Design of rank-one modification feedback controllers for second-order systems with time delay using frequency response methods

6 - Design and Performance of Feedback Controllers

The existence of multiple decision-makers and goals, spatial and non-linear forest management objectives and the combinatorial nature of forest planning problems are reasons that support the use of heuristic optimisation algorithms in forest planning instead of the more traditional LP methods. A heuristic is a search algorithm that does not necessarily find the global optimum but it can produce relatively good solutions within reasonable time. The performance of different heuristics may vary depending on the complexity of the planning problem. This study tested six heuristic optimisation techniques in five different, increasingly difficult planning problems. The heuristics were evaluated with respect to the objective function value that the techniques were able to find, and the time they consumed in the optimisation process. The tested optimisation techniques were 1) random ascent (RA), 2) Hero sequential ascent technique (Hero), 3) simulated annealing (SA), 4) a hybrid of SA and Hero (SA+Hero), 5) tabu search (TS) and 6) genetic algorithm (GA). The results, calculated as averages of 100 repeated optimisations, were very similar for all heuristics with respect to the objective function value but the time consumption of the heuristics varied considerably. During the time the slowest techniques (SA or GA) required for convergence, the optimisation could have been repeated about 200 times with the fastest technique (Hero). The SA+Hero and SA techniques found the best solutions for non-spatial planning problems, while GA was the best in the most difficult problems. The results suggest that, especially in spatial planning problems, it is a benefit if the method performs more complicated moves than selecting one of the neighbouring solutions. It may also be beneficial to combine two or more heuristic techniques.

Tracking control for multiple-integrator systems is regarded as a fundamental problem associated with nonlinear dynamic systems in the physical and mathematical sciences, with many applications in engineering fields. In this paper, we adopt the Zhang neural network method to solve this nonlinear dynamic problem. In addition, in order to adapt to the requirements of real-world hardware implementations with higher-order precision for this problem, the multiple-order derivatives in the Zhang neural network method are estimated using backward finite-divided difference formulas with quadratic-order precision, thus producing time delays. As such, we name the proposed method the Zhang neural network method with time delay. Moreover, we present five theorems to describe the convergence property of the Zhang neural network method without time delay and the quadratic-order error pattern of the Zhang neural network method with time delay derived from the backward finite-divided difference formulas with quadratic-order precision, which specifically demonstrate the effect of the time delay. Finally, tracking controllers with quadratic-order precision for multiple-integrator systems are constructed using the Zhang neural network method with time delay, and two numerical experiments are presented to substantiate the theoretical results for the Zhang neural network methods with and without time delay.

Spectral design of output feedback controllers for systems pre-compensated by input shapers

Control systems are pervasive in our lives. Our homes have environmental controls. The appliances we use, such as the washing machine, microwave, etc. carry embedded controllers in them. We fly in airplanes and drive automobiles that extensively use control systems. The industrial plants that produce consumer goods run on process control systems. The recent drive toward automation has increased our reliance on control systems technology. This book discusses control systems design from a model-based perspective for dynamic system models of single-input single-output type. The emphasis in this book is on understanding and applying the techniques that enable the design of effective control systems in multiple engineering disciplines. The book covers both time-domain and the frequency-domain design methods, as well as controller design for both continuous-time and discrete-time systems. MATLAB© and its Control Systems Toolbox are extensively used for design. Technical topics discussed in the book include: • Mathematical models of physical systems • Analysis of transfer function and state variable models • Control systems design objectives • Control system design with root locus • Control system design in the state-space • Control system design of sampled-data systems • Compensator design with frequency response methods

