Optimal Control System Design Research Articles

Adaptive learning-based optimal tracking control system design and analysis of a disturbed nonlinear hypersonic vehicle model

Adaptive learning-based optimal tracking control system design and analysis of a disturbed nonlinear hypersonic vehicle model

Adaptive optimal control system design for semi-active suspension system by supposing variable parameters under exogenous road disturbance

Adaptive optimal control system design for semi-active suspension system by supposing variable parameters under exogenous road disturbance

Design of Optimal Control Systems in the Frequency Domain by the Functional of the Generalized Work

The paper considers the problem of analytical design of optimal controllers (ADOC) for one-dimensional linear stationary objects according to the functional of generalized work (FGW) A. A. Krasovsky. The use of FGW in comparison with the quadratic performance functional greatly simplifies the calculation of the optimal controller — the calculation of its matrix of coefficients mainly consists in solving the linear matrix Lyapunov equation, which, in contrast to the nonlinear matrix Riccati equation, fundamentally reduces the amount of calculations. In addition, the use of FGW provides the best stability margins of the designed system in terms of amplitude and phase. This work is devoted to the development of a method for solving the ADOC problem A. A. Krasovsky in the frequency (complex) domain, which reduces the determination of the transfer function coefficients of the optimal controller for an object of order n to the solution of the corresponding system of n linear algebraic equations. In this regard, the proposed method for solving the ADOC problem by A. A. Krasovsky differs by a much smaller amount of calculations in comparison with the standard method, in which the Lyapunov equation is solved with the desired matrix of dimensions n * n. The proposed method for the synthesis of optimal control systems, which has an analytical nature, became the basis for solving the inverse problem ADOC A. A. Krasovsky, which consists in determining the values of the weight coefficients of the FGW, which provide the given primary quality indicators of the synthesized control system. Using its relations, a relatively simple method for calculating the FGW coefficients based on the given values of the error coefficients for the designed dynamic system has been developed.

A New Methodology for Optimal Design of Hybrid Vibration Control Systems (MR + TMD) for Buildings under Seismic Excitation

This study proposes a new methodology, based on the optimization procedure by a metaheuristic algorithm, for designing a hybrid vibration control system to mitigate the dynamic response of buildings under nonstationary artificial earthquakes (NSAEs). For illustration purposes, a 10-story shear building is studied. The hybrid control system involves the use of an MR damper (MR) and a tuned mass damper (TMD) located in different places of the structure. To describe the behavior of the MR, the modified Bouc–Wen model (MBW) was used. To calculate the damping force of the MR, the clipped optimal control associated with linear quadratic regulator (LQR), CO-LQR, was considered. The optimization was performed using the whale optimization algorithm (WOA) and seismic load generated by the Kanai–Tajimi spectrum. Different control scenarios were evaluated: MR-OFF, MR-ON, CO-LQR, STMD, and CO-LQR (MR + TMD) to determine the best control scenario that can effectively control the structure. Overall, the optimized hybrid control scenario (MR + TMD) was the only one able to adapt all story drifts to the control criterion of the consulted normative. Then, CO-LQR (MR + TMD), designed via the methodology proposed in this work, proved to be the best alternative to control the seismic response of this building.

Optimal Controller and Security Parameter for Encrypted Control Systems Under Least Squares Identification

Encrypted control is a framework for the secure outsourcing of controller computation using homomorphic encryption that allows to perform arithmetic operations on encrypted data without decryption. In a previous study, the security level of encrypted control systems was quantified based on the difficulty and computation time of system identification. This study investigates an optimal design of encrypted control systems when facing an attack attempting to estimate a system parameter by the least squares method from the perspective of the security level. This study proposes an optimal H2 controller that maximizes the difficulty of estimation and an equation to determine the minimum security parameter that guarantee the security of an encrypted control system as a solution to the design problem. The proposed controller and security parameter are beneficial for reducing the computation costs of an encrypted control system, while achieving the desired security level. Furthermore, the proposed design method enables the systematic design of encrypted control systems.

