Classical Linear Control Research Articles

Generalized Homogeneous Formation Control for Unicycle Multi-Agent Systems

In this paper, the formation control problem for unicycle multi-agent systems is considered. The design of a generalized homogeneous leader–follower formation control protocol is studied which shows that such a control protocol can be obtained by “upgrading” from the classical linear control. With this proposed control protocol, a finite-time stability of the formation error is ensured if the acceleration of the leader is bounded by some known value. In addition, if the leader acceleration is unknown but bounded, the robust formation is achieved by ensuring the formation error’s input-to-state stability. Simulations are carried out to verify the effectiveness of the proposed control protocol.

Nonlinear control of the permanent magnet synchronous motor PMSM using input-output linearization control and sliding mode control

Today, electric machines are becoming increasingly important in all sectors (industrial drives, the automotive industry, aviation, traction systems, and agriculture, etc.). Among these machines, permanent magnet synchronous machines (PMSMs) hold a significant place in the control of industrial mechanisms, automated systems, and in the fields of renewable energy like (wind energy, solar energy, and hybrid systems, etc ). Currently, in variable speed drives, the use of PMSM, especially for low power and certain special industrial applications, is replacing DC motors and asynchronous motors because they offer higher efficiency, power factor, and torque density. Moreover, PMSM do not have an excitation circuit in the rotor, which leads to reduced maintenance demands. The control of permanent magnet synchronous machines (PMSM) presents significant challenges due to their nonlinear behavior. Classical linear controllers, such as PI, perform well with linear systems that have constant parameters. However, for nonlinear systems with varying parameters, the conventional control methods may prove insufficient and exhibit a lack of robustness. To address the issues and achieve decoupled machine control, various methods have been proposed. Nonlinear robust control techniques have been extensively explored within the domain of power electronics and drive systems. Included in these, sliding mode control and nonlinear input-output feedback linearization (IOFL). Sliding mode control (SMC) is a control technique known for its excellent dynamic performance in PMSM drives. It offers high robustness and straightforward implementation in both software and hardware. However, a significant drawback of this method is the chattering phenomenon. By the way the input/output linearization control can provide good behavior in steady and dynamic regimes and also provides good decoupling between system variables. This article presents a design of tow control laws based on sliding mode and feedback linearization controller based on input-output feedback linearization to adjust the speed of a permanent magnet synchronous motor (PMSM). To highlight the effectiveness of the designed controllers, a comparison was carried out Matlab Simulink, revealing that the feedback linearization controller outperforms the SMC.

Data-driven acoustic control of a spherical bubble using a Koopman linear quadratic regulator.

Koopman operator theory has gained interest as a framework for transforming nonlinear dynamics on the state space into linear dynamics on abstract function spaces, which preserves the underlying nonlinear dynamics of the system. These spaces can be approximated through data-driven methodologies, which enables the application of classical linear control strategies to nonlinear systems. Here, a Koopman linear quadratic regulator (KLQR) was used to acoustically control the nonlinear dynamics of a single spherical bubble, as described by the well-known Rayleigh-Plesset equation, with several objectives: (1) simple harmonic oscillation at amplitudes large enough to incite nonlinearities, (2) stabilization of the bubble at a nonequilibrium radius, and (3) periodic and quasiperiodic oscillation with multiple frequency components of arbitrary amplitude. The results demonstrate that the KLQR controller can effectively drive a spherical bubble to radially oscillate according to prescribed trajectories using both broadband and single-frequency acoustic driving. This approach has several advantages over previous efforts to acoustically control bubbles, including the ability to track arbitrary trajectories, robustness, and the use of linear control methods, which do not depend on initial guesses.

Application of two-step input to reduce overshoot of the transient response at automated control systems

The problems of quality improving for technology control are very important and are considered in works on the theory of automatic control and related fields. Various approaches to solving the problems are known especially by the decreasing overshoot of step response. To provide this the most of existing methods require: to adjust a controller parameters; development of a mathematical model of a controlled object; additional filters applications, that as a whole is difficult to implement under industrial conditions. The authors have proposed another approach to solving the above problems, contrary to the known ones. Namely, to apply two successive inputs with lower amplitudes and delay in time instead of the known one step input. The response of the controlled system on the complex two step inputs was considered and the optimal time delay was defined. The investigations were conducted by the modelling a typical classic linear automation control system that consists of a static control object of the first order with time delay, proposal - integration - difference controllers. The modelling results for a transient under the various applied one and two step inputs, including their ramp variation were obtained. It was shown that the two-step inputs with their ramp application gives the decreasing of the maximum displacement for a transient in a typical control system: more than 3 times increase was shown comparing with the one-step approach. The optimal time interval between the steps was determined that leads to the maximum effectiveness of the technology application. The procedure to define the details of the approach application was developed

Using a Flywheel to Stabilize a Self-Balancing Bicycle

The designs of two linear control systems approach to stabilize the balance of an unmanned bicycle system are presented. Both approaches are based on the use of a reaction wheel or flywheel to balance the bicycle. The two linear control approaches, based on the linearization of a nonlinear model obtained using Lagrange formalism, are the classic linear controllers, PID and State Feedback control. The performance of both controllers is verified by digital simulation and real-time experimental results.

