Feedback Design Approach Research Articles

Fuzzy Adaptive Protective Control for High-Speed Trains: An Outstretched Error Feedback Approach

This paper presents a fuzzy adaptive protective control method for autonomous high-speed trains (HSTs) automatic operation using a new outstretched error feedback design approach. In order to stabilizing the error dynamics with respect to target position and speed profiles of controlled HSTs, nonlinear transformation in prescribed performance control methodology is used to convert running states subject to protective (constrained) information, imposed by automatic train protection (ATP) subsystem, to new coordinates in unconstrained form. By blending a new outstretched error feedback and fuzzy approximation, it is guaranteed above-mentioned errors are kept within regions characterized by error boundary (or prescribed performance) functions and control parameters simultaneously, which can be adjusted to arbitrarily small even without error decreasing boundary functions. Fuzzy approximation is used in compensating unknown running resistances. It is rigorously proved that the resulting closed-loop system is stable in sense of Lyapunov stability in the presence of unknown resistance, containing basis and aerodynamic resistances with uncertain parameters and piecewise continuously slope resistance over varying gradient profile. The proposed control is demonstrated to be effective by comparative simulations of train G1 running on Beijing-Shanghai railway line.

Multiple DC coordinated suppression method for ultra-low frequency oscillations

Systems with a high proportion of hydropower are prone to induce ultra-low oscillations when the local load or the delivered power of the DC system changes. For systems where multiple DC circuits exist, system damping can be greatly improved by coordinating supplementary control of the multiple DC circuits to suppress the ultra-low frequency oscillations. However, solving this problem based on the conventional output feedback design approach requires dealing with difficult bilinear matrix inequalities. In this paper, a controller-design approach based on a differential evolution algorithm is proposed. First, a centralized or decentralized structure of multiple DC coordinated controller of a specific order and the corresponding state space equations of the closed-loop system are derived. Next, the random method is used to generate the initial controllers, then the minimum damping ratios of the closed-loop system are calculated, and finally the minimum damping ratios of the closed-loop system are optimized using the differential evolution algorithm. This method can be used to solve for the DC supplementary controller based on the lead-lag structure, which is widely applied in engineering practice, by converting it to the state space form. Therefore, the proposed method can be used to solve the multiple DC coordinated controllers of three structures (i.e., centralized, decentralized, and decentralized based on the lead-lag link) in a unified framework. The proposed method is applied to two case studies, Cigre Nordic and China Southern Power Grid. Results indicate that the designed controllers of all three structures improved the system damping significantly and eliminated the risk of ultra-low frequency oscillations to the system operation. The proposed method is highly practical as it can be applied to DC supplementary controllers based on the lead-lag module.

An inverse optimal approach to design of feedback control: Exploring analytical solutions for the Hamilton‐Jacobi‐Bellman equation

SummaryDesign of feedback control by an optimal control approach relies on the solutions of the Hamilton‐Jacobi‐Bellman (HJB) equation, while this equation rarely admits analytical solutions for arbitrary choices of the performance measure. An inverse optimal feedback design approach is proposed here in which analytical solutions are explored for the HJB equation that optimize some meaningful, but not necessarily ideal, performance measure. Such performance measure is exclusively selected from a family of cost functionals with an intended structural constraint which inherently yields analytical solutions to the HJB equation. This family includes a set of free parameters which are exploited to construct cost functionals adequately representing the design requirements. The structural constraint imposed on this cost functional family indeed narrows down the scope of the proposed method; yet, it is shown by several examples that this method can successfully address certain classes of feedback design problems.

Adaptive output regulation of a class of nonlinear output feedback systems with unknown high frequency gain

This paper presents an output feedback design approach based on the adaptive control scheme developed for nonlinearly parameterized systems, to achieve global output regulation for a class of nonlinear systems in output feedback form. We solve the output regulation problem without the knowledge of the sign and the value of the high frequency gain a priori. It is not necessary to have both the limiting assumptions that the exogenous signal w and the unknown parameter μ belong to a prior known compact set and the high frequency gain has a determinate lower and upper bounds. The effectiveness of the proposed algorithm is shown with the help of an example.

Control allocation-based fault tolerant control

This paper describes a novel scheme for fault tolerant control using a robust optimal control design method. This scheme can also be employed as actuator redundancy management for over-actuated linear systems. In contrast to many existing methods in the literature, this scheme can be applied to systems whose control input matrix cannot be factorised into two matrices whose ranks are equal and less than the minimum of the number of columns and rows of the input matrix. The so-called virtual control, in this scheme, is calculated using a robust ℋ2-based feedback design approach constructed to be robust against uncertainties emanating from visibility of the control allocator to the controller and imperfection in the estimated effectiveness gain. Then, using a new control allocation scheme along with a novel Tikhonov-based re-distributor mechanism, the obtained virtual control signal is re-distributed among remaining (redundant or non-faulty) set of actuators. As the proposed scheme is modular-based, it can be employed as a real-time fault tolerant control scheme with no need to reconfigure the controller in the case of actuator faults or failures. The effectiveness of the proposed scheme is demonstrated by a numerical example.