Comparative Study between Type-1 and Interval Type-2 Fuzzy Systems in Parameter Adaptation for the Cuckoo Search Algorithm

The objective of this work is focused on improving the optimization ability of the cuckoo search algorithm (CS), and, for this reason, a comparison is made between type-1 and interval type-2 fuzzy logic to look for more promising results in the cuckoo search algorithm (CS), and to help performance, we dynamically adjust the alpha parameter. The idea is to enable CS in leaving the local optima, and then be able to reach the global optima. Currently, there are good results in improving the optimization of algorithms through intelligent fuzzy logic computing after finding the best adjustment parameters. The approach is based on finding the ideal rules with their respective linguistic variables to represent the real world as is perceived by humans. The membership functions that the fuzzy system uses are symmetrically defined for reducing the search space, and this symmetry is what makes the algorithm efficient. We plan to test the proposal in future works in the optimal design of control systems. In the present study, we use five benchmark mathematical functions with variation in the number of dimensions to validate the approach and perform the comparison of interval type-2 and type-1 fuzzy systems in parameter adaptation. For the dynamic adjustment of the parameters, we select the alpha parameter, and the values of Pa and Beta are defined based on the analysis of their behavior in previous works.

Compact neural network modeling of nonlinear dynamical systems via the standard nonlinear operator form

Dynamic artificial neural networks (DANNs) have become popular for the data-driven modelling of nonlinear dynamical systems. This article elucidates properties of a compact DANN model structure called the standard normal operator form (SNOF). Sets of nonlinear dynamical systems are characterized for which the SNOF can achieve the same model identification error with fewer neurons than needed by the popular DANN model structures. The results are demonstrated in a case study for a multi-stage bioreactor, which is a highly nonlinear dynamical system in which the cells have a sharp change in dynamics during a change in the feed composition as the bioreactor shifts from growth mode to production mode. The ability of the SNOF to model highly nonlinear dynamical systems with a very small number of neurons suggests its potential for serving as a basis for the design of model-based optimal control systems with theoretical guarantees of closed-loop stability and performance.

Control and dynamic optimization of middle vessel batch distillation column for the separation of ethanol/propanol/butanol mixture

The middle vessel batch distillation column is an alternative to the regular batch distillation column. This configuration allows simultaneous separation of the light fraction (accumulated at top), heavy fraction (accumulated at bottom) and the intermediate fraction (accumulated in the middle vessel) in a single column. The objective of this article is to extensively analyse and discuss different control systems for the middle vessel batch distillation column (MVBDC) and dynamically optimize the column. Three control structures such as composition level cascade, composition temperature cascade, and temperature control system, have been tested and evaluated. Further, a dynamic optimization study has been performed on the control system providing the fastest separation. The optimizer is set to minimize the total energy consumed during the process. This resulted in a decrease in batch time from 26.8 to 25.2h and a 13.5% decrease in overall energy usage. The presented dynamic optimization technique and control system design is useful for improving the performance of the MVBDC.

Method of predicting nonlinear pilot-induced oscillations due to flight control degradation based on digital virtual flight

Because few methods of predicting nonlinear pilot-induced oscillations are available, it is difficult to analyze the sensitive characteristics of such oscillations in the stage of aircraft scheme design. The pilot has the ability to self-adapt, and the control behavior may change before and after flight control degradation. To identify flight control degradation faults and adaptively adjust a pilot's manipulation behavior, three new modules, including pilot perception, flight control degradation judgment and adaptive adjustment, are established to construct a time-varying pilot model. Combined with a digital flight task model, a digital virtual flight simulation model of flight control degradation is built. An identification algorithm based on fuzzy logic is adopted to quantitatively evaluate the pilot-induced oscillation characteristics according to the numerical simulation results. Then, a nonlinear pilot-induced oscillation prediction method based on digital virtual flight is established. A pitch attitude tracking task is selected to predict the longitudinal, nonlinear pilot-induced oscillations. The results show that the prediction results of the simulations are basically consistent with those of a human-in-the-loop flight test with a ground simulator, which verifies the correctness of the proposed method. Through a sensitivity study of the stick force gradient after degradation, the influence of this parameter and the recommended value are determined. This method can be used to predict the nonlinear pilot-induced oscillation characteristics of fly-by-wire aircraft in the conceptual design stage and provide a theoretical reference for the optimal design of flight control systems.

A Reduced-order Model for Real-time NMPC of Ethanol Steam Reformers

One of the approaches to green energy of interest in recent years is through the use of hydrogen technologies in which the waste product of combustion is water rather than carbon dioxide, nitrous oxides, and other pollutants generated by the burning of hydrocarbon fuels. Ethanol steam reformers is one of the primary technologies with the potential to generate hydrogen efficiently and reliably. This article investigates the design of nonlinear optimal feedback control systems for ethanol steam reformers based on mechanistic models described by a system of nonlinear partial differential-algebraic equations, aka singular/descriptor systems. The mechanistic models are too complicated to simulate in real-time using the standard numerical discretization methods, much less to directly incorporate such models as nonlinear constraints into mechanistic model-based nonlinear model predictive control formulations. This article employs a rather sophisticated multivariate form of the method of characteristics to reformulate the nonlinear constraints into a much simpler form amenable to real-time control implementations.

