Optimal Control Design Research Articles

Enhanced and robust contrast in CEST MRI: Saturation pulse shape design via optimal control.

To employ optimal control for the numerical design of Chemical Exchange Saturation Transfer (CEST) saturation pulses to maximize contrast and stability against inhomogeneities. We applied an optimal control framework for the design pulse shapes for CEST saturation pulse trains. The cost functional minimized both the pulse energy and the discrepancy between the corresponding CEST spectrum and the target spectrum based on a continuous radiofrequency (RF) pulse. The optimization is subject to hardware limitations. In measurements on a 7 T preclinical scanner, the optimal control pulses were compared to continuous-wave and Gaussian saturation methods. We conducted a comparison of the optimal control pulses with Gaussian, block pulse trains, and adiabatic spin-lock pulses. The optimal control pulse train demonstrated saturation levels comparable to continuous-wave saturation and surpassed Gaussian saturation by up to 50 % in phantom measurements. In phantom measurements at 3 T the optimized pulses not only showcased the highest CEST contrast, but also the highest stability against field inhomogeneities. In contrast, block pulse saturation resulted in severe artifacts. Dynamic Bloch-McConnell simulations were employed to identify the source of these artifacts, and underscore the robustness of the optimized pulses. In this work, it was shown that a substantial improvement in pulsed saturation CEST imaging can be achieved by using Optimal Control design principles. It is possible to overcome the sensitivity of saturation to B0 inhomogeneities while achieving CEST contrast close to continuous wave saturation.

Optimal control design for power system stabilizer using a novel crow search algorithm dynamic approach

This paper proposes the first application of a novel improved metaheuristic optimization technique, dynamic crow search algorithm (DCSA) to find the optimal design of the power system stabilizer (PSS). Using the novel DCSA adaptive approach provides a global search capability as well as fastness and effectiveness to get the PSS best parameters under the search space constraints and local optimums. Moreover, PSS parameters has a crucial effect on power system stability that is a major nowadays engineering concern, where its best parameters could make a difference by damping small-signal stability oscillations effectively and in the smallest amount of time if they are obtained through a robust algorithm. As a result, PSS will prevent large types of instabilities which could reach up to some generation stations shedding. The novel proposed algorithm is for first time used and tested under different power system instabilities scenarios by using single-machine infinity bus model over multiple operating conditions to damp out perturbation signals effectively by means of getting optimal PSS design parameters, where Integral absolute error (IAE) performance index is used as an objective function to be minimized. Additionally, results obtained by the proposed approach are compared with those obtained by other methods. It is observed that the proposed method has better convergence characteristics and robustness compared to the original version and other comparison methods. It is revealed that the proposed adaptive method is able to improve the power system stability dynamics and damp out perturbation oscillations successfully.

Simultaneous optimal system and controller design for multibody systems with joint friction using direct sensitivities

AbstractReal-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the system and its controller. This work addresses the gradient-based optimization methodology for multibody dynamic systems with joint friction using a direct sensitivity approach. The Brown–McPhee model has been used to characterize the joint friction in the system. This model is suitable for the study due to its accuracy for dynamic simulation and its compatibility with sensitivity analysis. This novel methodology supports codesign of the multibody system and its controller, which is especially relevant for applications like robotics and servo-mechanical systems, where the actuation and design are highly dependent on each other. Numerical results are obtained using a software package written in Julia with state-of-the-art libraries for automatic differentiation and differential equations. Three case studies are provided to demonstrate the attractive properties of simultaneous optimal design and control approach for certain applications.

Optimal and simultaneous synthesis of fractional order QFT controllers and prefilters for non-minimum phase hydro power systems

Abstract Ideally, the operating frequency of the power units, working in parallel, must not deviate from its nominal value. However, due to the dynamic nature of the load, operating frequency varies throughout the day; thus, the control of governors in the prime movers is essential to balance out the demand, and prevent any frequency deviation. To address this, present study investigates the design of optimal and robust quantitative feedback theory based (QFT) controllers and pre-filters for single area load frequency control of hydro power systems. Hydropower system model considered in the present study features a right-hand side zero, thus exhibiting non-minimum phase; these characteristics make the control more challenging. Also, the work investigates the optimal design of the QFT controllers and prefilters simultaneously by automating the loop shaping procedure, which else follows a sequential manual process on Nichols charts. The proposed automation also empowers the control designer to predefine the controller structure. In the present work the design of fractional order QFT controllers and pre-filters is considered. The study also compares the proposed work with the methods proposed in the existing literature as well as the optimal controllers obtained using the time domain indices. The obtained results establishes that the developed fractional QFT controller offers good tracking, stability, and robustness to disturbances when compared to existing approaches. The proposed fractional order QFT controllers offer the elimination of the overshoot and the undershoot from the closed loop response of the system; outperforms the existing controllers in terms of disturbance rejection; offers 0% steady-state deviation, while providing improved phase margin (60.1°) for enhanced stability compared to existing controllers. Also, the proposed QFT-GA attains the ideal values for both the peak complementary sensitivity functions; thus, establishing excellent robustness. Also, the proposed controllers ensure adequate tolerance to frequency deviation in case of load change.

