Suboptimal Regulator Research Articles

DC microgrid fault‐tolerant control using state‐dependent Riccati equation techniques

AbstractAn attempt is made to design a fault‐tolerant control system using a nonlinear technique, called the state‐dependent Riccati equation (SDRE) method. The proposed mechanism consists of a master controller, an observer‐based fault detection and isolation system, and three emergency controllers, designed using the SDRE methods. The master controller, as a suboptimal nonlinear regulator, is designed to return DC microgrid (MG) to its desired equilibrium point in normal operation condition. On the other hand, an SDRE observer is designed to establish a unified framework for fault detection and isolation in the DC MG. Indeed, in the case of unexpected fault occurrence, the proposed mechanism can isolate the faulty DG, and then, the emergency controllers are triggered immediately to stabilize the MG. Simulation results indicate that the proposed method is so useful to achieve the control objectives and online protection of the considered MG.

Data-driven parameterizations of suboptimal LQR and H2 controllers

In this paper we design suboptimal control laws for an unknown linear system on the basis of measured data. We focus on the suboptimal linear quadratic regulator problem and the suboptimal H2 control problem. For both problems, we establish conditions under which a given data set contains sufficient information for controller design. We follow up by providing a data-driven parameterization of all suboptimal controllers. We will illustrate our results by numerical simulations, which will reveal an interesting trade-off between the number of collected data samples and the achieved controller performance.

Синтез субоптимального регулятора напряжения в системе электропитания глубоководного аппарата

Синтез субоптимального регулятора напряжения в системе электропитания глубоководного аппарата

STABILITY AND ACCURACY OF THE ROBUST SYSTEM FOR STABILIZING THE ROTOR FLUX-LINKAGE OF AN ASYNCHRONOUS ELECTRIC DRIVE AT RANDOM VARIATIONS OF THE UNCERTAIN PARAMETERS WITHIN THE SPECIFIED BOUNDARIES

Purpose. The aim is to investigate the stability and the accuracy of a robust system for stabilizing the rotor flux-linkage of an asynchronous electric drive at random variations of the uncertain parameters of the object and the regulator within the specified boundaries. Methodology. To make the research, the mathematical model of the rotor flux-linkage channel of the vector control system of an asynchronous electric drive with parametric uncertainty was applied. The transfer function of the Н∞-suboptimal regulator was calculated using the mixed sensitivity method. This transfer function was used to construct the regulator structural scheme in the form of a connection of proportional and integrating links and several adders. Analytical dependences of the coefficients of the regulator's transfer function on the parameters of links of such a connection are determined. These dependences served to researching the influence of uncertain parameters of the regulator links and the object on the stability of the robust system and the accuracy of flux-linkage stabilization. Results. Investigations of the robust system stability and the accuracy of flux-linkage stabilization in the Robust Control Toolbox are done. The curves of the flux-linkage transient processes and the Bode diagram for the open system at random variations of the indeterminate parameters of the object and the regulator links within the specified boundaries are constructed. A choice of variable parameters was carried out by the Monte Carlo method. By the scatter of the obtained curves of the transient processes, the accuracy of flux-linkage stabilization was determined, and according to the Bode diagram, stability reserves in the amplitude and the phase of the robust system were determined. A high accuracy of flux-linkage stabilization (deviation less than 1 %) in fairly wide ranges of changing the uncertain parameters of the object and the regulator, while maintaining the stability of the system with permissible reserves in amplitude and phase, is established. Originality. For the first time, analytical dependences of the coefficients of the transfer function of the Н∞-suboptimal regulator on the parameters of its structural scheme, which represented in the form of a connection of proportional and integrating links, are obtained. The method for calculating the stability of a robust flux-linkage control system and the accuracy of its stabilization at random variations of the uncertain parameters of the object and the regulator links within the specified boundaries is developed. Practical value. The use of the proposed method allows, during the design of the regulator, to ensure the selection of its elements from standard series.

On the Control Design for Linear Time–Invariant Systems with Moments Constraints of Disturbances in Anisotropy–based Theory

Abstract In this paper, the design procedure of anisotropic suboptimal dynamic output regulator for linear discrete time-invariant (LDTI) system is considered. The mean anisotropy level of exogenous disturbance is bounded by the certain positive value. Additional constraints of exogenous disturbance are connected with the first and the second moments. The anisotropic suboptimal regulator design problem is formulated in terms of solvability of linear matrix inequalities (LMI) under convex constraints.

Multi‐input and multi‐output proportional‐integral‐derivative controller design via linear quadratic regulator‐linear matrix inequality approach

This study considers the problem of designing a multi-input and multi-output (MIMO) proportional-integral-derivative (PID) controller via direct optimal or suboptimal linear quadratic regulator (LQR) approach. To design the controller, first the MIMO PID design problem is transformed into a state feedback control and then the gains of the state feedback controller are chosen through an optimal or suboptimal LQR design. Given a minimal state space representation (A, B, C) of the plant, a necessary and sufficient condition (based on matrices A, C) for which the optimal problem (i.e. PID design via optimal LQR) is solvable is obtained. When this optimal problem is not solvable, a suboptimal solution (i.e. PID design via suboptimal LQR), if exists, is obtained by converting the problem into trace minimisation one, which is solved using linear matrix inequality-based method. Suitable examples are considered to illustrate the approaches.

Load Frequency Control of Interconnected Power System Using Teaching Learning Based Optimization

This paper presents the design and performance analysis of teaching learning based optimization (TLBO) algorithm based PID controller for load frequency control (LFC) of an interconnected power system. A two area reheat thermal system equipped with PID controllers which is widely used in literature is considered for the design and analysis purpose. The design objective is to improve the transient performance of the interconnected system. The power system dynamic performance is analyzed based on time response plots achieved with the implementation of designed optimal and sub-optimal LFC regulators in the wake of 1% load disturbance in one of the areas. The results of the TLBO optimized PID controllers on a two area reheat thermal system are compared with those of artificial bee colony (ABC) and differential evolution (DE) optimized PID controllers. The TLBO optimized controllers are found to be superior in terms of peak transient deviation, settling times, and dynamic oscillations.

差分進化に基づくアーム型倒立振子の非線形準最適レギュレータ設計と実機実験による検証

差分進化に基づくアーム型倒立振子の非線形準最適レギュレータ設計と実機実験による検証

Discrete-time ℋ∞ control for nonlinear polynomial systems

This paper presents a solution of the suboptimal regulator problem for a class of discrete-time nonlinear polynomial systems. The solution is obtained by reducing the control problem to the corresponding one. A general solution has been obtained for a polynomial of an arbitrary order; then, finite-dimensional regulator equations are derived explicitly for a second-order polynomial. Numerical simulations have been carried out to show effectiveness of the proposed method.

Design of hybrid regrouping PSO–GA based sub-optimal networked control system with random packet losses

In this paper, a new approach has been presented to design sub-optimal state feedback regulators over Networked Control Systems (NCS) with random packet losses. The optimal regulator gains, producing guaranteed stability are designed with the nominal discrete time model of a plant using Lyapunov technique which produces a few set of Bilinear Matrix Inequalities (BMIs). In order to reduce the computational complexity of the BMIs, a Genetic Algorithm (GA) based approach coupled with the standard interior point methods for LMIs has been adopted. A Regrouping Particle Swarm Optimization (RegPSO) based method is then employed to optimally choose the weighting matrices for the state feedback regulator design that gets passed through the GA based stability checking criteria i.e. the BMIs. This hybrid optimization methodology put forward in this paper not only reduces the computational difficulty of the feasibility checking condition for optimum stabilizing gain selection but also minimizes other time domain performance criteria like expected value of the set-point tracking error with optimum weight selection based LQR design for the nominal system.

Sub-optimal automatic generation control of interconnected power system using constrained feedback control strategy

This paper presents sub-optimal AGC regulator designs for a 2-area interconnected power system using constrained feedback control strategy. The power system with identical thermal plants consisting of non-reheat thermal turbines interconnected via parallel AC/DC links is considered for the investigations. The formulation of optimal AGC problem involves solution of non-linear matrix equations, which requires an appropriate computational technique to yield a solution with high speed and accuracy. The implementation of optimal AGC regulator requires monitoring of all the state variables of the system or state reconstruction, which may be undesirable from cost and complexity considerations. Due to these limitations of optimal AGC regulators, sub-optimal AGC regulators are designed based on the constrained feedback control strategy using the feedback of system states which are accessible and available for measurement. Different structures of state cost weighting matrix ‘Q’ are also considered in the study. The power system dynamic performance is analyzed based on time response plots achieved with the implementation of designed optimal and sub-optimal AGC regulators in the wake of 1% load disturbance in one of the areas.

Sub-optimal Automatic Generation Control of Interconnected Power System Using Output Vector Feedback Control Strategy

This article presents the sub-optimal automatic generation control regulator designs of a two-area interconnected power system using output feedback control strategy. The power system consists of identical plants with reheat thermal turbines and is interconnected via parallel AC/DC links. Efforts have been made to propose sub-optimal automatic generation control regulators based on the feedback of output state variables, which may easily be accessible and available for measurement. In addition, the proposed regulators are designed using a modified area control error, which incorporates the DC tie-line power deviation in the modeling of area control errors. The system dynamic performance has been investigated with the implementation of designed sub-optimal automatic generation control regulators in the wake of 1% load disturbance in one of the two areas. Also, system dynamic responses with optimal automatic generation control regulators for the same power system model are obtained to compare the system dynamic response obtained with the proposed sub-optimal automatic generation control regulators.

SUBOPTIMUM NONLINEAR CONTROL BY OPERATION SPEED CRITERION BASED ON BELLMAN-LYAPUNOV METHOD

A general-theoretical task of suboptimal nonlinear control algorithm synthesis is discussed. As an example, a two-mass electromechanical control system of a crane moving mechanism is examined taking into account load oscillations damping. The task is solved on the basis of Bellman–Lyapunov method using the concept of «invariant immersion» by operation speed criterion. The dynamics of a closed-loop system with a synthesized suboptimal regulator is investigated.

Central suboptimal H ∞ control design for nonlinear polynomial systems

This article presents the central finite-dimensional H ∞ regulator for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the article reduces the original H ∞ control problem to the corresponding optimal H 2 control problem, using this technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H ∞ Control Problems’, IEEE Transactions on Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ regulator for nonlinear polynomial systems in a closed finite-dimensional form, based on the optimal H 2 regulator obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008b), ‘Optimal Controller for Uncertain Stochastic Polynomial Systems’, Journal of the Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal regulator for nonlinear polynomial systems against the central suboptimal H ∞ regulator available for the corresponding linearised system.

On the optimal reconstruction and control of adaptive optical systems with mirror dynamics

In adaptive optics (AO) the deformable mirror (DM) dynamics are usually neglected because, in general, the DM can be considered infinitely fast. Such assumption may no longer apply for the upcoming Extremely Large Telescopes (ELTs) with DM that are several meters in diameter with slow and/or resonant responses. For such systems an important challenge is to design an optimal regulator minimizing the variance of the residual phase. In this contribution, the general optimal minimum-variance (MV) solution to the full dynamical reconstruction and control problem of AO systems (AOSs) is established. It can be looked upon as the parent solution from which simpler (used hitherto) suboptimal solutions can be derived as special cases. These include either partial DM-dynamics-free solutions or solutions derived from the static minimum-variance reconstruction (where both atmospheric disturbance and DM dynamics are neglected altogether). Based on a continuous stochastic model of the disturbance, a state-space approach is developed that yields a fully optimal MV solution in the form of a discrete-time linear-quadratic-Gaussian (LQG) regulator design. From this LQG standpoint, the control-oriented state-space model allows one to (1) derive the optimal state-feedback linear regulator and (2) evaluate the performance of both the optimal and the sub-optimal solutions. Performance results are given for weakly damped second-order oscillatory DMs with large-amplitude resonant responses, in conditions representative of an ELT AO system. The highly energetic optical disturbance caused on the tip/tilt (TT) modes by the wind buffeting is considered. Results show that resonant responses are correctly handled with the MV regulator developed here. The use of sub-optimal regulators results in prohibitive performance losses in terms of residual variance; in addition, the closed-loop system may become unstable for resonant frequencies in the range of interest.

Design of Suboptimal Constrained Nonlinear Quadratic Regulator via Invariant Sets Switching

A design method for a suboptimal constrained nonlinear quadratic regulator (CNLQR) via invariant sets switching is presented. The CNLQR has the merits of both the control invariant set and the gain scheduling, and solves the constrained nonlinear quadratic regulation problem effectively. It first calculates the equilibrium surface of the nonlinear system, and then obtains the off-line local LQR control laws and the corresponding control invariant sets for several equilibrium points. These control invariant sets cover the equilibrium surface such that the closed-loop stability of the nonlinear system can be guaranteed by switching the local LQR laws on-line. The algorithm is computationally efficient, because the state feedback control law and control invariant sets are all solved off-line so that the computational burden of on-line optimization is greatly reduced. A simulation example illustrating the method is presented.

Line-of-sight Stabilization of an Optical Instrument Using Gained Magnetostrictive Actuators

A line-of-sight (LOS) stabilization system using gained magnetostrictive actuators is described in this paper. The system requires a relatively low supply voltage, has a wide frequency bandwidth and is relatively cheap. The system principle of operation is explained. The actuator and system design is described. The characterization tests are discussed and test results are shown. A coupled electromechanical model obtained from the measured transfer function is given. The design of a linear suboptimal regulator with output-integral feedback combined with a suboptimal estimator, is described. The controller test results are presented. It is shown that the system achieves 80% of the target isolation.

Suboptimal Regulators for Discrete-Time Jump Linear Systems with Time-Multiplied Performance Index

This paper addresses the suboptimal regulator design problem of discrete-time jump linear system by using a time-multiplied performance index. For a given state feedback control with constant gain matrices, the time-multiplied performance index is derived and a necessary condition for such a control to minimize the time-multiplied cost is provided. A gradient-based algorithm to find a suboptimal control law is developed and some numerical results are given to show the usefulness of the theoretical results.

A Frequency Condition for the Generalized Recurrent Difference in the Synthesis of H∞-Suboptimal, Decentralized, and Robust Regulators

A new approach to designing control laws under uncertainty produces easily verifiable tests for their generalized recurrent differences and does not require the solution of matrix equations or inequalities. This test is expressed as a frequency inequality, which is verified by verifying whether a polynomial has a real positive root of odd multiplicity. The underlying principles of the method are the necessary and sufficient conditions for a given stabilizing linear feedback to be the local minimax control satisfying the Bellman–Isaac inequality in a differential game with a general quadratic functional. The design of controls for Lur'e systems and systems with uncertain bounded parameters as well as the design of i>H∞-suboptimal regulators and decentralized controls for multiconnected systems with unknown cross-coupling are shown to involve a local minimax control problem.

Suboptimal design of regulators for jump linear system with time-multiplied quadratic cost

Considers the suboptimal regulator design problem of jump linear system with time-multiplied performance index. The time-multiplied performance index is derived. A necessary condition for a control law with constant gain matrix to minimize the time-multiplied cost is established and a gradient-based algorithm to find a suboptimal control law is developed. Some numerical results are worked out to show the usefulness of the theoretical results.