control successful for a wider range of sensing locations in laminar flow at Re = 100 and is essential for the success of the P control in turbulent flow at Re = 3900. With the optimal control parameters, the reductions of the mean drag and lift fluctuations for turbulent flow at Re = 3900 are about 11% and 61%, respectively. The present P control maintains the magnitude of the blowing/suction actuation less than 1% of the free-stream velocity, and thus, the control input power is very small, leading to an excellent control efficiency.

LCL‐filter resonance suppression in grid‐connected inverter based on strictly real positive plant strategy

AbstractResonance is one of the most significant challenges in a voltage source inverter interfaced with the grid through an LCL filter. The capacitor current (CC) damping control methodology is considered due to its high‐quality of grid injected current feature. It is widely accepted that the proportional CC feedback compensation damping method becomes ineffective at critical resonance frequency due to control loop delays and may result in an unstable system under grid impedance or filter parameters variations. A suitable differential compensator placed in the CC feedback path can address this issue with a trade‐off between robustness and noise rejection capability. This paper offers a different design method called parallel feedforward compensation (PFC) method, which builds an almost strictly real positive (ASRP) plant and realized damping with enhanced stability features. In the proposed alternative, a compensator consisting of a damping gain and a sampled delay is placed across the filter plant and filter CC feedback loop and the joint output of this augmented plant is then transmitted back at the reference point on the input side of the inverter to attenuate the undesirable resonance peak. The control response and stability performance analysis show that the suggested methodology offers a wide damping region, high robustness, and improved control performance. Simulation and experimental results are presented to confirm the theoretical findings.

An Improved Extended State Observer-Based Composite Nonlinear Control for Permanent Magnet Synchronous Motor Speed Regulation Systems

This paper addresses the problems of an improved extended state observer (ESO)-based composite nonlinear control for the permanent magnet synchronous motor (PMSM) speed regulation systems, which is primarily constituted by a linear ESO-based feedforward compensation and nonlinear proportional feedback (NPF) control law. Firstly, by taking the parametric perturbations and external disturbances into account, a novel linear ESO is designed and analyzed to estimate the lumped disturbance, such that the system anti-disturbance performance is preserved. Meanwhile, the estimation of system state is also performed. Then, an optimal control synthesis function-based tracking differentiator (TD) is developed to arrange the transition dynamic for the reference velocity value, while its high quality differential signal is facilitated. Furthermore, an adaptive proportional control law is proposed, resulting in the eventual composite nonlinear strategy by incorporating the estimate values into the designed NPF controller. Finally, a PMSM servo system is studied to demonstrate the advantages and effectiveness of the proposed approaches.

A Comparative Study of Particle Swarm Optimized Control Techniques for Active Suspension System

This work presents a comparative study for performance evaluation of quarter vehicle Active Suspension System (ASS) using different control techniques. Linear and non-linear mathematical models of the systems are presented and controlled using Proportional Integral Derivative (PID), Feedback Linearization, and Fuzzy Logic Control (FLC). Particle Swarm Optimization (PSO) technique is applied to optimize the gains of the implemented controllers. A simulation process is done using MATLAB/SIMULINK and the results show that the proposed PSO-optimized PID controller has enhanced the root mean square (r.m.s) values of ride comfort, load carrying, and road holding of the linear suspension system by 26.82%, 20.95%, and 22.72% respectively compared to the linear passive suspension system. Whereas, for the nonlinear suspension system, the PSO-optimized FLC has provided better compromise of the performance criteria. The controller has improved the r.m.s values of ride comfort, load carrying, and road handling by 40.61%, 44.21%, and 27.46% respectively compared to the non-linear passive suspension system.

Intelligent demolition robot: Structural statics, collision detection, and dynamic control

This paper presents a modified oriented bounding box method and a compound control law for the developed intelligent demolition robot working safely and accurately in a high-radiation environment. Combining statics and kinematics, the modified oriented bounding box method is applied to predict the real-time and accurate collision detection of possible collisions. The Newton–Euler method is then adopted to derive the dynamic model. A compound control law based on dynamic feedforward torque and proportional integral derivative feedback torque is established to achieve high-accuracy control. Furthermore, a simulation system and experiment prototype are developed to verify the functions of collision detection and dynamic control. Simulation results demonstrate that the modified oriented bounding box method predicts the collision detection properly. Compared with the traditional proportional integral derivative control law, experimental results demonstrate that the compound control law realizes higher tracking accuracy within 0.04 m for the intelligent demolition robot.

The Spectral Analysis and Exponential Stability of a 1-d 2 × 2 Hyperbolic System with Proportional Feedback Control

The Spectral Analysis and Exponential Stability of a 1-d 2 × 2 Hyperbolic System with Proportional Feedback Control