Design and analysis of a high-efficiency bi-directional DAB converter for EV charging

The escalating demand for electric vehicles (EVs) arises from apprehensions regarding fossil fuel depletion and the ecological repercussions of conventional combustion engines, propelling the transition towards environmentally sustainable alternatives. EVs are conventionally comprised of a powertrain, battery management system, and communication infrastructure, with the battery playing a pivotal role. Achieving an efficient EV battery charger necessitates the implementation of a proficient charging algorithm and a high-power converter capable of adeptly regulating battery parameters. Among the array of available options, a bi-directional DC/DC converter is often employed for this purpose. This study predominantly focuses on the Bi-Directional Dual Active Bridge Converter with Single-Phase Shift Control. It is renowned for attaining a broad voltage range through transformer turn ratio adjustments. Its controllable parameters, such as phase shift ratio and duty cycle, bolster its versatility. Moreover, due to its input–output isolation and minimal passive elements, this converter exhibits superior efficiency due to its soft-switching capabilities. The analytical framework encompasses steady-state and dynamic assessments, small-signal modeling, and system transfer function analysis, all of which contribute to formulating an optimized controller design. Additionally, the study conducts simulations of various battery charging techniques, including constant current (CC), constant voltage (CV), and CCCV mode, employing a 1.5 kW Dual Active Bridge DAB-based charger through MATLAB/SIMULINK. Furthermore, voltage mode control simulations for a 5 kW DAB converter augment the study's insights into effective EV charging strategies.

A flow-field integrated flight control: dynamic wind tunnel testing and simulation

Abstract Abrupt changes in aircraft attitude due to encountering terrain turbulence or wind shear at low altitudes can directly lead to serious accidents. Therefore, a highly responsive and reliable active attitude stabiliser on board is necessary to counteract low-level severe atmospheric disturbances. However, gust environments caused by local terrain and structures are difficult to represent with typical models, such as the Dryden continuous gust model in free space. As a result, an optimal model-based control design cannot be applied. To address this problem, this paper introduces an adaptive mechanism for updating motion equations based on atmospheric conditions using in-flight surface pressure-field sensing. Additionally, a dynamic wind tunnel experiment system, which can be constructed at universities at a low cost, is developed and described in detail. The effectiveness of the proposed scheme is evaluated through wind tunnel experiments and numerical simulations using a large number of gust samples.

Interval riccati equation-based and non-probabilistic dynamic reliability-constrained multi-objective optimal vibration control with multi-source uncertainties

Structural vibration control is used to ensure the safety of structures in service and has become an active research area in the past few years. In this study, uncertainties in structural dynamics are considered to propose an interval linear quadratic regulator (LQR) method based on an interval Riccati equation. Multi-objective optimization with non-probabilistic dynamic reliability as a constraint is performed to design an optimal uncertain vibration control system. To alleviate the difficulty of quantifying the probabilistic uncertainty and accurately characterize uncertainty information for small samples, multi-source uncertainties are regarded as interval parameters. The bounds on these uncertainties are determined, and the deterministic and uncertain parts of an interval state-space equation for vibration control are then formulated using an expanded-order matrix and the interval analysis method. Next, the interval perturbation method with a matrix series is used to develop a novel solution method for the linear inhomogeneous time-invariant equation in the interval state-space equation for the vibration control system and is used to accurately predict the interval bounds of the state responses. The conventional LQR method from modern control theory is used to propose a novel optimal control method based on a novel interval Riccati equation using the Lyapunov equation and interval uncertainty propagation. The proposed interval control method can be used to estimate the uncertain bounds of the controlled gain and cost function. A non-probabilistic dynamic reliability model is established to evaluate the reliability index of the system, which can overcome the limitations of the large computational cost of determining the probabilistic reliability. The deterministic controlled cost and uncertain states are considered as two optimization objectives with the proposed reliability constraint. The resulting constrained multi-objective optimal vibration control problem is designed and solved using c-DPEA. A flowchart is presented as a clear overview of the uncertain vibration control method, and the effectiveness of the proposed method is validated using two numerical examples. Different optimal control designs are obtained using different reliability constraints for quantitatively analyzing the safety of the control system.

