PI-type Controller Research Articles

WITHDRAWN: Robust voltage regulation of DC-DC buck converter with ZIP load via an energy shaping control approach

ZIP loads (the parallel combination of constant impedance loads, constant current loads and constant power loads) exist widely in power system. In order to stabilize buck converter based DC distributed system with ZIP load, an adaptive energy shaping controller (AESC) is devised in this paper. Firstly, based on the assumption that the lumped disturbances are known, a full information controller is designed in the framework of the port Hamiltonian system via energy shaping technique. An obvious merit is that it is PI-type controller, which is easy to implement in practical application. Besides, using mathematical deductive method, an estimation of the domain of attraction is given to ensure the strict stability. Furthermore, to eliminate the influence of parameter perturbations on the system, a disturbance observer is proposed to reconstruct the lumped disturbances and then the estimated terms are introduced to above controller to form an adaptive control scheme. In addition, the strict stability analysis of the closed-loop system is given. Lastly, the simulation and experiment results are presented for assessing the designed controller.

Development of a digital low-level RF system for the STCF

With the development of particle physics, higher requirements are put forward for the brightness and energy of the collider. A new collider — the Super Tau-Charm Facility (STCF) — is under study in China. To meet the high acquirement of the quality of the beam, a digital low-level RF (LLRF) system that achieves high stability plays a critical role as a part of the microwave system of Linacs. This paper introduces the design of a digital LLRF system that works in the S-band (2856 MHz) as required by Linacs of the STCF. The system architecture and hardware design as well as the control algorithms and software design are discussed and tested. The system includes a signal source, a frequency synthesis system and an IF signal processor. The phase noise of the signal source is as low as 20.3 fs, and the low-level IF signal processor adopts amplitude and phase control by a PI-type controller. They jointly realize ultra-low phase noise signal output. The table experiments show that the short-term amplitude and phase stability of the system is better than 0.01% and 0.01°, respectively. The beam experiments show that the closed-loop phase stability in the cavity is about 0.1°. The results prove that the LLRF system meets the requirement of the STCF.

Improved Performance for PMSM Sensorless Control Based on Robust-Type Controller, ESO-Type Observer, Multiple Neural Networks, and RL-TD3 Agent.

This paper summarizes a robust controller based on the fact that, in the operation of a permanent magnet synchronous motor (PMSM), a number of disturbance factors naturally occur, among which both changes in internal parameters (e.g., stator resistance Rs and combined inertia of rotor and load J) and changes in load torque TL can be mentioned. In this way, the performance of the control system can be maintained over a relatively wide range of variation in the types of parameters mentioned above. It also presents the synthesis of robust control, the implementation in MATLAB/Simulink, and an improved version using a reinforcement learning twin-delayed deep deterministic policy gradient (RL-TD3) agent, working in tandem with the robust controller to achieve superior performance of the PMSM sensored control system. The comparison of the proposed control systems, in the case of sensored control versus the classical field oriented control (FOC) structure, based on classical PI-type controllers, is made both in terms of the usual response time and error speed ripple, but also in terms of the fractal dimension (DF) of the rotor speed signal, by verifying the hypothesis that the use of a more efficient control system results in a higher DF of the controlled variable. Starting from a basic structure of an ESO-type observer which, by its structure, allows the estimation of both the PMSM rotor speed and a term incorporating the disturbances on the system (from which, in this case, an estimate of the PMSM load torque can be extracted), four variants of observers are proposed, obtained by combining the use of a multiple neural network (NN) load torque observer and an RL-TD3 agent. The numerical simulations performed in MATLAB/Simulink validate the superior performance obtained by using properly trained RL-TD3 agents, both in the case of sensored and sensorless control.

Comparative Performance of UPQC Control System Based on PI-GWO, Fractional Order Controllers, and Reinforcement Learning Agent

In this paper, based on a benchmark on the performance of a Unified Power Quality Conditioner (UPQC), the improvement of this performance is presented comparatively by using Proportional Integrator (PI)-type controllers optimized by a Grey Wolf Optimization (GWO) computational intelligence method, fractional order (FO)-type controllers based on differential and integral fractional calculus, and a PI-type controller in tandem with a Reinforcement Learning—Twin-Delayed Deep Deterministic Policy Gradient (RL-TD3) agent. The main components of the UPQC are a series active filter and an Active Parallel Filter (APF) coupled to a common DC intermediate circuit. The active series filter provides the voltage reference for the APF, which in turn corrects both the harmonic content introduced by the load and the VDC voltage in the DC intermediate circuit. The UPQC performance is improved by using the types of controllers listed above in the APF structure. The main performance indicators of the UPQC-APF control system for the controllers listed above are: stationary error, voltage ripple, and fractal dimension (DF) of the VDC voltage in the DC intermediate circuit. Results are also presented on the improvement of both current and voltage Total harmonic distortion (THD) in the case of, respectively, a linear and nonlinear load highly polluting in terms of harmonic content. Numerical simulations performed in a MATLAB/Simulink environment demonstrate superior performance of UPQC-APF control system when using PI with RL-TD3 agent and FO-type controller compared to classical PI controllers.