Free-energy dissipations via various surface intermediates on Rh-metals in the catalytic hydrogenation of propene at 314 K are evaluated from the values of a novel rate constant l (Yasuda and Kuno, 1998) determined empirically by the frequency response (FR) method, where a cell reactor composed of a proton-conducting membrane was adopted; hydrogen and propene were separated by the membrane in order to investigate separately various rate processes due to either hydrogen or propene. The dissipations concluded are (i) −0.27μHZR̄ and −0.45μHZR̄ via the surface intermediates H2(a) and H(a), respectively, and (ii) +1.62μEZR̄ and −1.31μEZR̄ via the intermediates C3H6(a) and C3H7(a), respectively; μHZ denotes the difference between chemical potentials of the reactant and product given by μ(H2(g))−μ(C3H8(g)) and μEZ is the difference given by μ(C3H6(g))−μ(C3H8(g)); R̄ is the appearance rate of propane. Because free energy of a system must dissipate in the course of any reaction according to the second law of thermodynamics, the stage accompanied by +1.62μEZR̄ (> 0) cannot occur spontaneously and therefore that stage may be regarded as the “real” rate-determining step. Because free-energy dissipation via an intermediate is expected to play a fundamental role in a catalytic reaction, the present FR method could open new aspects of heterogeneous catalysis in a kinetic study.

The integration of a high proportion of renewable energy has significantly reduced the grid inertia level and markedly increased the risk of transient frequency instability in power systems. Meanwhile, the large-scale integration of diverse heterogeneous resources-such as wind power, photovoltaics, energy storage, and high voltage direct current (HVDC) transmission systems-has considerably enriched the portfolio of frequency regulation assets in modern power grids. However, the marked disparities in the dynamic response characteristics and actuation speeds among these resources introduce significant nonlinearity and high-dimensional complexity into the system's transient frequency behavior. As a result, conventional methods face considerable challenges in achieving accurate and timely prediction of such responses. However, the substantial differences in the frequency regulation characteristics and response speeds of these resources have led to a highly nonlinear and high-dimensional complex transient frequency response process, which is difficult to accurately and rapidly predict using traditional methods. To address this challenge, this paper proposes an online prediction method for transient frequency response that deeply integrates physical principles with data-driven approaches. First, a frequency dynamic response analysis model incorporating the frequency regulation characteristics of multiple resource types is constructed based on the Single-Machine Equivalent (SME) method, which is used to extract key features of the post-fault transient frequency response. Subsequently, information entropy theory is introduced to quantify the informational contribution of each physical feature, enabling the adaptive weighted fusion of physical frequency response features and Wide-Area Measurement System (WAMS) data. Finally, a physics-guided machine learning framework is proposed, in which the weighted physical features and the complete frequency curve predicted by the physical model are jointly embedded into the prediction process. An MLP-GRU-Attention model is designed as the data-driven predictor for frequency response. A physical consistency constraint is incorporated into the loss function to ensure that predictions strictly adhere to physical laws, thereby enhancing the accuracy and reliability of the transient frequency prediction model. Case studies based on the modified IEEE 39-bus system demonstrate that the proposed method significantly outperforms traditional data-driven approaches in terms of prediction accuracy, generalization capability under small-sample conditions, and noise immunity. This provides a new avenue for online frequency security awareness in renewable-integrated power systems with multiple heterogeneous frequency regulation resources.

The stability analysis and controller design of discrete linear systems with time-varying delay are addressed. Firstly, the uniformly asymptotical stability criterion with adjustable parameter is derived by Lyapunov-Razumikhin approach. Then, the stabilization approaches for linear systems with time delay by state feedback and observer based-on state feedback are also presented. Sufficient conditions for the existence of state feedback gain and the observer gain are derived through the numerical solution of a set of obtained linear matrix inequalities. Compared with methods in the references, the dynamic performance of systems, such as the overshoot and the convergence rate of the response, can be adjusted by changing the adjustable parameter. Lastly, an illustrative example is given to show the effectiveness of the proposed.

Systems with time delays are present in many applications and considerable research efforts have been made for design and analysis of controllers for this class of systems. Since time delay itself is nonlinear in nature, various approximation techniques have been developed based on restrictive assumptions. A common approximation technique for time delay is by using the Pade rational polynomials which expresses time delay transfer function e/sup -ts/ in the form of numerator and denominator in s. In this paper, systems with time delay are investigated directly in discrete time domain. The time delay is modeled accurately without linear assumption and an augmented state space model is obtained. Control law is developed and closed loop stability is proven. An example is given to demonstrate the technique.