Adaptive neural inverse optimal control for uncertain switched nonlinear systems: an improved predefined-time method

For the first time, this paper introduces an improved predefined-time inverse optimal method to address the adaptive tracking control problem of a class of uncertain switched nonlinear systems. The proposed approach enables the system to achieve optimal performance without resorting to the HJB equation. Firstly, we design two-time constants to improve the traditional predefined-time lemma. The improved predefined-time lemma exhibits faster convergence. Subsequently, to realise the design of a predefined-time inverse optimal controller, a specific form of the auxiliary controller is designed using Sontag functions and nonsingular functions. Furthermore, the stability of the system and the optimality of the inverse are proven through the use of a common Lyapunov function method, ensuring that tracking errors converge to the neighbourhood of zero within the predefined time. Finally, the rationality of the proposed control structure is demonstrated through the example results.

Design and evaluation of self-tuning optimal control for vibration suppression of magnetorheological semi-active suspension

The objective of this paper is to enhance the vibration damping capabilities of magnetorheological (MR) semi-active suspension by utilizing a self-tuning LQG control method. Firstly, to determine the mechanical model of MR damper using the hyperbolic tangent model, mechanical experiments were performed with a damping force test machine under various input excitations. Experimental and simulation data were compared to confirm the accuracy of the mechanical model for MR damper. The MR damper is then incorporated into the vehicle’s semi-active suspension system to create a quarter-car suspension model. In order to tackle the problems associated with low control accuracy and poor dynamic adjustment in traditional LQG controllers where the weighting matrix coefficients are difficult to determine, a self-tuning LQG controller based on gravity search algorithm (GSA-LQG) was designed. Finally, the designed controller performance was evaluated by the simulation and experimental results obtained from the random and sinusoidal excitation roads. Experimental data reveal that when subjected to GSA-LQG control, the suspension control performance is considerably enhanced compared to the passive control, PID control and conventional LQG control suspension. Based on these outcome, it can be concluded that the proposed algorithm is effective and the experimental platform is feasible.

Analysis of stability and bifurcation and design of optimal control for phytoplankton–zooplankton–fish model with additional food and fish harvesting

ABSTRACT This paper investigates the dynamics of a four-dimensional plankton-fish system that contains three communities of plankton: non-toxic phytoplankton, toxic-producing phytoplankton, and zooplankton. The zooplankton consumes both non-toxic and toxic-producing phytoplankton. First, the positivity and boundedness of the solutions in the plankton-fish model are evaluated. Then, we derive the conditions for the existence of ecologically possible equilibria and their local and global asymptotic nature. Furthermore, we evaluate the criteria for the existence of Hopf-bifurcation and transcritical bifurcation. By applying Pontryagin’s maximum principle, we investigate the optimal control of fish harvesting, where fishing effort is taken as a control parameter. By using phase-space diagrams, time responses, bifurcation diagrams, and numerical analyses validate the theoretical results. The numerical results including maximum Lyapunov exponent verify chaotic dynamics of the system. We notice that a suitable choice of harvesting, phytoplankton growth rate, and additional food parameters can control the chaotic behavior of the presented model. The proposed novel mathematical model gives deeper insights to theoretical ecologists on how toxic-producing phytoplankton affects zooplankton and fish populations in aquatic systems. Furthermore, the proposed model is more appropriate for fish harvesting to maximize profit as well as species conversion in the presence of toxic phytoplankton.

Optimal design of fractional-order proportional integral derivative controllers for structural vibration suppression

In designing control systems, it is known that fractional-order proportional integral derivative (FOPID) controllers often provide greater flexibility than conventional proportional integral derivative (PID) controllers. This higher level of flexibility has proven to be extremely valuable for various applications such as vibration suppression in structural engineering. In this paper, we study the optimization of FOPID controllers using twelve well-established algorithms to minimize structural responses under seismic excitations. The algorithms include crystal structure algorithm (CryStAl), stochastic paint optimizer, particle swarm optimization, krill herd, harmony search, ant colony optimization, genetic algorithm, grey wolf optimizer, Harris hawks optimization, sparrow search algorithm, hippopotamus optimization algorithm, and duck swarm algorithm. In addition to highlighting the benefits of fractional calculus in structural control, this study provides a detailed analysis of FOPID controllers as well as a brief description of the algorithms used to optimize them. To evaluate the efficiency of the proposed techniques, two building models with different numbers of stories are examined. FOPID controllers are designed based on oustaloup’s approximation and the El Centro earthquake data. Using five well-known metrics, the performances of the developed methods are evaluated against five earthquake scenarios, including the recent earthquake in Turkey. A non-parametric (Friedman) test is also employed to compare the algorithms based on their corresponding vibration reduction. The findings of this analysis show that CryStAl consistently performs better than the other algorithms for both building models, thus resulting in superior vibration suppression.