Improvement of Linear and Nonlinear Control for PMSM Using Computational Intelligence and Reinforcement Learning

Starting from the nonlinear operating equations of the permanent magnet synchronous motor (PMSM) and from the global strategy of the field-oriented control (FOC), this article compares the linear and nonlinear control of a PMSM. It presents the linear quadratic regulator (LQR) algorithm as a linear control algorithm, in addition to that obtained through feedback linearization (FL). Naturally, the nonlinear approach through the Lyapunov and Hamiltonian functions leads to results that are superior to those of the linear algorithms. With the particle swarm optimization (PSO), simulated annealing (SA), genetic algorithm (GA), and gray wolf Optimization (GWO) computational intelligence (CI) algorithms, the performance of the PMSM–control system (CS) was optimized by obtaining parameter vectors from the control algorithms by optimizing specific performance indices. Superior performance of the PMSM–CS was also obtained by using reinforcement learning (RL) algorithms, which provided correction command signals (CCSs) after the training stages. Starting from the PMSM–CS performance that was obtained for a benchmark, there were four types of linear and nonlinear control algorithms for the control of a PMSM, together with the means of improving the PMSM–CS performance by using CI algorithms and RL–twin delayed deep deterministic policy gradient (TD3) agent algorithms. The article also presents experimental results that confirm the superiority of PMSM–CS–CI over classical PI-type controllers.

Robust PI-Type Output Feedback Control of Unknown Nonlinear Systems

The proportional-integral (PI) control method is long well-known because of its simplicity as well as effectiveness. Although the PI control method overwhelmingly dominates engineering applications, the issue of developing a general PI control for nonlinear systems remains open. This paper considers the PI control problem for a family of unknown nonlinear systems. A structurally simple and computationally inexpensive PI-type control approach with constant gains is provided to solve the problem, which maintains pre-assigned transient as well as steady-state performance and guarantees the global stability of closed-loop systems. The key to possessing such properties comes down to the transformation and modification of tracking errors. The effectiveness of the presented control approach is assessed via the experiment on a pneumatic artificial muscle, and the results corroborate the theoretical findings.

Improvement of the Control of a Grid Connected Photovoltaic System Based on Synergetic and Sliding Mode Controllers Using a Reinforcement Learning Deep Deterministic Policy Gradient Agent

This article presents the control of a grid connected PV (GC-PV) array system, starting from a benchmark. The control structure used in this article was a cascade-type structure, in which PI or synergetic (SYN) controllers were used for the inner control loop of id and iq currents and PI or sliding mode control (SMC) controllers were used for the outer control loop of the udc voltage from the DC intermediate circuit. This paper presents the mathematical model of the PV array together with the main component blocks: simulated inputs for the PV array; the PV array itself; the MPPT algorithm; the DC-DC boost converter; the voltage and current measurements for the DC intermediate circuit; the load and connection to power grid; the DC-AC converter; and the power grid. It also presents the stages of building and training the reinforcement learning (RL) agent. To improve the performance of the control system for the GC-PV array system without using controllers with a more complicated mathematical description, the advantages provided by the RL agent on process controls could also be used. This technique does not require exact knowledge of the mathematical model of the controlled system or the type of uncertainties. The improvement in the control system performance for the GC-PV array system, both when using simple PI-type controllers or complex SMC- and SYN-type controllers, was achieved using an RL agent based on the Deep Deterministic Policy Gradient (DDPG). The variant of DDPG used in this study was the Twin-Delayed (TD3). The improvement in performance of the control system were obtained by using the correction command signals provided by the trained RL agent, which were added to the command signals ud, uq and idref. The parametric robustness of the proposed control system based on SMC and SYN controllers for the GC-PV array system was proven in the case of a variation of 30% caused by the three-phase load. Moreover, the results of the numerical simulations are shown comparatively and the validation of the synthesis of the proposed control system was obtained. This was achieved by comparing the proposed system with a software benchmark for the control of a GC-PV array system performed in MATLAB Simulink. The numerical simulations proved the superiority of the performance of control systems that use the RL-TD3 agent.