Rotor-Flux Vector Based Observer of Interior Permanent Synchronous Machine

The sensorless control system of the interior permanent magnet machine (IPMSM) is considered in this paper. The control system is based on classical linear controllers. In IPMSM, there occurs non-sinusoidal distribution of rotor flux together with the slot harmonics, these are treated as control system disturbances. In this case, the classical observer structure in the (d-q) is unstable for the low range of rotor speed resulting in disturbances. This negative effect can be minimized by using the observer structure which is based on the rotor flux vector in (α-β) stationary frame together with the classical rotor speed and position law of estimation. The performance of the observer structure is validated by simulation and experimental results in the sensorless control system with field-oriented control.

Design and FPGA-in-loop based validation of predictive hierarchical control for islanded AC microgrid

This paper proposes a decentralized control approach for the flexible operation of an autonomous AC microgrid (MG). AC MG typically consists of two or more voltage source inverters (VSI), capable of simultaneously regulating the voltage at the point of common coupling (PCC) and meeting the local power demand. The classical linear control techniques attain these functions. However, they have many limitations, such as slow transient response, high sensitivity to the parameter variations, and inability to handle the system nonlinearities. This paper aims to address these issues by presenting an improved finite control set model predictive control (FCS-MPC) approach for inverter-based distributed generation (DG). The proposed scheme tracks the voltage trajectory using cost function (CF) over two-step prediction horizons. The proposed control method is employed for the AC MG having two parallel DGs. Droop control is responsible for the power-sharing between the parallel DGs regardless of impedance mismatch at the distribution level of AC MG. The decentralized secondary control is developed to eliminate the deviation in the voltage and frequency caused due to overlooking the primary control. The proposed control scheme has been validated through extensive simulations and real-time controller hardware in the loop tests using an FPGA ZYBO Z7 board. Moreover, the proposed methodology depicts the enhanced transient response, less computational burden than the classic MPC, and shows robustness to parametric uncertainties in terms of THD than hierarchical linear control. The simulations and experimental results visually represent research outcomes, exhibiting the THD of 0.98 % for different dynamic loads, which is within the limit of IEEE and IEC standards. Furthermore, the proposed controller’s mathematical stability is further supported by analysis based on the Lyapunov stability theory.

Platooning Cooperative Adaptive Cruise Control for Dynamic Performance and Energy Saving: A Comparative Study of Linear Quadratic and Reinforcement Learning-Based Controllers

In recent decades, the automotive industry has moved towards the development of advanced driver assistance systems to enhance the comfort, safety, and energy saving of road vehicles. The increasing connection and communication between vehicles (V2V) and infrastructure (V2I) enables further opportunities for their optimisation and allows for additional features. Among others, vehicle platooning is the coordinated control of a set of vehicles moving at a short distance, one behind the other, to minimise aerodynamic losses, and it represents a viable solution to reduce the energy consumption of freight transport. To achieve this aim, a new generation of adaptive cruise control is required, namely, cooperative adaptive cruise control (CACC). The present work aims to compare two CACC controllers applied to a platoon of heavy-duty electric trucks sharing the same linear spacing policy. A control technique based on reinforcement learning (RL) algorithm, with a deep deterministic policy gradient, and a classic linear quadratic control (LQC) are investigated. The comparative analysis of the two controllers evaluates the ability to track inter-vehicle distance and vehicle speed references during a standard driving cycle, the string stability, and the transient response when an unexpected obstacle occurs. Several performance indices (i.e., acceleration and jerk, battery state of charge, and energy consumption) are introduced as metrics to highlight the differences. By appropriately selecting the reward function of the RL algorithm, the analysed controllers achieve similar goals in terms of platoon dynamics, energy consumption, and string stability.

