Robust tracking and disturbance rejection design for time delay systems

The digital control system of modular multilevel converters (MMCs) normally synchronizes with the switching actions. The switching frequency of an MMC is generally selected as low as possible from an efficiency point of view, which leads to an unavoidable and relatively long time delay in the control system. Such a time delay might deteriorate the MMC performance and even reduce the stability margin by introducing infinite uncertain eigenvalues into the system state functions. Without a proper time-delay model and quantitative system stability analyses, MMCs might suffer from uncertainties and unstable risks during their operations, especially when the switching frequency is low. This paper derives an MMC model considering the time delay in the digital control system. A Pade-based stability analysis method is then proposed, which consists of three steps: information integration and critical eigenvalue extraction, and trajectory visualization and critical angle (CA) calculation, and quantitative assessment and extreme value determination. By the proposed model and method, the critical eigenvalue can be effectively extracted. With the Hopf bifurcation, the time delay in the digital control system induces a pair critical conjugate eigenvalues into MMC systems, which is detected as an instability cause. The CA and the critical impact are defined to quantitatively assess the stability, while selecting the controller parameters and minimum switching frequency. The proposed method for the MMC stability assessment is experimentally verified.

This thesis presents some research results on control and deconvolution estimation for discrete-time linear systems with delay. The thesis focuses on two facets, the first is the robust deconvolution estimation of time-delay systems with stochastic parameter uncertainties and the other is the control of time-delay systems.

The contribution is focused on brief description of proposed control design process and primarily on practical application of obtained simple robust control algorithms. The synthesis is based on general solutions of Diophantine equations in the ring of proper and stable rational functions, Youla-Kučera parameterization and divisibility conditions and one of its main advantages can be seen in existence of single scalar tuning parameter. The real-time control behaviour has been tested on laboratory model of hot-air tunnel which has been mathematically described by various transfer functions containing parametric type of uncertainty.

Real Time Control For Time Delay System

The problem of forward and backward time delays is significantly important for both control and feedback loop of networked control systems. These time delays give rise to latency in performance and thereby may destabilize the system. Therefore numerous methods have been proposed about time delay identification/estimation and compensation for networked control systems, especially for bilateral teleoperation systems. However, most compensation methods have been accomplished by considering offline time delay estimation for linear/nonlinear time delay control systems. In this work, we propose an observer based estimation algorithm for round trip delay which is the sum of forward and backward time delays for a 1 degree-of-freedom nonlinear bilateral teleoperation system. Via Lyapunov based stability analysis, global boundedness of the observer errors along with their ultimate convergence and the convergence of the round trip delay estimator to the vicinity of its real value can be guaranteed in the closed-loop system. Finally, simulation and experimental studies are carried out utilizing the last link of a PHANToM Omni Haptic device moving like a one-link robot in the vertical plane.

Analysis and Control of Time Delayed Systems via the Lambert W Function

Flue gas desulfurization in thermal power plants is critical to the environmental and human health. Aiming for field application, this article presents a new predictor-and-observer-based active disturbance rejection control (ADRC) scheme for Wet Flue Gas Desulfurization (WFGD) process which is subject to long time delay and unknown disturbances. First, the working principles and control problems of WFGD system are illustrated, and the WFGD process model is identified based on the field experimental data. Then, a predictor-based ADRC approach is carefully devised to address its control issues. Specifically, a filtered smith predictor (FSP) is designed to obtain stable delay-free prediction output, and a reduced-order model-assisted extended state observer (MESO) is devised to estimate the “total disturbance” with less phase lag. Based on the equivalent control structure, its stability, including the perfect delay matching and delay mismatch cases, is theoretically investigated using the zero exclusion criterion. A simple “separation tuning procedure” is also provided, where the ADRC parameters are tuned directly based on the delay-free process, while the FSP filter is specified to achieve desired robustness. Finally, the validity of the proposed method is demonstrated by comparison simulations and field tests in a 1000MW thermal power unit. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article focuses on sulfur dioxide (SO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_2$</tex-math> </inline-formula> ) control and proposes a new predictor-based ADRC approach for the WFGD process subject to long time delay and unknown disturbances. Taking the WFGD system as an example, it systematically describes the whole process of modeling, control system design and simulation & experimental verification, which can provide an intuitive reference for practitioners. The zero exclusion criterion is used to analyze the closed-loop stability and determine the stable delay range for a given predictor-based ADRC control system. A detailed tuning procedure is also provided, which can simplify the time-consuming tuning process and help engineers grasp the performance and robustness of the control system. It is evident that the proposed method can be extended to a general class of industrial time-delay systems, which facilitates the practitioner’s practice in general single-input-single-output time-delay system control. The field test results demonstrate the superiority of the proposed method and show promise for practical application in other systems.

