Nonlinear Closed-loop Control Research Articles

Data-Driven Switch Fault Diagnosis for DC/DC Boost Converters in Photovoltaic Applications

Switch semiconductors are essential components in power electronics stages for photovoltaic (PV) systems, which are prone to failures caused mainly by thermal stress, thereby affecting PV energy production. Specifically, dc/dc boost power converters are commonly used as maximum power point tracking (MPPT) systems. Several works have been reported so far in the literature for switch fault detection and isolation (FDI) purposes in boost power converters. However, most of them require additional sensors and circuitry to those included in any PV system, which generate extra costs on the overall system. Hence, this work presents an efficient and low-cost switch fault diagnosis proposal, which requires only the most common measurements in PV systems, namely, PV current and voltage. This work departs from a data-driven FDI methodology for diagnosing switch open- and short-circuit faults in dc/dc boost converters. The experimental results have been evaluated against sudden irradiance changes and switch faults in a test bench of 350 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rm {W}$</tex-math></inline-formula> operating under a closed-loop nonlinear control action for MPPT purposes by using the dSpace 1104 board.

Closed-loop nonlinear optimal control design for flapping-wing flying robot (1.6 m wingspan) in indoor confined space: Prototyping, modeling, simulation, and experiment

The flapping-wing technology has emerged recently in the application of unmanned aerial robotics for autonomous flight, control, inspection, monitoring, and manipulation. Despite the advances in applications and outdoor manual flights (open-loop control), closed-loop control is yet to be investigated. This work presents a nonlinear optimal closed-loop control design via the state-dependent Riccati equation (SDRE) for a flapping-wing flying robot (FWFR). Considering that the dynamic modeling of the flapping-wing robot is complex, a proper model for the implementation of nonlinear control methods is demanded. This work proposes an alternative approach to deliver an equivalent dynamic for the translation of the system and a simplified model for orientation, to find equivalent dynamics for the whole system. The objective is to see the effect of flapping (periodic oscillation) on behavior through a simple model in simulation. Then the SDRE controller is applied to the derived model and implemented in simulations and experiments. The robot bird is a 1.6 m wingspan flapping-wing system (six-degree-of-freedom robot) with four actuators, three in the tail, and one as the flapping input. The underactuated system has been controlled successfully in position and orientation. The control loop is closed by the motion capture system in the indoor test bed where the experiments of flight have been successfully done.

A Maneuvering Model for an Underwater Vehicle Near a Free Surface—Part III: Simulation and Control Under Waves

This article incorporates free-surface and ambient wave effects into a nonlinear parametric model. Subsequently, its use is demonstrated via simulation of a scale model submarine maneuvering under the control of a nonlinear depth-keeping control system in a seaway. An energy-based model is presented, which represents the underactuated submarine in a free-surface-affected state. This model is then used to synthesize a control law using port-Hamiltonian theory and interconnection and damping assignment passivity-based control. The Lyapunov analysis is used to study the stability of the closed-loop system, and a simulation-based demonstration illustrates the performance of the control law. The results demonstrate that a closed-loop nonlinear controller is able to improve the quality of near-surface depth keeping by automatically compensating for parasitic effects in the hydrodynamics that can compromise depth-keeping performance during maneuvers.

Design of a Takagi–Sugeno Fuzzy Exact Modeling of a Buck–Boost Converter

DC–DC converters are used in many power electronics applications, such as switching power supply design, photovoltaic, power management systems, and electric and hybrid vehicles. Traditionally, DC–DC converters are linearly modeled using a typical operating point for their control design. Some recent works use nonlinear models for DC–DC converters, due to the inherent nonlinearity of the switching process. In this sense, a standout modeling technique is the Takagi–Sugeno fuzzy exact method due to its ability to represent nonlinear systems over the entire operating range. It is more faithful to system behavior modeling, and allows a nonlinear closed-loop control design. The use of nonlinear models allows the testing of controllers obtained by linear methods to operate outside their linearization point, corroborating with robust controllers for specific applications. This work aims to perform the exact fuzzy Takagi–Sugeno modeling of a buck–boost converter with non-ideal components, and to design a discrete proportional–integral–derivative (PID) controller from the pole cancellation technique, obtained linearly, to test the controller at different operating points. The PID control ensured a satisfactory result compared with the stationary value of the different operating points, but it did not reach the desired transient response. Since the proposed model closely represents the operation of the buck–boost converter by considering the components’ non-idealities, other control techniques that consider the system’s nonlinearities can be applied and optimized later.