Optimal IOFL-based economic model predictive control technique for boiler-turbine system

The optimal control design of the boiler-turbine system is vital to ensure feasibility and high responsiveness over desired load variations. Using the traditional linear control techniques realization of this task is difficult, as the boiler-turbine mechanism has strong nonlinearities. Besides, environmental and economic concerns have replaced existing tracking control ones as the primary concerns of advanced power plants. Thus, this study proposes an optimal economic model predictive controller (EMPC) scheme for this unit on the basis of the input/output feedback linearization (IOFL) method. By employing the IOFL method, this unit is decoupled into a new linearized model that is utilized for developing the suggested optimal IOFL EMPC technique. The proposed control scheme is formulated in an economic quadratic programming form that considers the input-rate and input limits of the unit for optimal economic performance. In addition, an adaptive iterative algorithm is utilized for constraints mapping with guaranteeing a feasible solution in a finite number of steps without violation of original constraints over the entire predictive horizon. The outcomes of the simulation show that the suggested optimal IOFL EMPC scheme offers an improved dynamic and economic output performance over fuzzy hierarchical MPC, fuzzy EMPC, and nonlinear EMPC techniques during various load variations.

An adaptive fractional order optimizer based optimal tilted controller design for artificial ventilator

An adaptive fractional order optimizer based optimal tilted controller design for artificial ventilator

On the optimal game control in the DC microgrid systems

AbstractThis paper introduces static and dynamic competitive optimal control of DC/DC converters in DC microgrids based on game theory considering mutual effects. Using static and dynamic game theories, the conditions for competitive optimal control of DC/DC converters in Nash equilibrium with static and dynamic states are determined. Also, to reduce the complexity in the design of competitive optimal control of DC/DC converters due to the bilinear dynamic model of the system, generalized objective functions are considered. The competitive optimal controls using the Lyapunov and Riccati equations are determined to track the system trajectory to Nash equilibrium. Also, the numerical and experimental results are presented and compared in several cases. The results show that the competitive optimal control of the DC/DC converters in the DC microgrids can effectively improve the performance of the system.

THE CHALLENGES OF MEDICAL RESOURCE LIMITATIONS FOR TUBERCULOSIS UNDER THE COVID-19 PANDEMIC: A MATHEMATICAL MODELING OF CO-INFECTION AND OPTIMAL CONTROL

Currently, more than 600 million people worldwide are diagnosed with COVID-19, while the implication of Tuberculosis cannot be ignored. The combination of COVID-19 and Tuberculosis exacerbates the catastrophe, dealing a serious blow to the healthcare system. This paper addresses how to develop effective and reasonable programs to combat the spread of COVID-19 and Tuberculosis in the absence of Tuberculosis medical resources, as well as exploring the impact of medical resources on optimal control implementation. Therefore, a co-infection dynamic of COVID-19 and Tuberculosis is constructed and analyzed. In order to investigate approaches to mitigate the disease transmission, a comprehensive and integrated study including sensitivity analysis, optimal control design and cost-effectiveness analysis is then performed. The simulation results illustrate that, the combination of the three control measures effectively achieves a win-win result in economic and epidemiological terms. In addition, the impact of Tuberculosis medical resources is highlighted, and the study shows that an appropriate increase in the medical resource supply for Tuberculosis during optimal control can have a stronger inhibitory effect on co-infection. Finally, based on the actual data, the model is validated by fitting the cumulative confirmed case curves of the two diseases.

On the optimal multi-objective design of fractional order PID controller with antlion optimization

This study introduces an optimal multi-objective design approach for a robust multimachine Fractional Order PID Controller (FOPID) using the Antlion algorithm. The research focuses on the need for effective stabilizers in multimachine power systems by employing traditional speed-based lead-lag FOPID controllers. The study formulates a multi-objective problem, optimizing the damping factor and damping ratio of lightly damped electromechanical modes to maximize a composite set of objective functions, tackled through the Antlion algorithm. Stability analysis of Single-Machine Infinite-Bus (SMIB) and multimachine power systems is conducted based on rotor speed and power deviation minimization in the time domain response, along with damping ratio and eigenvalue analysis. The proposed approach is implemented and tested on three IEEE test cases, showcasing significant improvements in stability through the reduction of maximum overshoot (Mp) and settling time (ts) of speed deviation. Comparative analysis with other optimization-based FOPID controllers underscores the superiority of the proposed approach in enhancing stability in multimachine power systems. The main impact of this research lies in its contribution to the advancement of stability enhancement techniques in multimachine power systems, offering a systematic framework for optimal FOPID controller design and empowering decision-making processes in power engineering.