Semi-global stabilization of discrete-time linear systems with unsymmetrical saturation

This paper deals with the stabilization problem for discrete-time linear system with unsymmetric saturation. To handle the structural properties of the unsymmetric saturation nonlinearity, the description of the transformation carries from the symmetric case to the unsymmetric case is employed. By using the parametric Lyapunov equation-based low gain feedback design approach, linear matrix inequality formulations for the state feedback and output feedback control design are given. The effectiveness of the proposed method is confirmed by numerical examples.

Polynomial control design for polynomial systems: A non-iterative sum of squares approach

This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum of squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide range of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tank reactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.

Stability criteria of linear systems with multiple input delays under truncated predictor feedback

The model reduction technique as a feedback design approach for linear systems with input delays achieves finite spectrum assignment of the closed-loop system in a delay free form. The resulting predictor-type feedback law contains a distributed term that involves the convolution between the past input and the state transition matrix and hence causes difficulty in its implementation. For the purpose of easy implementation, the truncated predictor feedback (TPF) simplifies the predictor feedback by discarding the distributed term, and delay independent truncated predictor feedback further eliminates the delay-dependent exponential factor. In this paper, we consider the stabilization of a general linear system with multiple time-varying input delays by TPF or delay independent TPF. Stability criteria expressed in terms of input delays and the feedback parameter are derived through Lyapunov–Krasovskii stability analysis, and then numerically studied under both feedback laws.

Feedback Design of Temperature Control Measures for Concrete Dams based on Real-Time Temperature Monitoring and Construction Process Simulation

Crack prevention is a significant issue in the construction process of concrete dams. The vast majority of concrete cracks are related to temperature variations, and hence, temperature control is a primary method used to prevent cracks. This paper presents a new integrated concept, named Feedback Design (FD) of temperature control measures, which incorporates real-time temperature monitoring, temperature field simulation and construction process simulation in a large system to optimize a temperature control scheme for concrete dams. We used a fiber-optic Distributed Temperature Sensing (DTS) system to monitor the temperature variation process of typical dam monoliths in real time. By incorporating a genetic algorithm, neural network algorithm, and finite element theory, we proposed an intelligent inversion method to obtain thermal parameters of concrete dams based on the temperature monitoring data. Meanwhile, we built a simulation model of a concrete dam’s construction process based on a cycling network technique to obtain accurate construction environmental parameters. Finally, we simulated the temperature field of a typical dam monolith based on initial temperature control measures, inversion thermal parameters, and accurate construction environmental parameters. Temperature variance lines of typical points in the model obtained from the finite element method (FEM) accord well with the measured values obtained from the DTS system. We applied the FD approach to the Xiluodu arch dam located in southwest China to forecast the temperature fields and optimize the temperature control scheme of the dam blocks planned for pouring. The FD approach has been proven reliable and efficacious.

Eigenstructure Assignment for Componentwise Ultimate Bound Minimization in Discrete-Time Linear Systems

This technical note presents a feedback design approach to minimise state ultimate-bounds (UBs) in linear time-invariant discrete-time systems subject to non-vanishing bounded disturbances. A target closed-loop eigenstructure is first constructed to achieve the lowest possible UBs for one or more state components of the system. Structural conditions on the system matrices are then derived to guarantee that the target eigenstructure can be assigned by state feedback. When the required structural conditions are satisfied, an eigenvector assignment procedure can be applied to simultaneously minimise multiple UBs in systems with multiple inputs. The results are illustrated by a numerical example drawn from a distributed voltage control problem in inverter-based microgrids.

Data-driven inversion-based control of nonlinear systems

In this paper, we introduce the Data-Driven Inversion-Based Control (D2-IBC) method for nonlinear control system design. The method relies on a two degree-of-freedom architecture, with a nonlinear controller and a linear controller running in parallel, and does not require any detailed physical knowledge of the plant to control. Specifically, we use input/output data to synthesize the control action by employing convex optimization tools only. We show the effectiveness of the proposed approach on a simulation example, where the D2-IBC performance is also compared to that of the Direct FeedbacK (DFK) design approach, a benchmark method for nonlinear controller design from data.

Parametric Lyapunov Equation Approach to Stabilization of Discrete-Time Systems With Input Delay and Saturation

This paper studies the problem of stabilization of discrete-time linear systems with input delay and saturation nonlinearity. By exploring some further intricate properties of the recently developed parametric Lyapunov equation-based low-gain feedback design approach, solutions are proposed to solve the problems by both state feedback and output feedback. This new approach is not only simpler than the existing method that is based on the eigenstructure assignment technique, but also provides explicit conditions on the low-gain parameter to guarantee the stability of the closed-loop system. Moreover, it is possible by adjusting the low-gain parameter online to achieve global results when the system is subject to both input saturation and time-delay. Also, the delay in the input is allowed to be time-varying in some cases.