Model-predictive control of linear multivariable systems having time delays and right-half-plane zeros

The robust control problem for a class of uncertain time-delay systems is investigated. The systems include multiple time delays and uncertain nonlinear functions. To our best knowledge, no controller design method for the systems is reported in the literature except for sliding mode control (SMC). However, the sliding mode controller must use the delayed state of the system, so that the precise time delays have to be known, and also a large memory is needed for controller implementation. To overcome the shortcomings, we employ the backstepping method to design a memoryless state feedback controller. By constructing a novel Lyapunov-Krasovskii functional, we show that the resulting closed-loop system is asymptotically stable. Simulations are done to verify the effectiveness of the proposed method.

Design of prestressed concrete flat slab using modern heuristic optimization techniques

Although heuristic optimization techniques are increasingly applied in environmental engineering applications, algorithm selection and configuration are often approached in an ad hoc fashion. In this study, the design of a multilayer sorptive barrier system served as a benchmark problem for evaluating several algorithm-tuning procedures, as applied to three global optimization techniques (genetic algorithms, simulated annealing, and particle swarm optimization). Each design problem was configured as a combinatorial optimization in which sorptive materials were selected for inclusion in a landfill liner to minimize the transport of three common organic contaminants. Relative to multilayer sorptive barrier design, study results indicate (i) the binary-coded genetic algorithm is highly efficient and requires minimal tuning, (ii) constraint violations must be carefully integrated to avoid poor algorithm convergence, and (iii) search algorithm performance is strongly influenced by the physical-chemical properties of the organic contaminants of concern. More generally, the results suggest that formal algorithm tuning, which has not been widely applied to environmental engineering optimization, can significantly improve algorithm performance and provide insight into the physical processes that control environmental systems.

In this paper a nonlinear controller has been designed for Static Synchronous Compensator (STATCOM) in order to improve transient stability of a power system. The nonlinear model of the power system is exactly linearized via state feedback linearization technique. The optimal gain constants of the nonlinear controller are determined applying a special class of non-cooperative dynamic game theory. The performance of this proposed nonlinear STATCOM controller is compared with a fixed structure lead-lag based conventional STATCOM controller. The set of tuning parameters of the conventional controller are optimized through heuristic optimization technique, Genetic Algorithm (GA). The performance of both nonlinear and the conventional controllers are validated with application of a typical transient disturbance to a SMIB test power system. It has been revealed that the proposed nonlinear controller is more effective in the face of contingency in comparison to the GA based controller.

Current research on active flutter suppression considering time delays tends to focus on fixed time delays. To address situations where the control loop may experience time-varying delays with uncertainty, a time-varying-delay Active Disturbance Rejection Control (TVD-ADRC) is proposed. First, a parameterized unsteady aerodynamic reduced-order model (ROM) based on a long short-term memory network is introduced into the aeroservoelastic modeling. This model is applied to predict unsteady aerodynamic forces and aeroservoelastic (ASE) behaviors across a wide range of Mach numbers. Its effectiveness in capturing the characteristics of unsteady aerodynamics is validated through comparisons with the high-fidelity computational fluid dynamics (CFD) simulations. Second, the proposed method integrates ADRC with a delayed input and a time-delay identification module in the controller design. Specifically, the time-varying delay is identified using the cross-correlation function method with a moving window, and this method dynamically updates the time-delay compensation module. Additionally, a genetic algorithm is employed to optimize controller parameters, and the integral of the time-weighted absolute error is selected as the performance evaluation index for the control system. Finally, a three-degree-of-freedom aeroservoelastic system of an airfoil with a trailing-edge control surface is studied for flutter suppression. Flutter control under uncertain time-varying delays during flutter occurrence is investigated, and the impact of the magnitude of the time delay on the effectiveness of the flutter control is analyzed. Simulation results indicate that the proposed TVD-ADRC controller could effectively suppress the aeroelastic instabilities across a wide range of Mach numbers and effectively counteract the negative effects of time-varying delays.