Adaptive Fault-Tolerant Tracking Control for Discrete-Time Nonstrict-Feedback Nonlinear Systems With Stochastic Noises

This paper discusses the problem of fault-tolerant tracking control for discrete-time nonstrict-feedback nonlinear systems in the presence of stochastic noises and actuator faults. The system is characterized by a discrete-time nonstrict-feedback structure and multiplicative stochastic noise related to the states, which poses a challenge for the design and analysis of the fault-tolerant controller. Moreover, the considered actuator faults include multiplicative and additive faults without prior information. By integrating the properties of the backstepping framework and neural networks, and by introducing an adaptive fault compensation term, a novel fault-tolerant tracking control strategy is proposed. The effects of faults are compensated and the difficulties caused by the system structure are overcome, avoiding the algebraic loop problem and overcoming the causal contradiction. Given specific parameters, the designed fault-tolerant controller can ensure that the tracking error converges to an adjustable region regarding the origin and that all system signals are uniformly bounded concerning the mean-square sense. The simulation examples illustrate the effectiveness of the designed fault-tolerant control method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As system complexity has been increasing, practical systems are often affected by faults when performing tracking control. Fault-tolerant control can provide acceptable robustness and improve system safety. On the one hand, many practical systems are nonlinear, difficult to model mathematically and accurately, and affected by stochastic noises. On the other hand, with digital control, the object is a discrete-time system. In practical applications, the upper bounds of the faults and the noises are often unknown. In this paper, a novel adaptive fault-tolerant control method is proposed for the more general uncertain discrete-time nonlinear systems, i.e., nonstrict-feedback nonlinear systems, with stochastic noises and actuator faults. Neural networks and an adaptive fault compensation term are integrated into the fault-tolerant controller. By adjusting the controller parameters properly, it is ensured that the tracking error converges to a small neighborhood of zero in the event of a fault occurring. In future research, sensor faults, input constraints, optimal control design, and applications in multi-agent systems will be considered.

Optimal switching boundary control for two-dimensional piecewise linear dynamical systems

This paper deals with the optimal control design for a family of two-dimensional piecewise linear systems having a switching boundary defined by a straight line and vector fields with regular equilibrium points. Such a family is derived from discontinuous control systems characterized by exhibiting sliding motion and a single pseudo-equilibrium point at the switching boundary, which is the desired operating point of the system in the control design. The initial objective is to obtain conditions on the slope of the switching boundary so that the pseudo-equilibrium is asymptotically stable, at least locally. The second and main objective is, based on the pseudo-equilibrium stability result, to find the optimal slope for the switching boundary in order to minimize the transient response time. A numerical method for obtaining the optimal slope is presented, and the effects caused by uncertainties in the parameters are discussed. The used approach explores an innovative way of determining the optimal slope of the switching boundary based on finite-time stability conditions. The results obtained are applied to a power electronic system that describes the dynamics of a Buck Converter under a sliding mode control strategy.

An Alternative Optimal Design of Dynamic Straight-Right Lane Control for T-Shaped Intersections

An Alternative Optimal Design of Dynamic Straight-Right Lane Control for T-Shaped Intersections

Optimal design of robust control for belt conveyor systems based on fuzzy dynamic model and Nash game

An optimized robust control method is proposed in this paper to deal with the disturbances of nonlinear factors such as uncertainty in belt conveyor and to realize the speed control of belt conveyor. By controlling the subsystems to track the same desired speed, belt breaks and overlaps caused by varying belt speeds from one section to another are limited. First, a fuzzy model is developed by applying fuzzy set theory to describe uncertainties of belt conveyor such as masses, stiffness, damping and frictions. Second, a robust control is designed for the nominal system and compensating for the uncertainty. With the robust control, the belt conveyor system is proved to be uniformly bounded and uniformly ultimately bounded by the Lyapunov approach. Third, the parameters of controller are optimized based on a non-cooperative game approach. The optimal solution is the Nash equilibrium. Optimal solution allows the controller system to perform better and decrease the cost of control. Finally, by comparing with LQR control and different parameters, the feasibility of robust control and the rationality of the optimal parameters are proven.