A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation

This paper is concerned with semi-global stabilization of discrete-time linear periodic systems subject to actuator saturation. Provided that the open loop characteristic multipliers are within the closed unit circle, a low gain feedback design approach is proposed to solve the problem by state feedback. Our approach is based on the solution to a parametric discrete-time periodic Lyapunov equation. The proposed approaches not only generalize the corresponding results for time-invariant systems to periodic systems, but also reveal some important intrinsic properties of this class of periodic matrix equations. A numerical example is worked out to illustrate the effectiveness of the proposed approaches.

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.

A Remark on Sensor Disturbance Rejection of Nonlinear Systems

When disturbances enter sensors, the states of a plant cannot be precisely measured and the state feedback controllers are not implementable. Instead, the so-called measurement feedback controllers become interesting. For nonlinear systems, the output regulation theory is widely used for handling actuator and plant disturbances. This note gives a remark how the output regulation theory can be applied for sensor disturbances, and hence provides a novel measurement feedback design approach.

Stability and Feedback Design of a Class of Time-Delay Systems with Discontinuity: Functional Differential Inclusion-Based Approach

To analyze and synthesize time-delay systems with discontinuity, the framework of differential inclusion in the sense of Filippov is extended to functional differential inclusion. Based on the extension, the concept of Filippov solution is introduced for the time-delay systems with discontinuity at first, and then it is shown that both the Lyapunov stability and the LaSalle invariance principle results can be extended to such kind of systems. Moreover, by using the proposed analysis tools, a stabilization feedback design approach is proposed for a class of nonlinear time-delay systems with discontinuity. Simulation results of numerical examples are given to demonstrate the proposed control approaches.

Feedback control of oxygen uptake during stimulated cycle ergometry in subjects with paraplegia

Regulation of exercise intensity is important for aerobic training and exercise testing. Automatic control of oxygen uptake has potential for exercise prescription and in tests to characterise cardiopulmonary status. Here, the feasibility of closed-loop control of oxygen uptake during stimulated leg-cycling exercise in paraplegia is investigated. A new control structure for this purpose is proposed, consisting of a dynamic feedback controller monitoring target and actual oxygen uptake and adjusting an exercise work rate command signal in real time. A further feedback controller automatically adjusts the stimulation intensity to achieve the commanded work rate. The approach was experimentally evaluated in a subject with paraplegia. Empirical parameter estimation results show considerable day-to-day variability in the oxygen uptake response dynamics. Feedback control tests then demonstrate that the proposed controller provided accurate tracking of the oxygen uptake command profile on separate test days, pointing to an underlying robustness of the feedback design approach against day-to-day variability in the subject's physiological response. The variance of the oxygen uptake response was considerably lower under closed-loop control than in open-loop conditions. The results of the study provide evidence for the feasibility of feedback control of oxygen uptake during stimulated cycle-ergometer exercise in paraplegic subjects.

Robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization

This paper investigates the problem of robust output feedback stabilization for a family of uncertain nonlinear systems with uncontrollable/unobservable linearization. To achieve global robust stabilization via smooth output feedback, we introduce a rescaling transformation with an appropriate dilation, which turns out to be very effective in dealing with uncertainty of the system. Using this rescaling technique combined with the nonseparation principle based design method, we develop a robust output feedback control scheme for uncertain nonlinear systems in the p-normal form, under a homogeneous growth condition. The construction of smooth state feedback controllers and homogeneous observers uses only the knowledge of the bounding homogeneous system rather than the uncertain system itself. The robust output feedback design approach is then extended to a class of uncertain cascade systems beyond a strict-triangular structure. Examples are provided to illustrate the results of the paper.

Global stabilization of cascade systems by C/sup 0/ partial-state feedback

This paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization, and the notion and properties of the input-to-state stability Lyapunov function can be effectively coupled, resulting in globally stabilizing C/sup 0/ partial-state feedback controllers for a class of cascade systems which may not be smoothly stabilizable, even locally.

Simultaneous LQ Optimal Control for Periodic Discrete-Time Systems

In this paper, simultaneous stabilization and simultaneous optimal design for a collection of periodic discrete-time systems via periodic constant output feedback are addressed. First, a constant output feedback design approach on simultaneous optimal control is presented for a collection of linear time-invariant discrete-time systems and a heuristic iterative linear matrix inequality algorithm is developed to compute the feedback gain. Then the result is extended to design the periodic constant output feedback gain minimizing the given performance indices for a set of periodic discrete-time systems. Numerical examples are used to demonstrate the effectiveness of the proposed algorithm.