Parameter-adaptive reference governors with learned robust constraint-admissible sets

Reference governors (RGs) provide an effective method for ensuring safety via constraint enforcement in closed-loop nonlinear control systems. When the system parameters are uncertain but constant, robust formulations of RGs that consider only the worst-case effect may be overly conservative and exhibit poor performance. This paper proposes a parameter-adaptive reference governor (PARG) architecture that is capable of generating safe trajectories in spite of parameter uncertainties, without being as conservative as robust RGs. The proposed approach employs machine learning on a combination of off-line simulations and on-line measurements to estimate parameter-robust constraint-admissible sets (PRCASs) that can be leveraged by the PARG. We illustrate the robust set learning and constraint enforcement qualities of the PARG using a two-dimensional electromagnetic actuator example, and further demonstrate the potential of the PARG on a vehicle case study for preventing rollover despite aggressive maneuvering.

Extremum seeking controller tuning for heat pump optimization using failure-robust Bayesian optimization

Extremum seeking controllers have been investigated for multivariable data-driven energy optimization in heat pumps. In particular, proportional–integral extremum seeking control (PI-ESC) has demonstrated potential for significant acceleration compared to other ESC variants for nonlinear closed-loop control systems. A barrier to PI-ESC’s utilization in self-optimizing control is the fact that the PI-ESC algorithm is fragile. That is, unless the PI-ESC gains (e.g., controller gains, estimator gains) are carefully tuned, small perturbations to these gains can render the closed-loop unstable. Since arbitrary combinations of PI-ESC gains can result in instabilities, we propose a failure-robust Bayesian optimization (FRBO) algorithm that computes PI-ESC gains that ensure the closed-loop system can be driven rapidly to the optimum, while identifying and avoiding regions in the space of PI-ESC gains that are likely to result in instabilities (i.e., failures). The FRBO-tuned PI-ESC is shown to result in rapid closed-loop convergence to optimal values both on benchmark examples and a production-level model of an air conditioning system.

Performance Analysis and Comparison of Non-Inverting Buck-Boost Converter Using PI, OCC, and Hybrid OCC-PI Control

The study compares and analyses the performance of the one-cycle control (OCC), hybrid one-cycle-proportional integral control (OCC-PI), and the conventional PI control method applied to the non-inverting buck-boost converter. The hybrid OCC-PI control method combines the OCC and PI control techniques to provide a hybrid non-linear closed-loop control technique for regulating the buck-boost converter. The MATLAB/Simulink equivalent system model was simulated with design parameter variations using a wide input voltage range of 9 – 36 V, a nominal output voltage of 28 V, and a fixed switching frequency of 250 kHz to validate the control response speed, reliability, and robustness of the proposed control technique. The simulation results due to input voltage, output voltage, and load variations were carried out whiles recording the settling time, overshoots, efficiency, output voltage, and inductor current ripples due to each applied control technique. The simulation results indicated that the Hybrid OCC-PI control provides better response speed and a lower output voltage overshoot relative to the PI. It also provides better reference voltage tracking compared to the OCC control method.

Motorized FES-cycling and closed-loop nonlinear control for power tracking using a finite-time stable torque algorithm