Necessary and Sufficient Conditions for Perfect Command Following and Disturbance Rejection in Fractional Order Systems

Composite disturbance rejection and tracking control design for fuzzy model based systems with cyber attacks

This paper addresses the problem of design of a two degree of freedom (2-DOF) PID controller for time delay systems. The proposed approach is to design 2-DOF PID controller using a novel method which combines model order reduction, approximate model matching (AMM) concepts as well as optimisation techniques. The conventional PID controllers are usually in 1-DOF structure. The problem of finding the parameters of the 2-DOF PID controller is formulated as that of obtaining the solution of a set of non-homogeneous linear equations. The proposed method not only ensures the stability of the closed loop system with a 2-DOF PID controller but also satisfies the required performance criteria. The developed method does not pose any restriction either on the order of the model or on the structure/order of the controller transfer function. Moreover, this method is computationally simple and easy to implement. Simulation results demonstrate the effectiveness of the proposed method.

An image-based inverted pendulum control system with a large time delay of camera has some analogies with human stick balancing control. Cabrera and his group pointed out that time delays and state-dependent fluctuations play an essential role in neural control mechanism. In this paper, we investigate some properties of the time delays and the fluctuations using our new model which is consistent with the actual inverted pendulum control system. For noise free case, a sufficient condition for the stability of our time-delayed control system is derived.

This paper proposes a novel method to graphically compute all feasible gain and phase margin specifications-oriented robust and optimal fractional PID controllers to stabilize time delay processes (TD) of any order. The gain-phase margin tester method is utilized to guarantee the concerned systems certain robust safety margins and test the constant gain margin boundary, constant phase margin boundary, and stability boundary in the parameter plane. The overlapping region of these plotted boundaries, which represents all feasible robust stabilizing PID controllers and allows the considered TD processes to retain pre-specified safety margins, is graphically determined as the gain and phase margin specifications-oriented region (GPMSOR). The variations of the GPMSOR and the stability region with respect to the variations of the noninteger orders of the integral and derivative terms have been investigated. According this, it is possible to slightly enlarge the GPMSOR by altering the noninterger order of the integral and derivative terms. This modifications in GPMSOR through altering the noninteger orders of the integral and derivative terms allows us to find the robust and optimal PID controller gain set for the considered TD systems. In other words, the selected fractional order PID controllers from the GPMSOR not only retain the prescribed GM and PM specifications but minimize the integral of the absolute error (IAE) or the integral of the squared error (ISE) performance criterion. Finally, an illustrative example cited from the literature with computer simulations is provided to demonstrate the effectiveness and confirm the validity of the proposed methodology.

This paper discusses Smith predictor scheme for controlling processes with time delay. The tuning method used here had improved capacities of smith predictor designed by Liu et.al for reference input tracking in presence of load disturbances. A new optimization technique, Grey Wolf Optimization Based disturbance estimator had been proposed here and has been used for tuning the parameters of the disturbance estimator and the same optimization algorithm has been used for optimizing the set point tracking controller for the plant. Comparison is done between Harmony search, Ant Colony and Particle Swarm Optimization for estimating the same parameters. Simulation examples are included to show the superiority of the proposed estimator over Maclaurin PID disturbance estimator proposed by Liu et. al as well as the other optimizing algorithm quoted above.

The high frequency oscillation (HFO) of renewable energy integrated into MMC brings serious challenges to the stable operation of power system. This article proposes the mathematical impedance model of MMC with considering control system time delay, sequence component separation, control system. Besides time delay, the main factors of HFO such as SCS, virtual filter of voltage and current, inner-loop controller are derivate in this article. It is proved that SCS may lead to the fluctuation of phase character of MMC high frequency impedance and lead to low damping character of MMC system. Virtual filter of voltage and current can enhance the damping ratio of MMC system. Lower proportional gain of inner-loop control lead to a higher damping character of MMC system. The solutions of HFO are validated in Zhangbei project. The 1550Hz HFO in the project is suppressed by the optimization of control system.

Enhanced IMC-based Load Disturbance Rejection Design for Integrating Processes with Slow Dynamics