Controlled synchronization of coupled pendulums by Koopman Model Predictive Control

We propose a method to solve a class of control problems arising from a system of coupled pendulums. The system considered in this work is a one-dimensional array of pendulums pivoting around a single axis with adjacent pendulums coupled through torsion springs. Only a single torque motor attached to one of the two boundary pendulums actuates the system. This setup of coupled pendulums is a mechanical realization of the Frenkel–Kontorova (FK) model – a spatially discrete version of the sine-Gordon equation describing (nonlinear) waves. The main challenges of controlling this system are high order (the number of pendulums can be high), nonlinear and oscillatory dynamics, and only one actuator. The proposed class of problems can be characterized as controlled synchronization – designing a closed-loop controller that synchronizes the motion of the pendulums. Controlled synchronization is a special case of reference tracking, where all pendulums reach a common point or a trajectory. One can formulate many practically motivated problems within this class; here, we identify three problems: a vibration control of a flexible structure, swing-up control of all pendulums in the array, and low-friction sliding of an atomic-scale structure. We show that the presented problems can be dealt with by the Koopman Model Predictive Control (KMPC). The KMPC allows for controlling nonlinear systems by combining the classical linear model predictive control (MPC) with the Koopman operator approach for nonlinear dynamical systems. The main idea of the method is to construct a linear predictor of a nonlinear system in a higher-dimensional, lifted space and use the predictor within the linear MPC. The optimization problem formulation within the KMPC can then be tailored to a specific problem in the class. Simulations and experiments on a hardware platform realizing the FK model show the effectiveness of the method.

Nonlinear active disturbance rejection control for deformable mirror

The disturbance in the adaptive optical system includes not only the low-frequency broadband disturbance but also the high-frequency narrow-band disturbance caused by the vibration of system components and atmospheric turbulence. A nonlinear active disturbance rejection control (NLADRC) method is proposed to solve the control problem of a deformable mirror under high-frequency narrow-band disturbance. This method does not completely depend on the mathematical model, and the algorithm structure is simple. The differential tracker flattens the abrupt part of the signal, and the extended state observer is used to estimate the disturbance in real time. Finally, the nonlinear control rate is used to compensate the disturbance. The simulation results show that compared with the classical PID control and the classical linear active disturbance rejection control, the NLADRC method can effectively improve the bandwidth of the control system and show good suppression performance against high-frequency narrow-band disturbance, and the system is more robust. Both in time domain and frequency domain, it can accurately track the system state, reduce the system delay and system error, and has better dynamic performance.

A note on the minimum‐norm in dual space approach to some classical linear optimal control problems

AbstractSome classical optimal control problems of linear systems can be characterized as finding minimum‐norm vectors from within linear varieties in appropriate dual spaces. Then, the solution to such an optimal control problem can be derived from the alignment between the optimal vector in the dual space and the optimal vector in the primal space, and the dual maximization problem of the minimum‐norm problem. This note presents a detailed introduction to this minimum‐norm in dual space approach by examples of minimum‐supremum‐norm, minimum‐energy, and minimum‐time optimal control problems of linear systems. Connections and differences between these problems in light of the introduced approach are discussed.

An Overall Linearized Modeling Method and Associated Delay Time Model for the PV System

There are some significant nonlinearity and delay issues in photovoltaic (PV) system circuits. Therefore, it is very difficult for the existing classic linear control theories to be used in PV systems; this hinders the design of the optimal energy dispatch by considering real-time generation power forecasting methods. To solve this problem, an overall linearized model with variable weather parameters (OLM-VWP) of the PV system is proposed on the basis of small-signal modeling. Meanwhile, a corresponding simplified overall linearized model with variable weather parameters (SOLM-VWP) is presented. The SOLM-VWP avoids analyzing delay characteristics of the complex high-order PV system. Moreover, it can reduce hardware cost and computation time, which makes analysis of the transient performance index of the PV system more convenient. In addition, on the basis of the OLM-VWP and SOLM-VWP, a delay-time model with variable weather parameters (DTM-VWP) of the PV system is also proposed. The delay time of the system can be accurately calculated using the DTM-VWP, and it provides a preliminary theoretical basis for carrying out real-time energy scheduling of the PV system. Finally, simulations are implemented using the MATLAB tool, and experiments are conducted. The results verify that the proposed linearization model of the PV system is accurate and reasonable under varying irradiance and temperature conditions. Meanwhile, the results also verify that the proposed SOLM-VWP and DTM-VWP of the PV system are feasible. Additionally, the results show that some transient performance indexes (delay time, rise time, settling time, and peak time) can be solved by means of equations when the circuit parameters and real-time weather parameters are given.