Functional electrical stimulation (FES)-induced cycling is a rehabilitation strategy that activates lower-limb muscles to achieve coordinated pedaling in individuals with movement disorders. An electric motor is included in-the-loop assisting the rider as needed to prolong exercise duration and mitigate muscle fatigue. Power tracking objectives have been prescribed for motorized FES-cycling, where muscles and the electric motor are assigned to track desired cadence (speed) and torque trajectories. However, predetermined desired trajectories can yield poor cycling performance since the functional capacity of each individual is unknown. In particular, when muscles are tasked to track a desired torque, a dynamic approach is well-motivated to adjust the torque demand for the rider in real-time (e.g., a constant torque demand may be unfeasible throughout a cycling session since muscles fatigue). In this paper, input-output data is exploited using a finite-time algorithm to estimate the target desired torque leveraging an estimate of the active torque produced by muscles via FES. The convergence rate of the finite-time algorithm can be adjusted by tuning selectable parameters. The cycle-rider system is modeled as a nonlinear, time-varying, state-dependent switched system to activate lower-limb muscles and an electric motor. To achieve cadence and torque tracking, nonlinear robust tracking controllers are designed for muscles and motor. A robust sliding mode controller is designed for the electric motor to track a desired constant cadence trajectory. Moreover, an integral torque feedback controller is designed to activate quadriceps, hamstrings, and gluteus muscle groups to track the desired torque trajectory computed by the finite-time algorithm. A Lyapunov-based stability analysis is developed to ensure exponential tracking of the closed-loop cadence error system and global uniformly ultimate bounded (GUUB) torque tracking. A discrete-time Lyapunov-based stability analysis leveraging a recent tool for finite-time systems is developed to ensure convergence and guarantee that the finite-time algorithm is Hölder continuous. The developed tracking controllers for the muscles and electric motor and finite-time algorithm to compute the desired torque are implemented in real-time during cycling experiments in seven able-bodied individuals. Multiple cycling trials are implemented with different gain parameters of the finite-time torque algorithm to compare tracking performance for all participants.

A novel model-free robust saturated reinforcement learning-based controller for quadrotors guaranteeing prescribed transient and steady state performance

For the purpose of improving the performance of trajectory tracking for quadrotors with the control input saturation, a novel model-free saturated prescribed performance reinforcement learning framework is proposed in the presence of the model uncertainties, nonlinearities and external disturbances. In this paper, saturation functions are employed to deal with input saturation, and the actuator's saturation nonlinearity is compensated by an intelligent method to decrease the saturation effects. Moreover, the prescribed performance control is utilized to ensure an adjustable transient and steady state response for the tracking errors. Besides, adaptive robust controllers are introduced to handle the effects of external disturbances online. A novel controller is proposed in collaboration with a reinforcement learning method based on actor-critic neural networks. The actor neural network is employed to estimate nonlinearities, actuator saturation nonlinearity, and model uncertainties, and the critic neural network is applied to estimate the reinforcement signals, which regulates the control action of the actor neural network online. The proposed actor-critic-based control structure benefits from a model-free calculation and only depends on the measurable signals of the closed-loop system. This freedom from system dynamics leads to a significant low computational load for the controller and, therefore, the proposed control method is computationally cost-effective. The adaptive robust controllers and the proposed actor-critic structures are trained online, and the convergence behavior of their learning laws is investigated in the course of stability examination. For the proof of stability, Lyapunov's direct method is used to show that all error variables of the closed-loop nonlinear control system are uniformly ultimately bounded. Finally, simulations along with some quantitative comparisons verify the efficiency and usefulness of the proposed control scheme.

Instability Condition Derivation for Hydraulic AGC System under Pressure Closed-Loop Control

In strip rolling, hydraulic automatic gauge control (HAGC) system is the key element to guarantee the precision of strip gauge. The stability of the kernel pressure closed loop (PCL) in the HAGC system plays an essential role in guaranteeing the rolling process with high performance. Nevertheless, there is some difficulty in exploring the instability mechanism of the HAGC system due to the fact that the PCL is a representative nonlinear closed-loop control system. In this work, for each component of the HAGC system, the mathematical model was established. And on the basis of the linking relation of various elements, we derived the incremental transfer model of the PCL system. Furthermore, in accordance with the deduced information transfer relation, the transfer block diagram of disturbing variable of the PCL system was obtained. Moreover, for the purpose of deriving the instability condition of the PCL system, the Popov frequency criterion was employed. The instability conditions of the HAGC system were obtained under PCL control. Furthermore, the derived instability conditions of the HAGC system were experimentally verified under various working conditions. The research results provide a fundamental foundation for studying the instability mechanism of the HAGC system.

Experimental Investigation on Control of an Infinitely Variable Transmission System for Tidal Current Energy Converters

High operation performance of a tidal current energy converter (TCEC) requires a gear transmission with a continuously variable speed ratio for low-speed and high-torque conditions. A nonlinear closed-loop control combined with an integral time-delay feedback control is developed to adjust the speed ratio of an infinitely variable transmission (IVT) system for TCECs. A speed ratio control for the IVT system involves a forward speed controller and a crank length controller for different tidal current speed ranges. The time-delay control is designed to reduce speed fluctuations of the output speed of the IVT with an accurate speed ratio. Experimental investigation was carried out to test the validity of the proposed control strategy for the IVT system. An instrumented rotation speed measurement system is designed so that quantities needed for the time-delay control variable can be measured. Experimental results show that the speed ratio of the IVT with the proposed control strategy can achieve an excellent tracking response for the desired constant output speed and reduce speed fluctuations of the output speed of the IVT by the time-delay feedback control.