Optimal Design of Passive and Active Control Systems in Seismic-excited Structures Using a New Modified TLBO

Vibration control devices have recently been used in structures subjected to wind and earthquake excitations. The optimal design problems of the passive control device and the feedback gain matrix of the controller for the seismic-excited structures are some attractive problems for researches to develop optimization algorithms with the advancement in terms of simplicity, accuracy, speed, and efficacy. In this paper, a new modified teaching–learning-based optimization (TLBO) algorithm, known as MTLBO, is proposed for the problems. For some benchmark optimization functions and constrained engineering problems, the validity, efficacy, and reliability of the MTLBO are firstly assessed and compared to other optimization algorithms in the literature. The undertaken statistical indicate that the MTLBO performs better and reliable than some other algorithms studied here. The performance of the MTLBO will then be explored for two passive and active structural control problems. It is concluded that the MTLBO algorithm is capable of giving better results than conventional TLBO. Hence, its utilization as a simple, fast, and powerful optimization tool to solve particular engineering optimization problems is recommended.

A control model of the operating head dynamics of Jebba hydropower system

Electricity availability in Nigeria has been very poor over the years, underscoring the need for a better approach for managing generating resources. This paper presents the development of a dynamical model of the operating head of Jebba hydroelectric power plants for system studies and control system design. The mathematical model of the plant was developed from flow continuity conditions, some model parameters were obtained from the source while others were estimated from observations and analysis of the measured data. The developed dynamical equation was validated by comparing the response produced with values obtained by measurement. Upon integrating the model equation in Microsoft EXCEL VBA® environment, a deviation of 2% from measured values was observed. Operators can therefore use the model as a decision support system, while control engineers can find the model directly applicable for optimal and robust control system design for the station.Keywords: Control, Dynamical model, Hydropower, Inflow, Operating head.

Message delay time distribution analysis for controller area network under errors

Controller area network (CAN) is a widely used fieldbus protocol in various industrial applications. To understand the network behavior under errors for the optimal design of networked control systems, the message response time of the CAN network needs to be analyzed. In this study, a novel delay time distribution analysis method for the response messages is proposed when considering errors. In this method the complex message queues are decomposed into typical message patterns and cases. First, a stochastic fault model is developed, and the probability factor is defined to calculate the error distribution. Then the message delay time distribution for the single slave node configuration is analyzed based on the error distribution. Next, based on the delay time distribution analysis of typical patterns and cases, an analysis framework of message delay time distribution for the master/slave configuration is developed. The testbed is constructed and case studies are conducted to demonstrate the proposed methodology under different network configurations. Experimental results show that the delay time distributions calculated by the proposed method agree well with the actual observations

Multi‐objective optimal motion control of a laboratory helicopter based on parallel simple cell mapping method

AbstractThis paper presents a study of multi‐objective optimal design of nonlinear control systems and has validated the control design with a twin rotor model helicopter. The gains of the porportional integral differential (PID) control are designed in the framework of multi‐objective opitmization. Eight design paramaters are optimized to minimize six time‐domain objective objective functions. The study of multi‐objective optimal design of feedback control with such a number of design paramaters and objective functions is rare in the literature. The Pareto optimal solutions are obtained by the proposed parallel simple cell mapping method consisting of a robust Pareto set recovery algorithm and a rolling subdivision technique. The proposed parallel simple cell mapping algorithm has two features: the number of cells in the invariant set grows linearly with the rolling subdivisions, and the Pareto set is insensitive to the inital set of seed cells. The current control design is compared with the classical LQE control for linear systems, and is also experimentally validated. The current design provides improved control performance as compares with the LQR control, and is applicable to complex nonlinear systems.

