Proposed Feedback Control Research Articles

Semiglobal Exponential Stability for Dual-Quaternion-Based Rigid-Body Tracking Control

Semi-Global Exponential Stability (SGES) is proven for the combined attitude and position rigid-body motion tracking problem, presenting a significant upgrade compared to previously proposed controllers which can only guarantee asymptotic stability. Dual quaternions are used to jointly represent the rotational and translational tracking error dynamics of the rigid body. A novel nonlinear feedback tracking controller is proposed, and a Lyapunov-based analysis is provided to prove SGES of the closed-loop dynamics. The analysis does not place any restrictions on the reference trajectory or the feedback gains. This stronger SGES result aids in further analyzing the robustness of the rigid-body system by establishing input-to-state stability (ISS) in the presence of time-varying additive and bounded external disturbances. Motivated by the fact that, in many aerospace applications, stringent adherence to safety constraints such as approach path and input constraints is critical for overall mission success, a framework for safe control of spacecraft is presented that combines the proposed feedback controller with control barrier functions. Numerical simulations are provided to verify the SGES and ISS results and also showcase the efficacy of the proposed nonlinear feedback controller in several nontrivial scenarios, including trajectory tracking, transposition and docking, flip maneuvers, collision avoidance, and rendezvous.

Robust Tracking Control of Wheeled Mobile Robot Based on Differential Flatness and Sliding Active Disturbance Rejection Control: Simulations and Experiments.

This paper proposes a robust tracking control method for wheeled mobile robot (WMR) against uncertainties, including wind disturbances and slipping. Through the application of the differential flatness methodology, the under-actuated WMR model is transformed into a linear canonical form, simplifying the design of a stabilizing feedback controller. To handle uncertainties from wheel slip and wind disturbances, the proposed feedback controller uses sliding mode control (SMC). However, increased uncertainties lead to chattering in the SMC approach due to higher control inputs. To mitigate this, a boundary layer around the switching surface is introduced, implementing a continuous control law to reduce chattering. Although increasing the boundary layer thickness reduces chattering, it may compromise the robustness achieved by SMC. To address this challenge, an active disturbance rejection control (ADRC) is integrated with boundary layer sliding mode control. ADRC estimates lumped uncertainties via an extended state observer and eliminates them within the feedback loop. This combined feedback control method aims to achieve practical control and robust tracking performance. Stability properties of the closed-loop system are established using the Lyapunov theory. Finally, simulations and experimental results are conducted to compare and evaluate the efficiency of the proposed robust tracking controller against other existing control methods.

Networked Evolutionary Game-Based Demand Response via Feedback Controls

In this paper, the demand response considering interactive decision making between residential users and utility companies is modelled and controlled using networked evolutionary game (NEG) theory. The NEG is achieved via a widely used mathematical tool, namely the semi-tensor product (STP) of matrices, through which, feedback controls can be implemented to dynamically regulate the game-based networks. Firstly, the dynamic interactions between utility companies who provide various energy consumption packs and residential users who can intelligently choose preferable packs are modelled in the state-space form, in which both sides are consistently pursuing their maximum payoffs. Then, a quantitive analysis of such system’s equilibria is conducted using rigorous mathematical derivations, followed by the design of a profile feedback controller when the existing equilibria are not satisfactory towards the required energy consumption. Finally, an illustrative example is demonstrated, where the dynamic gaming between utility companies and users is illustrated and the effectiveness of the proposed feedback control is validated. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper addresses a very practical engineering problem, which is the demand response in the modern smart grid. Different from general optimization approaches in the existing works, the method proposed by this paper improves the demand response via feedback control of networked systems, which is based on the rigorous matrix approaches via state space equations. In addition, the work in this paper considers very practical factors in actual engineering (i.e., users with different action choices and decision logics being all together), which also provides much value to practitioners than the relevant works with similar theoretical approaches. The method proposed in this paper provides an effective regulation of the demand response in practice and can be flexibly adjusted according to actual situations.

Optimal Output Consensus of Heterogeneous Linear Multiagent Systems Over Weight-Unbalanced Directed Networks.