Synergetic synthesis of aggregated discrete regulators for induction motors

The paper presents the method of synergetic synthesis of a nonlinear discrete control system for induction motors. The proposed approach is based on using the methods of the synergetic control theory and nonlinear mathematical models of induction motors. This approach allows to create nonlinear closed-loop piecewise-continuous control systems which guarantee the asymptotic stability of the controlled induction motors, accomplishment of the determined technological and electromagnetic invariants and selective invariance to the unknown external disturbances acting on the system. The invariance of the designed systems is ensured due to the usage of a dynamic discrete regulator which increases the astatism of the synthesized system.

Phase-Locked Loop Independent Second-Order Generalized Integrator for Single-Phase Grid Synchronization

Second-order generalized integrator (SOGI) requires fast and accurate grid voltage frequency information for quadrature signal generation (QSG) in single-phase systems. Conventionally, synchronous reference frame phase-locked loop (PLL) (SRFPLL) is used in a cascade manner and provides frequency feedback to SOGI. PLL is a non-linear closed-loop control system that requires adequate gain parameter design trade-off to provide accurate grid synchronization. Additionally, it creates interdependent loops while estimating the grid frequency and phase-angle. This results in unwanted frequency disturbances during grid transients, such as voltage sag and phase-angle jumps (PAJs) which are fed back to the SOGI as well. Thus, this article proposes two PLL independent frequency-feeding approaches for SOGI: Type-A and -B. The frequency is estimated using the normalized single-phase grid voltage signal in both types. In Type-A, the normalization is done using cascaded recursive discrete-Fourier transform (RDFT) and inverse RDFT (IRDFT). On the other hand, in Type-B, SOGI outputs are used for normalization. The grid voltage amplitude is estimated using the absolute value of the in-phase and in-quadrature components of the proposed frequency-adaptive SOGI. Furthermore, the third-order polynomial approximation of the arctangent function is implemented for phase-angle estimation in both types. The performance of both the types during transients and steady-state grid voltage disturbances (dc offset and harmonics) are compared with SOGIPLL using both simulations and experiments.

On Nonlinear Pest/Vector Control via the Sterile Insect Technique: Impact of Residual Fertility.

We consider a minimalist model for the Sterile Insect Technique (SIT), assuming that residual fertility can occur in the sterile male population. Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we study different control strategies that involve either continuous or periodic impulsive releases. We show that a combination of open-loop control with constant large releases and closed-loop nonlinear control, i.e., when releases are adjusted according to the wild population size estimates, leads to the best strategy in terms of both number of releases and total quantity of sterile males to be released. Last but not least, we show that SIT can be successful only if the residual fertility is less than a threshold value that depends on the wild population biological parameters. However, even for small values, the residual fertility induces the use of such large releases that SIT alone is not always reasonable from a practical point of view and thus requires to be combined with other control tools. We provide applications against a mosquito species, Aedes albopictus, and a fruit fly, Bactrocera dorsalis, and discuss the possibility of using SIT when residual fertility among the sterile males, can occur.

Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System

In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly accurate numerical computations over simulating guaranteed enclosures of all reachable states of a dynamic system model with bounded uncertainty in parameters and initial conditions, to the solution of global optimization tasks. By exploiting the fundamental enclosure properties of interval analysis, this paper aims at computing invariant sets of nonlinear closed-loop control systems. For that purpose, Lyapunov-like functions and interval analysis are combined in a novel manner. To demonstrate the proposed techniques for enclosing invariant sets, the systems examined in this paper are controlled via sliding mode techniques with subsequently enclosing the invariant sets by an interval based set inversion technique. The applied methods for the control synthesis make use of a suitably chosen Gröbner basis, which is employed to solve Bézout’s identity. Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets.

