Design of reduced-order controller by using real-coded genetic algorithm

We propose a method to design reduced-order output-feedback controllers for fluid flows with the use of data produced by full-order controllers. First, the full-order controller is obtained by combining an ensemble Kalman filter (EnKF) and a model predictive controller (MPC) that are designed based on the Navier–Stokes equations. The full-order controller has high computational complexity and, therefore, is not suitable for real-time implementation. Hence, we use the full-order controller in offline numerical simulations to generate data for data-driven design of the reduced-order controller with low computational complexity. We find a reduced-order subspace of a closed-loop system under the full-order control from the data. This subspace underlies the reduced-order output-feedback controller. The reduced-order state-feedback law is obtained by approximating the full-order MPC with the use of its input/output data. The reduced-order observer is designed for a reduced-order model that is derived by using the Gaussian process regression (GPR). The GPR enables us to design the reduced-order observer which can evaluate uncertainty due to state-dependent residuals of the reduced-order model. We demonstrate the proposed method for a control problem of a flow around a cylinder at the Reynolds number 100. Numerical simulations reveal that the reduced-order controller performs as almost well as the full-order controller for a set of initial states. In addition, robustness of the reduced-order controller to a temporal disturbance that is not considered in the control design is confirmed in the simulations.

A new class of reduced-order controllers is obtained for the H/sub /spl infin// problem. The reduced-order controller does not compromise the performance attained by the full-order controller. An algorithm for deriving the reduced-order H/sub /spl infin// controller is presented in the case of continuous time. The reduction in order is related to unstable invariant zeros of the subsystem from disturbance inputs to measurement outputs. In the case where the subsystem has no infinite zeros, the resulting order of the H/sub /spl infin// controller is lower than that of the existing reduced-order H/sub /spl infin// controller designs which are based on reduced-order observer design. Furthermore, the mechanism of the controller order reduction is analyzed on the basis of the two-Riccati equation approach.

The design of a linear, reduced-order, continuous or discrete-time feedforward controller (FFC) is presented. The FFC is located in the reference value branch of a linear feedback system of any order which is designed according to the damping optimum. The aim of the FFC is to decrease the control system reference response time, while retaining a low overshoot and a well-damped form of the reference step response. This is achieved by locating the FFC zeros with the aid of the extended magnitude optimum, which is provided in the continuous or discrete-time variant. The influence of a suboptimally designed feedback system with a reduced-order feedback controller on feedforward control is analyzed. Reduced and full-order FFCs are compared.

ABSTRACTIn this paper, a controller order reduction method for linear parameter-varying systems is presented. The proposed method is based on the frequency-weighted balanced truncation technique, which has the advantage to reduce the order in a specific frequency range. The approach is discussed and is proved to preserve the closed-loop stability with a guaranteed upper error bound. Effectiveness and performance of the obtained reduced-order controller are investigated by applying it to an automotive semi-active suspension control. The obtained simulation results show that objectives such as the road handling and the passenger comfort realised with the reduced-order controller are kept in the same performance level as with the full-order controller. Moreover, a comparison with an other-order reduction method is shown and confirms the advantage of the developed method.

Reduced Order Controller Design for Discrete Time Systems

This paper describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized H/sub /spl infin// problem. It is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented. When the approximation is performed on the controller generator, guaranteed a priori stability and performance bounds are obtained in terms of the synthesis Riccati equation solutions of the normalized H/sub /spl infin// control problems.

This paper concerns reduced-order stable controllers in a unified way for two typical examples of underactuated robots called the Acrobot and the Pendubot which are two-link planar robots moving in a vertical plane with a single actuator at joints 1 and 2, respectively. The main contributions of this paper are threefold. First, using properties of the mechanical parameters of two-link planar robots, this paper proves via a constructive procedure that stable controllers exist for a local stabilization of the upright equilibrium point (two links are in upright position) of each robot by designing a specific output with an adjustable parameter and employing the pole-zero relation of the linearized model around the equilibrium point. Second, the paper presents a design method to obtain explicitly a formula of second-order (reduced-order) stable controllers by choosing the adjustable parameter. Third, in terms of strong stabilization (stabilization with a stable controller), some new features of the Acrobot and the Pendubot are revealed and are compared with those of the cart-pendulum system. Simulation results for the two robots are presented to validate the theoretical results.