This article investigates the distributed optimal output consensus problem of heterogeneous linear multiagent systems over weight-unbalanced directed networks. A novel distributed continuous-time state feedback controller is proposed to steer the outputs of all the agents to converge to the optimal solution of the global cost function. Under the standard condition that the unbalanced digraph is strongly connected and the local cost functions are strongly convex with global Lipschitz gradients, the exponential convergence of the closed-loop multiagent system is established. Then, the proposed state feedback control law is extended to an observer-based output feedback setting. Two examples are finally provided to illustrate the effectiveness of the proposed control schemes.

Bioprocess Intensification of a Continuous-Flow Enzymatic Bioreactor via Productivity Dynamic Optimization under Modeling Uncertainty

In this contribution, a class of observer-based optimal feedback control is designed. The proposed feedback control is based on the Euler–Lagrange theoretical framework, and it is motivated by the productivity intensification from the chemical reactors, which is optimally increased. A Lagrangian is computed by employing the corresponding mass balance equation of a specifically selected biochemical compound. The resulting optimal controller is coupled with a novel uncertainty estimator with bounded feedback to derive an accurate estimation of the unknown terms and functions, mostly related to the reaction rate. Via Lyapunov analysis, it was shown that the proposed observer is asymptotically stable. The estimation of the unknown terms and functions is used by the proposed controller. The proposed methodology is applied to a generic model of an enzymatic biochemical continuous reactor with complex oscillatory dynamic behavior described by mass balance equations, so, in general, the proposed controller may be applied to any continuous stirred tank bioreactor; that is, the controller is independent of the specific kinetic functions. Numerical simulations show a satisfactory performance of the proposed control strategy.

Maximum Convergence Rate Control of a Switched Electrical Network with Symmetries

The purpose of the present research endeavor is to propose a novel control strategy for a DC-DC electrical converter realized as a switched circuit. The present endeavor is based on an early work by Leonard and Krishnaprasad where a prototypical DC-DC converter was modeled as a state space dynamical system and controlled by an open-loop strategy based on Lie group theory. In this work, we shall rather introduce a closed-loop control strategy based on maximum convergence rate, study some features of the novel method, and illustrate its behavior by numerical simulations. A numerical comparison of the two methods complements the paper. The numerical comparison shows how the proposed feedback control method outperforms the static one in terms of convergence rate and resiliency against parameters mismatch.

MIMO state feedback control for redundantly-actuated LiBr/H[formula omitted]O absorption heat pumping devices and experimental validation

Absorption heat pumping devices (AHPDs, comprising absorption heat pumps and chillers) use mainly thermal energy instead of electricity as the driving energy to provide resource-efficient heating and cooling when using waste heat or renewable heat sources. Despite this benefit, AHPDs are still not a very common technology due to their complexity. However, better modulation and part-load capability, which can be achieved through advanced control strategies, can simplify the use of AHPDs and help to better integrate them into complex energy systems. Therefore, this paper presents a new, dynamic model-based control approach for single-stage AHPDs that can extend an AHPD’s operating range by employing multi-input-multi-output (MIMO) control methods. The control approach can be used for different AHPD applications and thus control configurations, i.e., different combinations of manipulated and controlled variables, and can also be used for redundantly-actuated configurations with more manipulated than controlled variables. It consists of an observer for the state variables and unknown disturbances, a state feedback controller and, in case of redundantly-actuated configurations, a dynamic control allocation algorithm. The proposed control approach is experimentally validated with a representative AHPD for two different control configurations and compared to two benchmark control approaches – single-input-single-output (SISO) PI control representing the state-of-the-art, and model-predictive control (MPC) as an alternative advanced control concept. The experimental validation shows that the two MIMO control approaches (the proposed state feedback and the MPC approach) allow for a wider operating range and hence better part load capability compared to the SISO PI control approach. While MPC generally results in a comparably high computational effort due to the necessity of continuously solving an optimization problem, the proposed state feedback control approach is mathematically simple enough to be implemented on a conventional programmable logic controller. It is therefore considered a promising new control approach for AHPDs with the ability to extend their operating range and improve their part load capability, which in turn facilitates their implementation and thus the use of sustainable heat sources in heating and cooling systems.