Double Closed-Loop Controller Design for Boost Pressure Control of Turbocharged Gasoline Engines

The precise boost pressure control is the key to guaranteeing reliable turbocharged gasoline engine operation. The closed-loop control requires fast boost pressure tracking performance in wide engine operating range. This paper presents a double closed-loop nonlinear control scheme to improve transient tracking performance. The air-path system of the turbocharged gasoline engine is described by a physics-based, nonlinear, mean value model that presents a long regulation channel from the control input, wastegate-opening, to the control output, boost pressure and brings challenges for the controller design with satisfied tracking performance. To address this problem, the outer loop treats the turbine speed as a downstream control demand and adjusts it by using a feedforward-feedback control to achieve fast boost pressure tracking. Subsequently, a disturbance-observer-based nonlinear inner-loop controller is designed to regulate the wastegate that stabilizes the turbine speed tracking error while handles the uncertainties due to operating variation. The stability of the whole closed-loop system is analyzed by the Lyapunov stability theory and the robustness against operating variation is discussed based on input to state stability (ISS). The effectiveness of the proposed controller is validated through a higher fidelity model in AMESim and its performances are compared with well-tuned baseline controllers.

Nonlinear control of a subscale submarine in emergency ascent

This paper presents a nonlinear parametric model and proof-of-concept motion control system for a scale model submarine undertaking an emergency ascent. An energy-based model is presented that represents the underactuated submarine in a non-neutrally buoyant state. This model is then used to synthesize a control law using Port-Hamiltonian theory and interconnection and damping assignment passivity-based control. Lyapunov analysis is used to demonstrate stability of the closed-loop system, and a simulation-based study is presented to demonstrate performance of the control law. The results demonstrate that a closed loop non-linear controller is able to improve the quality of emergency rise by automatically compensating for some parasitic effects in the hydrodynamics that can compromise ascent performance.

Learning-Based Predictive Control for Discrete-Time Nonlinear Systems With Stochastic Disturbances.

In this paper, a learning-based predictive control (LPC) scheme is proposed for adaptive optimal control of discrete-time nonlinear systems under stochastic disturbances. The proposed LPC scheme is different from conventional model predictive control (MPC), which uses open-loop optimization or simplified closed-loop optimal control techniques in each horizon. In LPC, the control task in each horizon is formulated as a closed-loop nonlinear optimal control problem and a finite-horizon iterative reinforcement learning (RL) algorithm is developed to obtain the closed-loop optimal/suboptimal solutions. Therefore, in LPC, RL and adaptive dynamic programming (ADP) are used as a new class of closed-loop learning-based optimization techniques for nonlinear predictive control with stochastic disturbances. Moreover, LPC also decomposes the infinite-horizon optimal control problem in previous RL and ADP methods into a series of finite horizon problems, so that the computational costs are reduced and the learning efficiency can be improved. Convergence of the finite-horizon iterative RL algorithm in each prediction horizon and the Lyapunov stability of the closed-loop control system are proved. Moreover, by using successive policy updates between adjoint time horizons, LPC also has lower computational costs than conventional MPC which has independent optimization procedures between two different prediction horizons. Simulation results illustrate that compared with conventional nonlinear MPC as well as ADP, the proposed LPC scheme can obtain a better performance both in terms of policy optimality and computational efficiency.

Design of Lyapunov Based Nonlinear Position Control of Electrohydraulic Servo Systems

This paper studies the nonlinear closed loop control of an electrohydraulic servo system. The control strategy is developed based on Lyapunov theory of nonlinear systems using integrator backstepping approach. Highly nonlinear nature of electrohydraulic servo system is well known. Main reasons for nonlinear and non-differentiable mathematical description of systems dynamics are the fluid compressibility, leakage flows, friction forces and nonlinear fluid flow through servo valve orifices. These nonlinear terms influence also the dynamic errors of the control system. Two different nonlinear design procedures are employed feedback linearization and integrator backstepping. Backstepping is used here because it is a powerful and robust nonlinear strategy. These techniques are used for construction of nonlinear control algorithm. The effectiveness of it, to stabilize any operating point of the system is proved by computer simulation. The systems error dynamics significantly depends on tuning parameters of the controller. The wrong selection of these parameters may lead to saturation or chattering of control signals. All derived results are validated by computer simulation of a nonlinear mathematical model of the system. The results are also compared to these obtained with a conventional P controller to prove that classic linear controllers fail to achieve a good tracking of the desired output, especially, when the hydraulic actuator operates at the maximum load. The research studies represented in the paper shows big potential of Lyapunov based nonlinear controller design procedures, to obtain desired control objectives.

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.