Online discrete-time LQR controller design with integral action for bulk Bucket Wheel Reclaimer operational processes via Action-Dependent Heuristic Dynamic Programming

In this paper, a novel approach for online design of optimal control systems applied to the bulk resumption process by bucket wheel reclaimer (BWR) is presented. This approach is based on reinforcement learning paradigms, more specifically Action Dependent Heuristic Dynamic Programming (ADHDP), that learn online in real-time the Discrete Linear Quadratic Regulator (DLQR) optimal control solution with integral action. Due to the geometric irregularities of the storage yard stacks and variation in physical and chemical characteristics of the stacked material, the flow control of solid bulks by bucket wheel reclaimer requires methods that are suitable with the high degree of imprecision of process variables and environment uncertainties. The resumption of bulk solids is carried out by dividing the stack into layers, each layer is approximately 4 m high, and the layers are divided into workbenches up to 12 m in length. To take up a workbench several translation steps are required (penetration in the stack), with the translation step varying from 0 to 1 m. In order to maintain the desired ore flow throughout the process, the BWR lance speed must be periodically adjusted. The main advantage of the proposed control method is that besides the decision rule is fully independent of plant model, the gains of the resulting controller are self-adjustable. The control system was designed in such a way that the ADHDP-based DLQR controller with integral action would act in real-time in the plant control, using only the input and output signals and states measured along the system trajectory.

State-Space Modelling of a Rocket for Optimal Control System Design

In this study, we present the derivation of the mathematical model for a rocket’s autopilot in state-space. The basic equations defining the airframe dynamics of a typical six-Degree-of-Freedom (6DoF) are non-linear and coupled. Separation of these nonlinear coupled dynamics is presented as lateral and longitudinal dynamic equations. The need to determine aerodynamic coefficients and there derivative components are brought to light here, which is the crux of the equations. Methods of obtaining such coefficients and their derivatives in a sequential form are also put forward. After the aerodynamic coefficients and their derivatives are obtained, the next step is to trim and linearize the decoupled non-linear 6DoFs. In a novel way, we presented the linearization of the decoupled 6DoF equations in a generalized form. This provides a lucid and easy way to implement trim and linearization using any computer program.

Pitch Control of a Rocket with a Novel LQG/LTR Control Algorithm

This paper presents the design, simulation and analysis of a novel LQG and LQG/LTR control algorithm for the pitch angle of a sounding rocket. These improved LQG and LQG/LTR control algorithms stem from the fact that a Riccati Differential Equation (RDE) rather than the popular Algebraic Riccati Equation (ARE) is used to obtaining the Kalman gain in the observer of the traditional Linear quadratic Gaussian (LQG) control algorithm. Thus, eight (8) different controllers were design, simulated and analysed, three (3) of such controllers are novel and two out of these novel controllers were able to recover completely the robustness lost in the traditional LQG controller. All controllers synthesized were analysed using time response characteristics of closed-loop system and compared with the LQR and LQG control system. Using the LQR controller as the benchmark for best performance and the LQG as the worst. This study shows an application option that demonstrates optimal control system design in MATLAB/Simulink® and the approach put forward here proves to be very effective.

Output Feedback Q-Learning Control for the Discrete-Time Linear Quadratic Regulator Problem.

Approximate dynamic programming (ADP) and reinforcement learning (RL) have emerged as important tools in the design of optimal and adaptive control systems. Most of the existing RL and ADP methods make use of full-state feedback, a requirement that is often difficult to satisfy in practical applications. As a result, output feedback methods are more desirable as they relax this requirement. In this paper, we present a new output feedback-based Q-learning approach to solving the linear quadratic regulation (LQR) control problem for discrete-time systems. The proposed scheme is completely online in nature and works without requiring the system dynamics information. More specifically, a new representation of the LQR Q-function is developed in terms of the input-output data. Based on this new Q-function representation, output feedback LQR controllers are designed. We present two output feedback iterative Q-learning algorithms based on the policy iteration and the value iteration methods. This scheme has the advantage that it does not incur any excitation noise bias, and therefore, the need of using discounted cost functions is circumvented, which in turn ensures closed-loop stability. It is shown that the proposed algorithms converge to the solution of the LQR Riccati equation. A comprehensive simulation study is carried out, which illustrates the proposed scheme.

선박자동접안을 위한 최적 추종 제어계 설계에 관한 연구

선박자동접안을 위한 최적 추종 제어계 설계에 관한 연구

Nonlinear impulsive optimal control synthesis with optimal impulse timing: A pseudo-spectral approach

Following the philosophy of pseudo-spectral approach, a nonlinear variable-time impulsive optimal control system design approach is presented in this paper for a class of problem with hard terminal constraint. In this approach the impulse application time instants are also take as ‘decision variables’ and are fixed through an optimization process in addition to the magnitudes of control at those instants. This gives additional freedom for optimization and hence leads to better performance than the fixed timing approach. Three benchmark problems which include a scalar linear problem, the Van-der Pol’s oscillator problem and an inverted pendulum problem are solved to demonstrate the effectiveness of the new technique. The proposed approach is also computationally efficient owing to the usage of the pseudo-spectral philosophy.