Wafer Temperature Control Using Helium Pressure and Observer-Based Model Predictive Control

Abstract Stabilizing a wafer’s temperature during plasma etching is a critical issue in semiconductor manufacturing. In this study, we propose feedback control of the wafer temperature using the pressure of helium gas (He) that is fed into the gap between the wafer and an electrostatic chuck (ESC) and an algorithm of the model predictive control (MPC) combined with an observer. The temperatures are measured only at the wafer edge zone and the ESC ceramic plate that are accessible during the process. The observer estimates wafer temperatures of center and edge zones and the injected heat power with the help of the measured edge zone temperature. The MPC determines the optimal He pressures based on the estimated temperatures to control both zone temperatures. The algorithm of the feedback control was formulated, and its validity was experimentally confirmed. Results showed that the observer worked well to estimate both zone wafer temperatures and the injected heat power. Results also showed that the temperatures were successfully controlled.

Optimal Robust Tracking Control of Injection Velocity in an Injection Molding Machine

Injection molding is a critical component of modern industrial operations, and achieving fast and stable control of injection molding machines (IMMs) is essential for producing high-quality plastic products. This paper focuses on solving an optimal tracking control problem of the injection velocity that arises in a typical nonlinear IMM. To this end, an efficient optimal robust controller is proposed and designed. The nonlinear injection velocity servo system is first approximately linearized at iteration points using the first-order Taylor expansion approach. Then, at each time node in the optimization process, the relevant algebraic Riccati equation is introduced, and the solution is used to construct an optimal robust feedback controller. Furthermore, a rigorous Lyapunov theorem analysis is employed to demonstrate the global stability properties of the proposed feedback controller. The results from numerical simulations show that the proposed optimal robust control strategy can successfully and rapidly achieve the best tracking of the intended injection velocity trajectory within a given time.

Design and analysis of experimental adaptive feedback system for active noise control (ANC) in a duct

The limitations of passive noise control methods impose a need for new technical solutions to solve the problem of reducing low-frequency noise, which is considered to be a dominant component of noise disturbance. In recent years, the subject of intensive research are the active noise control systems, which have aroused considerable interest and represent a promising solution to the problem of low-frequency noise control. This paper proposes a robust methodology for simplified design and analysis of an experimental active noise control system for real-time control of acoustic environment in a duct. The proposed feedback control model is based on using the LMS algorithm, combined with FxLMS algorithm for estimation and neutralization of the secondary path in the electro-acoustic system. The study shows the potential of the FPGA module and the Real-time module of cRIO from National Instruments, combined with the LabView software environment when applied in adaptive system for active noise control. The reliability and validity of the developed active noise control system is tested for a frequency range of 100 to 1000 [Hz], by measuring the amplitude-time domain in [V] and sound level in [dB]. The comparison of the experimental results shows great efficiency of the system at lower frequency range from 200 to 400 [Hz], where a maximum reduction in sound level achieved at a frequency of 200 [Hz] is 14 [dB] or 17 [%]. A significant sound level reduction is also achieved at both 300 [Hz] and 400 [Hz] which is 12 % or 10 [dB] in both cases. Given the analysis of the challenges and opportunities of the developed active noise control system, recommendations for advancements and future work are proposed.

The One-Wheel Cubli: A 3D inverted pendulum that can balance with a single reaction wheel

This article presents a novel 3D inverted pendulum that can balance on one of its corners using only a single reaction wheel. This is achieved by a careful design of the mass moment of inertia in such a way that the inertia along the two principal tilt axes is significantly different. The consequence is a time-scale separation of the underlying tilt dynamics, which renders the system controllable. We show that controllability is maximized when the ratio of the two principal inertia values amounts to the square of the silver ratio and discuss a sensor placement that minimizes variance in our tilt estimates. Both of these aspects lead to a principled design of the system. A model is derived from first-principles and used for delay compensation, state estimation, and to design a linear-quadratic regulator that stabilizes the highly underactuated system in its upright equilibrium. Thereby, the modeling and compensation of cantilever deflections, which arise from the lightweight design, is crucial. The article includes experimental results, which underline the efficacy of the system design and highlight an excellent balancing performance of the proposed feedback controller.