EXPERIMENTAL ANALYSIS OF HYBRID ENERGY STORAGE SYSTEM BASED ON NONLINEAR CONTROL STRATEGY

In this paper, a nonlinear integral sliding mode control for a hybrid energy storage system (HESS) based stand-alone dc microgrid has been proposed and applied experimentally. This hybrid system comprises a PV, super-capacitor, and battery. A classical PI-based linear control strategy has been designed to control battery and super-capacitor systems based on decoupling the high and low-frequency components to estimate reference current. Since the frequent discharge during operation, super-capacitor power can reach the lowest value, affecting controller performance and making the system unstable. From the experimental result, a nonlinear Integral sliding mode control ISMC is performed as an inner loop controller to regulate battery and super-capacitor power. Also, the PI controller is implemented as an outer loop controller to regulate the dc-link. The proposed control approach is compared with the linear PI controller to improve life extension and minimize stress on the battery. As a result, the proposed control strategy has achieved high dynamic system performance.

Experimental Validation for Artificial Data-Driven Tracking Control for Enhanced Three-Phase Grid-Connected Boost Rectifier in DC Microgrids

This article introduces the control and operation of a grid-connected converter with an energy storage system. A complete mathematical model was presented for the developed converter and its control system. The system under study was a small microgrid comprising an AC grid that is feeding a DC load through a converter. The converter was connected to the AC grid through an R-L filter. The classical linear controllers have limitations due to their slow transient performance and low robustness against parameter variations and load disturbances. In this paper, machine-learned controllers were used to dealing with those drawbacks of the traditional controller. First, a study for conventional nested loop Proportional Integral (PI) was introduced for both outer and inner loops PI-PI controller. A Data-Driven Online Learning (DDOL) controller was then proposed. A comparison between the normal traditional PI-PI controller and the proposed DDOL ones was made under different operating scenarios. The converter control was tested under various operational conditions, and its dynamic and steady-state behavior was analyzed. The model was done through a MATLAB Simulink to check the normal operation of the network in a grid-connected mode under different load disturbances and AC input voltage. Then, the system was designed, fabricated, and implemented in a hardware environment in our Energy Systems Research Laboratory (ESRL) testbed, and the hardware test results were verified. The results showed that the proposed DDOL controller was more robust and had better transient and steady state performances.

A Modular Circuit Synthesis Oriented Modelling Approach for Non-Isolated DC-DC Converters in CCM

The continued commissioning of DC microgrids in an effort to achieve net-zero carbon levels in the atmosphere demands the large-scale deployment of converters to make the power from renewable energy sources, such as solar PV, usable. To control these inherently non-linear converters using classical linear control methods, averaged modelling techniques are employed. These methods are laborious and easily become intractable when applied to converters with increased energy storage elements. A modular modelling approach is proposed. This approach is based on the synthesis of converters using refined basic building blocks. The refined basic building blocks are independently modelled as two-port networks and used in a circuit synthesis-oriented manner to derive power stage models of commonly used DC-DC converters. It is found that most of the converters considered in the study can be described as a cascade combination of these basic building blocks. As such, transmission parameters are mainly used to model the two-port networks. Moreover, it is also found that using this modelling technique enables the computation of generalized expressions for all power stage models of interest. The use of two-port networks curtails the size of the matrices describing the basic building blocks to 2 × 2, and thus simplifies the entire modelling procedure. Additionally, two-port network analysis makes this modelling technique modular, thus making it more suited to be employed in DC microgrids. The independence of the two-port models on the circuit topology and functionality makes it possible to even model new converters containing the described basic building blocks solely based on circuit connection.

Implementation and Analysis of a Fuzzy Logic and Sliding Mode Controller on a Boost DC/DC Converter in a PV Array

The DC/DC converters are primarily and practically used for switch-mode regulated power source and renewable energies such as photovoltaic or wind turbine. the principal purpose of these converters is to adapt the input with the output in other words, to preserve a consistent output voltage no matter the variations of the internal and external parameters of the converter. Different control techniques are commonly used to adapt and regulate the output voltage of these converters and make them more efficient and more robust in the event of unwanted disturbances, such as classic linear controllers for instance (proportional integrator and derivator controller PIDC ) and nonlinear controllers as (fuzzy logic FLC, sliding mode controller SMC). This article presents a comparative performance of Fuzzy Logic Control (FLC) and Sliding Mode Control (SMC) on a DC/DC Boost converter submitted to different type of variations. The performance evaluation criteria depend on speed and precision of the transient response. The two proposed controllers are modeled, designed and simulated using MATLAB/SIMULINK. The results of the comparison between the two controllers confirm the effectiveness of sliding mode control in terms of rapidity and precision compared with FLC.