Improvement of PMSM Sensorless Control Based on Synergetic and Sliding Mode Controllers Using a Reinforcement Learning Deep Deterministic Policy Gradient Agent

The field-oriented control (FOC) strategy of a permanent magnet synchronous motor (PMSM) in a simplified form is based on PI-type controllers. In addition to their low complexity (an advantage for real-time implementation), these controllers also provide limited performance due to the nonlinear character of the description equations of the PMSM model under the usual conditions of a relatively wide variation in the load torque and the high dynamics of the PMSM speed reference. Moreover, a number of significant improvements in the performance of PMSM control systems, also based on the FOC control strategy, are obtained if the controller of the speed control loop uses sliding mode control (SMC), and if the controllers for the inner control loops of id and iq currents are of the synergetic type. Furthermore, using such a control structure, very good performance of the PMSM control system is also obtained under conditions of parametric uncertainties and significant variations in the combined rotor-load moment of inertia and the load resistance. To improve the performance of the PMSM control system without using controllers having a more complicated mathematical description, the advantages provided by reinforcement learning (RL) for process control can also be used. This technique does not require the exact knowledge of the mathematical model of the controlled system or the type of uncertainties. The improvement in the performance of the PMSM control system based on the FOC-type strategy, both when using simple PI-type controllers or in the case of complex SMC or synergetic-type controllers, is achieved using the RL based on the Deep Deterministic Policy Gradient (DDPG). This improvement is obtained by using the correction signals provided by a trained reinforcement learning agent, which is added to the control signals ud, uq, and iqref. A speed observer is also implemented for estimating the PMSM rotor speed. The PMSM control structures are presented using the FOC-type strategy, both in the case of simple PI-type controllers and complex SMC or synergetic-type controllers, and numerical simulations performed in the MATLAB/Simulink environment show the improvements in the performance of the PMSM control system, even under conditions of parametric uncertainties, by using the RL-DDPG.

Robust LFC of Power Systems With Wind Power Under Packet Losses and Communication Delays

Network-induced packet losses and communication delays, as well as load fluctuations and uncertain wind power have a negative effect on the frequency regulation of power system. This paper is concerned with designing a robust load frequency control (LFC) scheme for a multi-area power system penetrated by wind power via sampled-data control. Firstly, considering the effects of the inertia reduction, packet losses, communication delays and measurement noise, a decentralized aperiodic sampled-data LFC model with time delay is constructed, where the maximum sampling interval is characterized by limiting the maximum count of successive packet losses (MCSPL). Secondly, by applying Lyapunov theory and linear matrix inequality technique, a new exponential stability condition for the modeled LFC system with given controller is proposed based on a combination method of Lyapunov-Krasovskii functional and loop function, which is dependent on delay and MCSPL. It can be used to find the delay margin and allowable MCSPL of the LFC system. Thirdly, based on the <inline-formula> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula>-gain performance condition developed by the stability condition above, a design method of robust PI-type controller is proposed by maximizing an exponential decay rate (EDR). The larger EDR, the faster frequency response speed to cope with the effect of inertia reduction, but the worse robustness to load fluctuations, packet losses and delays, and vice versa. Finally, case studies are carried out by a one-area power system and a three-area power system with wind power. By comparing with the existing LFC schemes, simulation results show that the proposed LFC scheme for the tested system is more effective and has better robustness.

Event-based consensus control for multi-agent systems against joint sensor and actuator attacks

The paper focuses on the observer-based consensus control issue for a class of discrete-time multi-agent systems suffering from the joint actuator and sensor attacks. An event-triggered communication rule with the adaptive threshold update is introduced to reduce the communication burden. A PI-type controller with a finite-time window integral loop is constructed to achieve bounded consensus in the mean-square sense (BCMS). With the help of common properties of Laplace matrices, the closed-loop multi-agent system is converted into an easy-to-analyze pattern. In light of such a pattern, a sufficient condition is derived to realize the desired consensus by the stochastic analysis. Furthermore, the expected gains of the controller and the observer are determined by resorting to matrix inequalities in combination with the cone complementarity linearization algorithm. Finally, a numerical example and a simulation of the platooning vehicle are proposed to illustrate the effectiveness of the proposed control scheme.

A robust nonlinear PI-type controller for the DC–DC buck–boost power converter

In this study, a novel Lyapunov function-based robust nonlinear proportional–integral (PI)-type controller for regulating the output voltage of the direct current to direct current (DC–DC) inverting buck–boost power converter operating in continuous conduction mode (CCM) is presented. The control scheme guarantees global asymptotic stability of the closed-loop system even in case of parameter uncertainty. The analysis of the closed-loop trajectories is carried out using Lyapunov method and LaSalle’s invariance principle. Robustness to additive disturbances is shown and simple gain tuning guidelines are given. Real-time experiments support the theoretical results. Experimental tests are presented where the proposed PI-type control design is compared with other PI-type schemes found in the literature. The proposed scheme presents very good consistent performance under line and load disturbance.

Optimal PI Parameters Tuning for a DC-DC Boost Converter

This paper designs a nonlinear PI-type controller for the robust control of a boost DC-DC converter using a particle swarm optimization (PSO) algorithm for increasing the output voltage of the photovoltaic (PV) system. In addition, the PI controller is used to tracking the maximum power from the PV panel, at different atmospheric condition. For tuning PI controllers is a tedious work and it is difficult to tune the PI gains optimally due to the nonlinearity. This paper presents an approach to use the particle swarm optimization algorithm to design the optimal PI controllers. The Simulations results show that the proposed controller exhibits better behavior in terms of settling time and overshoot and better performance of the converter.

A Unified Controller for Multi-State Operation of the Bi-Directional Buck–Boost DC-DC Converter

DC grid interfaces for supercapacitors (SCs) are expected to operate with a wide range of input voltages with fast dynamics. The class-C DC-DC converter is commonly used in this application because of its simplicity. However, it does not work if the output voltage (V2) becomes smaller than the input voltage (V1). The non-isolated bi-directional Buck–Boost DC-DC converter does not have this limitation. Its two half-bridges provide a means for controlling the power flow operating in the conventional dual-state mode, as well as multi-state, tri, and quad modes. These can be used for mitigating issues such as the Right Half Plane (RHP) zero that has a negative impact on the dynamic response of the system. Multi-state operation typically requires multi-variable control, which is not easy to realize with conventional PI-type controllers. This paper proposes a unified controller for multi-state operation. It employs a carrier-based modulation scheme with three modulation signals that allows the converter to operate in all four possible states and eight different modes of operation. A mathematical model is developed for devising a multi-variable control scheme using feedback linearization. This allows the design of control loops with simple PI controllers that can be used for all multi-state modes under a wide range of operating conditions with the same performance. The proposed scheme is verified by means of simulations.

Linear Drive Based on Silicon/Ethanol Composite.

The paper presents a concept of an actuator, based on a silicon/ethanol composite placed in the brass bellows. Such actuator is operating based on a change in the physical state of ethanol, which is enclosed in bubbles surrounded by a matrix of silicone rubber. In this paper, the prototype of the actuator is described, and a series of its test results, in the open and closed loops, are presented. Two laser distance-sensors, with different accuracies, were used as a source of the feedback signal. During the investigations the temperature of the actuator was also measured. This has allowed us to determine the delay in heat flow from the heater to the composite. In the closed loop, P- and PI-type controllers were used in the drive positioning experiments. It was discovered that in the closed loop control, it was possible to achieve a positioning error of less than 200 µm. During the tests, the temperature inside the drive and the ambient temperature were also measured. In order to improve the dynamics of the drive, a small fan was used, controlled by the automation system. It allowed us to shorten the time to return the drive to its starting position. The results of frequency tests of the drive have also been presented.

PI-Type Controllers and Σ–Δ Modulation for Saturated DC-DC Buck Power Converters

Departing from analyzing a general input-saturated second-order system, a Lyapunov-based constructive procedure for the output-feedback stabilization of the constantly perturbed DC-DC buck power converter is presented. The proposed scheme also incorporates a Σ-Δ modulator. The obtained control scheme is developed in two parts: a proportional-integral-type family of algorithms devoted to regulating the uncertain system by using measurements of the output voltage and a Σ-Δ modulator dedicated to transforming the control action into a {0, 1} discrete-valued signal. This modulator is a kind of a sliding controller, which can be seen as a subsystem with an on-off output. This combination, the PI-type family of controllers and the Σ-Δ modulator, assures the global stability of the closed-loop system, even if parametric uncertainties are presented. The convergence analysis was carried out using Lyapunov's method. The theoretical results are confirmed using real-time experimental tests, which demonstrate the anti-windup scheme and the Σ-Δ modulator efficiency. The experiments consider the saturation of the control input and disturbances, having obtained convincing results.

H ∞ performance for load frequency control systems with random delays

This paper investigates the problem of performance analysis for PI-type load frequency control (LFC) of power systems with random delays. By taking the probability distribution characteristic of communication delays into account in the LFC design, the power systems with a PI controller are modelled as stochastic time-delay systems. Furthermore, a delay-product-type augmented Lyapunov-Krasovskii functional (LKF) is constructed, and a new extended reciprocally convex matrix inequality combining Wirtinger-based integral inequality with convex combination approach is utilized to reduce the conservatism of main results. As a result, less conservative performance criteria are derived, which guarantee the asymptotically stable in the mean-square of the considered systems. Numerical examples are also provided to illustrate the superiority of our proposed methods.

Application of D-Decomposition Technique to Selection of Controller Parameters for a Two-Mass Drive System

In this work, issues related to the application of the D-decomposition technique to selection of the controller parameters for a drive system with flexibility are presented. In the introduction the commonly used control structures dedicated to two-mass drive systems are described. Then the mathematical model as well as control structure are introduced. The considered structure has only basic feedbacks from the motor speed and PI type controller. Due to the order of the closed-loop system, the free location of the system’s poles is not possible. Large oscillations can be expected in responses of the plant. In order to improve the characteristics of the drive, the tuning methodology based on the D-decomposition technique is proposed. The initial working point is selected using an analytical formula. Then the value of controller proportional gain is decreasing, until the required value of overshoot is obtained. In the paper different advantages of the D-decomposition technique are presented, for instance calculation of global stability area for the selected gain and phase margin, the impact of parameter changes, and additional delay evident in the system. Theoretical considerations are confirmed by simulation and experimental results.

Switching system-based load frequency control for multi-area power system resilient to denial-of-service attacks

Load frequency control (LFC) scheme of modern power systems tends to employ open communication networks to transmit control/measurement signals, which makes the LFC scheme more vulnerable to cyber-attacks such as a denial-of-service (DoS) attack. The DoS attack prevents signal transmission and degrades the performance of or even results in instability in the LFC scheme. This paper proposes a switching system-based approach to the LFC scheme of a multi-area power system that is resilient to DoS attacks. After modelling the LFC scheme under DoS attacks as switching subsystems based on the duration of DoS attacks, a new stability criterion in terms of the duration and frequency of DoS attacks is developed. The derived criterion can be used to calculate the maximum duration and frequency of DoS attacks that the LFC system with a given proportional–integral (PI)-type controller can tolerate and to determine the control gains of the PI-type controller for a given duration and frequency of DoS attack. Moreover, a resilient LFC scheme is proposed based on a dual-loop communication channel equipped with the designed PI controller. The effectiveness of the proposed LFC scheme is evaluated on a traditional three-area power system and a deregulated three-area power system under DoS attacks.

Sensorless Fractional Order Control of PMSM Based on Synergetic and Sliding Mode Controllers

The field oriented control (FOC) strategy of the permanent magnet synchronous motor (PMSM) includes all the advantages deriving from the simplicity of using PI-type controllers, but inherently the control performances are limited due to the nonlinear model of the PMSM, the need for wide-range and high-dynamics speed and load torque control, but also due to the parametric uncertainties which occur especially as a result of the variation of the combined rotor-load moment of inertia, and of the load resistance. Based on the fractional calculus for the integration and differentiation operators, this article presents a number of fractional order (FO) controllers for the PMSM rotor speed control loops, and id and iq current control loops in the FOC-type control strategy. The main contribution consists of proposing a PMSM control structure, where the controller of the outer rotor speed control loop is of FO-sliding mode control (FO-SMC) type, and the controllers for the inner control loops of id and iq currents are of FO-synergetic type. Superior performances are obtained by using the control system proposed, even in the case of parametric variations. The performances of the proposed control system are validated both by numerical simulations and experimentally, through the real-time implementation in embedded systems.

Design of Generalized Predictive Control for the Stabilizing Loop from a two-axis Gimbal Seeker, Considering Cross-Coupling in Between two Channels

In this research, Generalized Predictivecontrol (GPC) is proposed for the control of a stabilizing loop from a two axis gimbal seeker. In fact, there are some views about using GPC type controller which are two folds. First, it drives the stabilization loops that are made by a DC motor, Rate Gyro, inertia and cross coupling unit in between two channels using the predictive model type controller. Second, the theory is to excavate the results of flight simulation on the efficiency of two-axis gimbal seeker. The simulations, based on different scenarios, are valuated for the proficiency of the designed system considering the dynamic mass imbalance and the cross-coupling in between two channels and the flight simulation. The flight simulation results are explained the accuracy of the designed system with predictive control in opposite of conventional PI controller. For example, the simulation results in altitude of 2km show the suggested system in comparison with conventional PI controller improves miss-distance and flight time 11.98% and 1.5% respectively. Moreover, the suggested system in maximum control signal is 72.61%, minimum control signal is 1.55% and final time is 80.43% (control effort parameter), which is better than PI type controller.