Robust Global stabilization of aerial continuum manipulation systems via hybrid feedback

In this paper, the control problem of aerial continuum manipulation systems (ACMSs) is considered. This study introduces a new platform for ACMSs in which a quadrotor is equipped with a tendon-bent concentric tube continuum robot. The decoupled dynamic modeling of ACMSs is utilized to derive the proposed feedback control law. The control design process is split into two distinct control loops. In the first loop, a terminal synergetic controller is presented to control the continuum robot’s tip to track the desired trajectory. In the second loop, an improved synergetic controller is introduced to control the position and velocity of the quadrotor, which ensures asymptotic stability of the origin of the error dynamic. Moreover, in this loop a hybrid feedback law is designed to operate with the improved synergetic controller, which overcomes topological obstructions and globally stabilizes the attitude of the quadrotor. Furthermore, the stability of the resultant closed-loop system is verified utilizing the Lyapunov stability theorem. The efficiency and advantages of the proposed controller are verified by a comparative analysis in simulations.

New fuzzy control design for photovoltaic system using LMI technique

The T-S Fuzzy model-based technique (T-S: Takagi-Sugeno) is used in this research to offer a new fuzzy state feedback control for solar systems with output charge. We discuss a DC-DC boost converter to manage the output power of a solar panel array under shifting meteorological circumstances. To reach optimal power point, a T-S reference model is employed to create a fuzzy state feedback control that must be tracked. Solving a series of linear matrix inequalities (LMIs) yields controller gains. Furthermore, the proposed solution reduces the oscillation disadvantage near the highest power point while simultaneously shortening the tracking time. Finally, simulation of the solar system employing the proposed state feedback control shows that the proposed approach is effective even in the face of climate change.

Dissipative constraint-based control design for singular semi-Markovian jump systems using state decomposition approach

This paper proposes a unified control design for a class of singular semi-Markovian jump systems with a time-varying delay in the state vector by employing the state decomposition approach and dissipative theory. To begin, the addressed system is decomposed into differential–algebraic form with new state vectors, from which a mode-dependent augmented Lyapunov–Krasovskii functional is constructed. The desired stochastic admissibility and dissipative conditions are then obtained, where the auxiliary function-based integral inequality, the generalized free-weighting-matrix approach and the augmented zero equality approach are used in the derivation to achieve less conservative results. In accordance with these conditions, a relationship for determining the mode-dependent gain parameters of the proposed state feedback control is given. As a result, the theoretical findings of this paper lead to better results than some previously published ones, as demonstrated by four numerical examples.

Improved Feedback Control and Optimal Management for Battery Storage System in Microgrid Operating in Bi-Directional Grid Power Transfer

This paper presents an improved feedback controller and optimal management system to operate a battery storage system in a microgrid. The aim is to optimize the storage usage by reducing the battery degradation. The feedback controller regulates the battery current to track a reference despite uncertainties. It includes a disturbance observer to compensate unknown uncertainties and improve its tracking performance. The current reference is carried out using a management system based on the power balance in the microgrid connected to the main grid. Furthermore, the management system uses a coefficient to operate the battery depending on its constraints and the grid electricity price. This allows online optimization of the battery operation based on the price variations to reduce its degradation. The control and management systems are validated by simulation and the results are provided to demonstrate their effectiveness. Furthermore, experimentation is conducted to evaluate the control performance. The results show that the proposed feedback controller and disturbance observer provide better mean absolute error (0.0846) for the current tracking compared to only feedback controller (0.2073) and conventional proportional-integral controller (0.1126). Moreover, the proposed management system represents a reduction in the battery degradation by 74.56% compared to the conventional management system.

A novel feedback controller design with robust fault isolation ability

This paper proposes a novel feedback controller design scheme which can achieve fault isolation based on the control signal or its embedded signal, i.e., with the self-fault-isolation ability. First of all, according to the well-known Youla parameterization, a controller structure consisting of state and residual joint feedback is developed. Then, the residual feedback gain and observer gain are designed to make the cooperative structured residual feedback signal have fault isolation ability. Some free design parameters in the two gains are further utilized for robust self-fault-isolation. Moreover, the state feedback gain is designed, in the framework of switched system, to realize the self-fault-diagnosis and isolation, based on the control signal directly. The proposed control structure also has the advantage of cooperative fault tolerance. Finally, the simulation of HVAC (Heating, Ventilation and Air Conditioning) system, composed of four rooms in one story building scenario, is carried out to demonstrate the effectiveness and superiority of the proposed feedback controller design approach.

Spiral wave drift under optical feedback in cardiac tissue.