Control of a closed dry grinding circuit with ball mills using predictive control based on neural networks

Closed circuit dry grinding using ball mills is essential in mineral processing industries. This process is characterized by significant dead times, highly coupled variables, limitations by operating ranges and complex modeling, making it difficult for classical controls to obtain fast responses with low overshoot. An alternative to overcome these difficulties is intelligent controls, such as the artificial neural network model predictive control (NNMPC). This study aimed to develop a NNMPC for dry grinding in a closed circuit with a ball mill. Artificial Neural Network represented the multi-input-multi-output system for the model to predict the outputs in the predictive control strategy. Compared to the classical controls and linear model predictive control, the results obtained by the NNMPC were superior with lower errors and better robustness, reaching a reduction of up to 79% and 74.2% for overshoot and settling time, respectively, besides being more efficient in simulations with simultaneous disturbances of the controlled variables.

Mechatronic design of dynamically decoupled manipulators based on the control performance improvement

AbstractThe control of industrial robot manipulators presents a difficult problem for control engineers due to the complexity of their nonlinear dynamics models. Nonlinear controls based on feedback linearization are developed to meet control requirements. Model-based nonlinear control is highly sensitive to parameter errors and leads to problems of robustness for tracking trajectories at high speeds, and there is the additional problem of a heavy computational burden to consider in the design of nonlinear controllers. In this paper, a mechatronic design approach is proposed, which aims to facilitate controller design by redesigning the mechanical structure. The problem is approached in two steps: first, the dynamic decoupling conditions of manipulators are described and discussed, involving redistribution of the moving mass, which leads to the decoupling of motion equations. A classical linear control law is then used to track the desired efficient bang-bang profile trajectory. Then, in the presence of parameter uncertainty and external disturbances, the nonlinear controls with simple structures are adopted to stabilize the decoupled system asymptotically. An analysis of the results from a simulation of this approach demonstrates its effectiveness in controller design. The proposed improvement in control performance is illustrated via two spatial manipulators.

Model-Free Control of Single-Phase Boost AC/DC Converters

Conventionally, the benchmark proportional-integral control method is implemented to realize power factor correction and output voltage regulation of single-phase ac/dc converters. However, the performance is deteriorated due to the influence of uncertainties and disturbances, e.g., periodic input voltage and load variation. Concerning this problem, this article proposes a model-free control (MFC) strategy of single-phase ac/dc converters. The MFC principle is revisited and a frequency response analysis is presented for the algebraic estimators of uncertainties and disturbances. Consequently, the closed-loop performance of MFC systems is allowed to be analyzed in frequency domain via classical linear control theory. Based on the theoretical results, the model-free current and voltage control systems are synthesized in detail to achieve control objectives of the converter. Simulation results demonstrate the performance of MFC systems in reference tracking and disturbance rejection. The feasibility and validity of the presented MFC strategy for single-phase boost ac/dc converters is also confirmed experimentally as compared to the benchmark scheme.

A PD-Type State-Dependent Riccati Equation With Iterative Learning Augmentation for Mechanical Systems

This work proposes a novel proportional-derivative (PD)-type state-dependent Riccati equation (SDRE) approach with iterative learning control (ILC) augmentation. On the one hand, the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers. On the other hand, the SDRE adds nonlinear and optimality characteristics to the controller, i.e., increasing the stability margins. These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning. The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{K}(\mathrm{x})$</tex> for the control input law <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{u}=-\mathrm{R}^{-1}(\mathrm{x})\mathrm{B}^{T}(\mathrm{x})\mathrm{K}(\mathrm{x})\mathrm{x}$</tex> . The sub-blocks of the overall gain <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{R}^{-1}(\mathrm{x})\mathrm{B}^{T}(\mathrm{x})\mathrm{K}(\mathrm{x})$</tex> , are not necessarily symmetric positive definite. A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{u}= -\mathrm{K}_{\mathrm{SP}}(\mathrm{x})\mathrm{e}-\mathrm{K}_{\mathrm{SD}}(\mathrm{x})\dot{\mathrm{e}}$</tex> . The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems; and presents guaranteed uniform boundedness in finite-time between learning loops. The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation (SDDRE) to manipulate the final time. The SDDRE expresses a differential equation with a final boundary condition, which imposes a constraint on time that could be used for finite-time control. So, the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool. The learning rules benefit from the gradient descent method for both regulation and tracking cases. One of the advantages of this approach is a guaranteed-stability even from the first loop of learning. A mechanical manipulator, as an illustrative example, was simulated for both regulation and tracking problems. Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark.