Robust Control Synthesis Research Articles

Robust Controllers Synthesis and Order Reduction of Unmanned Underwater Vehicle Submerging Control System with Interval Parametric Uncertainty

Modern marine robotic systems are often complex high-order dynamic systems with uncertain parameters. It is not always possible to apply common methods of controller synthesis to such systems. The research is dedicated to a problem of mathematical modeling and synthesizing motion control systems of high order for unmanned underwater vehicles. Proposed synthesis method is based on a modal approach to control and a robust control theory. The method allows setting allocation areas for dominant poles determining control quality of the system and then reducing the order of the transfer function by excluding other poles from it. Example of synthesizing a submerging speed control system via proposed method is also provided. The example shows, that the synthesis method proposed is efficient and allows successfully reducing the order.

IMPROVING OF ELECTROMECHANICAL SERVO SYSTEMS ACCURACY

Aim. Improving of accuracy parameters and reducing of sensitivity to changes of plant parameters of nonlinear robust electromechanical servo systems of guidance and stabilization of lightly armored vehicle weapons based on multiobjective synthesis. Methodology. The method of multicriterion synthesis of nonlinear robust controllers for controlling by nonlinear multimass electromechanical servo systems with parametric uncertainty based on the choice of the target vector of robust control by solving the corresponding multicriterion nonlinear programming problem in which the calculation of the vectors of the objective function and constraints is algorithmic and associated with synthesis of nonlinear robust controllers and modeling of the synthesized system for various modes of operation of the system, with different input signals and for various values of the plant parameters. Synthesis of nonlinear robust controllers and non-linear robust observers reduces to solving the system of Hamilton-Jacobi-Isaacs equations. Results. The results of the synthesis of a nonlinear robust electromechanical servo system for the guidance and stabilization of lightly armored vehicle weapons are presented. Comparison of the dynamic characteristics of the synthesized servo electromechanical system showed that the use of synthesized nonlinear robust controllers allowed to improve the accuracy parameters and reduce the sensitivity of the system to changes of plant parameters in comparison with the existing system. Originality. For the first time carried out the multiobjective synthesis of nonlinear robust electromechanical servo systems of guidance and stabilization of lightly armored vehicle weapons. Practical value. Practical recommendations are given on reasonable choice of the gain matrix for the nonlinear feedbacks of the regulator and the nonlinear observer of the servo electromechanical system, which allows improving the dynamic characteristics and reducing the sensitivity of the system to plant parameters changing in comparison with the existing system.

Robust lateral control of long-combination vehicles under moments of inertia and tyre cornering stiffness uncertainties

ABSTRACTA robust steering-based controller synthesis is presented for an A-double combination vehicle with a steerable dolly. The controller ensures robust stability and performance in the face of uncertainties in the cornering stiffness of the tyres and the moments of inertia of the semitrailers, which are treated as time-varying and time-invariant parameters respectively. A descriptor-type representation of the system is employed since a standard state-space model depends rationally on the moments of inertia. The controller synthesis is formulated as an -type static output feedback, which uses information from only one articulation angle. The driver steering input is also used by including a static feed-forward. The proposed synthesis method is based on linear matrix inequality (LMI) optimisation. The controller is verified based on the simulation results obtained from both (approximate) linear and (high-fidelity) nonlinear vehicle models. The results indicate significant improvement in the high-speed lateral performance of the A-double in the presence of parametric uncertainties.

Design of Optimal QFT Controller and Prefilter for Buck Converter Using Metaheuristic Algorithms

A buck converter is a step-down switching regulator. Buck convertors are being widely used in industrial applications that rely on regulated output voltage under fluctuating input voltage. A buck convertor works in the following modes: (a) current-controlled or (b) voltage-controlled mode. But these convertors manifest several nonlinearites because of the switching operation. Hence, in order to generate a quality output of the convertor, the design of a controller becomes crucial. In this paper, the synthesis of a QFT-based robust controller and prefilter has been carried out for an uncertain buck converter with varying input voltage and varying load. The controller synthesis problem has been posed as an optimization problem, and metaheuristic algorithms have been used for obtaining the optimal gains for the QFT controller and prefilter. By doing this, the QFT synthesis can be carried out in a single step instead of following the sequential classical QFT process on Nichols charts and the need for the generation of templates and bounds has be eliminated. The designed 2-degree-of-freedom QFT control system offers a robust behavior and efficiently handles the parametric uncertainties. The robustness of the designed controller has been confirmed through simulation results for large input voltage and load fluctuations.

Polynomial LPV approach to robust H ∞ control of nonlinear sampled-data systems

This paper addresses -gain analysis and robust control of nonlinear sampled-data systems described by a polynomial linear parameter varying (PLPV) model. First, conditions for -gain analysis of sampled-data PLPV systems are derived using a modified Krasovskii functional in which the distance between the real and measured parameters are considered as uncertainties. The resulting conditions are formulated in terms of parameterised linear matrix inequalities (PLMI). Second, a solution approach for satisfying PLMI conditions over the set of whole parameters and uncertainties is proposed using the sum-of-squares decomposition method. Third, conditions for robust sampled-data controller synthesis for nonlinear systems described by PLPV models are derived in terms of parameterised bilinear matrix inequalities (PBMI) with the maximum allowable sampling period as the parameter. To make the resulting bilinear matrix inequality (BMI) problems tractable, an iterative algorithm is developed and utilised to solve the problem. Finally, the effectiveness of the proposed approach is verified using several real-world examples.

Optimal tuning of H∞ fixed‐structure robust controller against multiple high‐level requirements using evolutionary computation

SummaryThis work deals with the optimal controller synthesis against high‐level multiple requirements using evolutionary computation. Indeed, such stochastic algorithms are interesting to solve problems based on complex industrial specifications and so seem to be particularly well suited to optimal robust controller synthesis. Using the H∞ loop‐shaping framework, the optimal weights/controller tuning without any structural assumption (in terms of poles/zeros/damping) on the searched filters (except of course their order) is investigated. The absence of such any structural assumption is important to avoid affecting the quality of the solution toward a complex specification and allows reducing the synthesis problem to a simple one with static scalings in place of frequency weights. Using a version of differential evolution algorithm well adapted for high dimensional control problems, computing directly a fixed‐structure controller for complex industrial specifications toward a generic nonconstraint fitness with quite reasonable computing time is achieved. The illustrating example deals with the line‐of‐sight stabilization problem.

Multiobjective Robust Controller Synthesis for Nonlinear Mechanical System

In the paper multiobjective robust controller synthesis problem for nonlinear mechanical system described by Lagrange’s equations of the second kind is considered. Such tasks have numerous practical applications, for example in controller design of robotic systems and gyro-stabilized platforms. In practice, we often have to use uncertain mathematical plant models in controller design. Therefore, ensuring robustness in presence of parameters perturbations and unknown external disturbances is an important requirement for designed systems. Much of modern robust control theory is linear. When the actual system exhibits nonlinear behavior, nonlinearities are usually included in the uncertainty set of the plant. A disadvantage of this approach is that resulting controllers may be too conservative especially when nonlinearities are significant. The nonlinear H∞ optimal control theory developed on the basis of differential game theory is a natural extension of the linear robust control theory. Nonlinear theory methods ensure robust stability of designed control systems. However, to determine nonlinear H∞-control law, the partial differential equation have to be solved which is a rather complicated task. In addition, it is difficult to ensure robust performance of controlled processes when using this method. In this paper, methods of linear parameter-varying (LPV) systems are used to synthesize robust control law. It is shown, that Lagrange system may be adequately represented in the form of quasi-LPV model. From the computational point of view, the synthesis procedure is reduced to convex optimization techniques under constraints expressed in the form of linear matrix inequalities (LMIs). Measured parameters are incorporated in the control law, thus ensuring continuous adjustment of the controller parameters to the current plant dynamics and better performance of control processes in comparison with H∞-regulators. Furthermore, the use of the LMIs allows to take into account the transient performance requirements in the controller synthesis. Since the quasi-LPV system depends continuously on the parameter vector, the LMI system is infinite-dimensional. This infinitedimensional system is reduced to a finite set of LMIs by introducing a polytopic LPV representation. The example of multiobjective robust control synthesis for electro-optical device’s line of sight pointing and stabilization system suspended in two-axes inertially stabilized platform is given.

Multiobjective Robust Controller Synthesis for Airborne Electro-Optical Device Line-of-Sight Stabilization System

A technique of multiobjective robust controller synthesis for airborne electro-optical device line-of-sight stabilization system is developed. The multiobjective synthesis of the robust control law for the stabilization system being considered is performed.

The μ–synthesis and analysis of water level control in steam generators

The robust controller synthesis and analysis of the water level process in the U-tube system generator (UTSG) is addressed in this paper. The parameter uncertainties of the steam generator (SG) are modeled as multiplicative perturbations which are normalized by designing suitable weighting functions. The relative errors of the nominal SG model with respect to the other operating power level models are employed to specify the weighting functions for normalizing the plant uncertainties. Then, a robust controller is designed based on μ -synthesis and D-K iteration, and its stability robustness is verified over the whole range of power operations. A gain-scheduled controller with H ∞ -synthesis is also designed to compare its robustness with the proposed controller. The stability analysis is accomplished and compared with the previous QFT design. The μ –analysis of the system shows that the proposed controller has a favorable stability robustness for the whole range of operating power conditions. The proposed controller response is simulated against the power level deviation in start-up and shutdown stages and compared with the other concerning controllers.

Anisotropic Suboptimal Control for Systems with Linear-Fractional Uncertainty

The problem of synthesis of robust anisotropic suboptimal controllers is stated and solved for systems with uncertain parameters. This paper considers a general case of unstructured parametric linear-fractional uncertainty bounded in spectral norm. The initial synthesis problem for the uncertain system is embedded into the synthesis problem for some auxiliary system with certain parameters, augmented controlled output, and additional input.

Robust model predictive control for inventory system with uncertain demand using linear matrix inequalities

In this paper, we develop an optimal control strategy on inventory systems with uncertain demand. To deal with these uncertainties we use a synthesis of robust model predictive control with linear matrix inequalities. The goal is to minimize the difference between the prediction and the reference trajectory subject to the objective function of each period, based on the input and output constraints. Using standard techniques, the optimization problem that minimizes the difference between the prediction and the reference trajectory, is reduced to a convex optimization problem involving linear matrix inequalities (LMIs). We provide numerical simulations on this system using MATLAB and then observe how robust predictive control models produce optimized strategy at the inventory level. In the simulation results, robust predictive control models provide an optimal strategy for controlling inventory levels with minimum total cost and inventory levels following inventory levels on issues.

Evaluation of block-oriented models use for the purpose of robust controllers synthesis

Evaluation of block-oriented models use for the purpose of robust controllers synthesis

SYNTHESIS OF A BOILER STEAM PRESSURE ROBUST CONTROL SYSTEM USING THE INTERVAL SYSTEMS FAMILY EXTENDED ROOT LOCUS

A vast class of industrial control systems should be properly controlled in conditions of substantial plant uncertainties and external perturbations. Robust control synthesis methods such as H∞ optimization, LMI approach are not efficient if a plant model order is not defined. For this reason, the aim of this paper is to recommend a technique for robust control implementation based on interval polynomial generation. The polynomials roots location theory permits to generate an interval polynomial providing the roots location in a dedicated area on the complex plane when a plant is subject to uncertainty. The limits of such an area are selected in order to minimize the negative effect of disturbances and to provide appropriate quality of system dynamics. The polynomials order is defined by controller order. Thus, for the second order PID-controller parameterization the second order is assumed for a plant model. Hence, the polynomial order is four. The robust PID-controller parameterization is achieved for a boiler steam pressure control. The simulation results are presented for this system which demonstrate quality of system dynamics improvement in conditions of parametric and external perturbations.

Synthesis of robust controllers for the control systems of technological units at iron ore processing plants

In order to synthesize a robust system of control over technological units, an analysis of appropriate mathematical models was performed. The uncertainty of models of technological iron ore processing units was accounted for by connecting a diagonal block at the top using a fractional linear transformation. To study robust control systems of technological units, we applied the following types of robust controllers: suboptimal H ∞ -controller, a controller that was synthesized using the method of circuit formation, and µ-controller. We performed an analysis of results of the study into indicators of robust quality and stability of control, created on the basis of these types of controllers. The best results were obtained using μ-controller, which ensures a minimal overshoot value of 2 %. Reducing the order of the selected μ-controller to the fourth order was performed by approximation using the Hankel norm. Under such a condition, a root-mean-square error relative to the base controller is 0.027. Results of present research could be used in the synthesis of control over technological iron ore processing units under conditions of uncertainty in parameters.

Neural robust stabilization via event-triggering mechanism and adaptive learning technique

The robust control synthesis of continuous-time nonlinear systems with uncertain term is investigated via event-triggering mechanism and adaptive critic learning technique. We mainly focus on combining the event-triggering mechanism with adaptive critic designs, so as to solve the nonlinear robust control problem. This can not only make better use of computation and communication resources, but also conduct controller design from the view of intelligent optimization. Through theoretical analysis, the nonlinear robust stabilization can be achieved by obtaining an event-triggered optimal control law of the nominal system with a newly defined cost function and a certain triggering condition. The adaptive critic technique is employed to facilitate the event-triggered control design, where a neural network is introduced as an approximator of the learning phase. The performance of the event-triggered robust control scheme is validated via simulation studies and comparisons. The present method extends the application domain of both event-triggered control and adaptive critic control to nonlinear systems possessing dynamical uncertainties.

Optimising supply chain management using robust control synthesis

The inventory management of supply chain is concerned with an efficient transportation of materials and products through supply chain members. In this paper, a series of linear models have been presented with lag time uncertainty for improving inventory management. In addition, a fluid analogy has been used for a single-product manufacturing system, or the basic unit of a supply chain. Robust control synthesis, which has been proven to cope with its ability for the system with high uncertainty, is utilised in optimising the inventory management and guaranteeing high performance of complete system. In addition, this control scheme aims to ensure the customer satisfaction by tracking and keeping the actual inventory close to target inventory under the influence of uncertainty. The extensive numerical simulations have been carried out to validate the proposed approach against disturbances. Finally, the simulation results show that the robust control system ensures good ability on keeping the target inventory under uncertainty.

Optimising supply chain management using robust control synthesis

The inventory management of supply chain is concerned with an efficient transportation of materials and products through supply chain members. In this paper, a series of linear models have been presented with lag time uncertainty for improving inventory management. In addition, a fluid analogy has been used for a single-product manufacturing system, or the basic unit of a supply chain. Robust control synthesis, which has been proven to cope with its ability for the system with high uncertainty, is utilised in optimising the inventory management and guaranteeing high performance of complete system. In addition, this control scheme aims to ensure the customer satisfaction by tracking and keeping the actual inventory close to target inventory under the influence of uncertainty. The extensive numerical simulations have been carried out to validate the proposed approach against disturbances. Finally, the simulation results show that the robust control system ensures good ability on keeping the target inventory under uncertainty.

Stable and Robust Controller Synthesis for Unstable Time Delay Systems via Interpolation and Approximation

In this paper, we study the robust stabilization of a class of single input single output (SISO) unstable time delay systems by stable and finite dimensional controllers through finite dimensional approximation of infinite dimensional parts of the plant. The plant of interest is assumed to have finitely many non-minimum phase zeros but is allowed to have infinitely many unstable poles in the open right half plane. Conservatism of the proposed methods is illustrated by numerical examples for which infinite dimensional strongly stabilizing controllers are derived in the literature.

Robust control synthesis for the activated sludge process

Control of the activated sludge process (ASP) is a challenging problem due to the complexity of the biological and chemical reactions, and large variations in the influent flow.

Density control in ITER: an iterative learning control and robust control approach

Plasma density control for next generation tokamaks, such as ITER, is challenging because of multiple reasons. The response of the usual gas valve actuators in future, larger fusion devices, might be too slow for feedback control. Both pellet fuelling and the use of feedforward-based control may help to solve this problem. Also, tight density limits arise during ramp-up, due to operational limits related to divertor detachment and radiative collapses. As the number of shots available for controller tuning will be limited in ITER, in this paper, iterative learning control (ILC) is proposed to determine optimal feedforward actuator inputs based on tracking errors, obtained in previous shots. This control method can take the actuator and density limits into account and can deal with large actuator delays. However, a purely feedforward-based density control may not be sufficient due to the presence of disturbances and shot-to-shot differences. Therefore, robust control synthesis is used to construct a robustly stabilizing feedback controller. In simulations, it is shown that this combined controller strategy is able to achieve good tracking performance in the presence of shot-to-shot differences, tight constraints, and model mismatches.