Spiral waves occur in various types of excitable media and their dynamics determine the spatial excitation patterns. An important type of spiral wave dynamics is drift, as it can control the position of a spiral wave or eliminate a spiral wave by forcing it to the boundary. In theoretical and experimental studies of the Belousov-Zhabotinsky reaction, it was shown that the most direct way to induce the controlled drift of spiral waves is by application of an external electric field. Mathematically such drift occurs due to the onset of additional gradient terms in the Laplacian operator describing excitable media. However, this approach does not work for cardiac excitable tissue, where an external electric field does not result in gradient terms. In this paper, we propose a method of how to induce a directed linear drift of spiral waves in cardiac tissue, which can be realized as an optical feedback control in tissue where photosensitive ion channels are expressed. We illustrate our method by using the FitzHugh-Nagumo model for cardiac tissue and the generic model of photosensitive ion channels. We show that our method works for continuous and discrete light sources and can effectively move spiral waves in cardiac tissue, or eliminate them by collisions with the boundary or with another spiral wave. We finally implement our method by using a biophysically motivated photosensitive ion channel model included to the Luo-Rudy model for cardiac cells and show that the proposed feedback control also induces directed linear drift of spiral waves in a wide range of light intensities.

Exponential Stabilization for a Class of Strict-Feedback Nonlinear Time Delay Systems via State Feedback Control Scheme

This paper considers the exponential stabilization problem for a class of strict-feedback nonlinear systems with multiple time-varying delays, whose nonlinear terms satisfy the linear growth condition. The state feedback controller that relies on a positive parameter to be determined is constructed to deal with nonlinear terms. By tactfully introducing the Lyapunov–Krasovskii functional with an exponential function and selecting the applicable parameter to be determined, the implementable state feedback controller can be obtained to guarantee that the closed-loop system is exponentially stable. The proposed state feedback control scheme is finally applied to the control design of two-stage chemical reactor system, which illustrates the effectiveness of the control method.

Nonpharmaceutical Stochastic Optimal Control Strategies to Mitigate the COVID-19 Spread

This article proposes a stochastic nonlinear model predictive controller to support policymakers in determining robust optimal nonpharmaceutical strategies to tackle the COVID-19 pandemic waves. First, a time-varying SIRCQTHE epidemiological model is defined to get predictions on the pandemic dynamics. A stochastic model predictive control problem is then formulated to select the necessary control actions (i.e., restrictions on the mobility for different socioeconomic categories) to minimize the socioeconomic costs. In particular, considering the uncertainty characterizing this decision-making process, we ensure that the capacity of the healthcare system is not violated in accordance with a chance constraint approach. The effectiveness of the presented method in properly supporting the definition of diversified nonpharmaceutical strategies for tackling the COVID-19 spread is tested on the network of Italian regions using real data. The proposed approach can be easily extended to cope with other countries’ characteristics and different levels of the spatial scale. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the emerging need for developing effective methods to support policymakers in mitigating the effects of the COVID-19 pandemic. The proposed feedback control strategy—combining a multiregion epidemiological model with a nonlinear stochastic model predictive control approach—allows the robust identification of the most effective restrictive measures considering the corresponding effects on the healthcare and socioeconomic systems. The proposed framework is a general and flexible method that can be applied to various real scenarios, leveraging mobility data, available from the Google mobility service, to recognize patterns and predict future behaviors of individuals.

A Time-Optimal Feedback Control for a Particular Case of the Game of Two Cars

In this article, a computationally efficient time-optimal feedback solution to the game of two cars, for the case where the pursuer is faster and more agile than the evader, is presented. The concept of continuous subsets of the reachable set is introduced to characterize the time-optimal pursuit–evasion game under feedback strategies. Using these subsets, it is shown that, if initially the pursuer is distant enough from the evader, then the feedback saddle point strategies for both the pursuer and the evader are coincident with one of the common tangents from the minimum radius turning circles of the pursuer to the minimum radius turning circles of the evader. Using geometry, four feasible tangents are identified and the feedback <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\min -\max$</tex-math></inline-formula> strategy for the pursuer and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\max \text{--}\min$</tex-math></inline-formula> strategy for the evader are derived by solving a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\times 2$</tex-math></inline-formula> matrix game at each instant. Insignificant computational effort is involved in evaluating the pursuer and evader inputs using the proposed feedback control law, and hence, it is suitable for real-time implementation.