The performances of Particle Swarm Optimization and Genetic Algorithm have been compared to develop a methodology for concurrent and integrated design of mechanical structure and controller of a 2-dof robotic manipulator solving tracking problems. The proposed design scheme optimizes various parameters belonging to different domains (that is, link geometry, mass distribution, moment of inertia, control gains) concurrently to design manipulator, which can track some given paths accurately with a minimum power consumption. The main strength of this study lies with the design of an integrated scheme to solve the above problem. Both real-coded Genetic Algorithm and Particle Swarm Optimization are used to solve this complex optimization problem. Four approaches have been developed and their performances are compared. Particle Swarm Optimization is found to perform better than the Genetic Algorithm, as the former carries out both global and local searches simultaneously, whereas the latter concentrates mainly on the global search. Controllers with adaptive gain values have shown better performance compared to the conventional ones, as expected.

A parametrization method is proposed for reduced-order H/sup /spl infin// controller design. By using the standard state-space H/sup /spl infin// optimization approach, one can characterize the set of all (sub)optimal controllers in terms of a parameter matrix. It is shown that there always exists a suitable parameter matrix such that a reduced-order H/sup /spl infin// controller can be constructed. The procedure for obtaining such a parameter matrix is also presented in this paper. >

This paper presents a two-Riccati inequality approach for the design of fixed-order H/sub /spl infin// suboptimal controllers with an observer-based structure. The two Riccati inequalities are only one-way coupled and can be solved consecutively. The fixed-order controller has the structure of a fixed-order estimator of the state feedback control law in the presence of the worst case disturbances. It retains the observer-based compensator structure of the full-order central controller of the standard H/sub /spl infin// design, but adds a fixed-order dynamic and mappings between the full-order and the fixed-order state spaces. In the full-order special case, this controller recovers to the minimal entropy central controller of the standard H/sub /spl infin// design.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents a method of designing reducedorder robust controllers for smart structural systems. We consider two kinds of uncertainties in the structural systems, norm bounded unstructured uncertainty and the variations of structural parameters. The smart structure with lead zirconate titanate (PZT) sensors and actuators is represented by a high order analytical model. Model error due to the uncertainties in structural parameters is modeled by parametric uncertainty in natural frequencies and damping ratios. By generalizing balanced truncation method for uncertain system, the high order model with uncertainties is reduced to a low order model with preserved parametric uncertainty. Based on linear matrix inequalities (LMIs) and Popov criterion, a robust controller is designed to suppress the lowfrequency vibrations caused by external disturbances and to guarantee the stability and performance of the closed-loop system under uncertainties. The order of the controller is further reduced by a frequency weighted model reduction method using LMI. The procedure was experimentally tested on a smart structural test article.

The complexities of physical systems make their analysis rather difficult and possibly a non desirable task, mainly due to difficult economical and computational considerations involved. This makes the use of reduced-order controller in physical system, which constitutes a good approximation of full order control system. In this paper we developed a method which preserves time domain as well as the frequency domain characteristics of original discrete time systems with higher order controller and their application for the control of discrete-time systems. A new mixed method, improved Routh stability method using p-domain transformation have been proposed which patches up the short comings of bilinear transformation and yields stable system with reduced order controller. It provides comparatively favorable results in comparison of other existing methods.

An application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system is presented. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order H/sub /spl infin// controller subject to the H/sub /spl infin//-norm of a frequency-weighted error between the approximated controller and the high-order H/sub /spl infin// controller is minimized. However, because solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with a nuclear-norm that can be reduced to a semidefinite program so that it can be solved efficiently. Application to the active suspension system of the Automatic Laboratory of Grenoble provides a fourth-order controller. The experimental results show that the control specifications are met to a large extent.

In this article a comparative study on the effectiveness of Real-coded Genetic Algorithm (RGA) approach in finding the compromised near-to-optimal solution and to by-pass the allocation rule of (m+n−1) for a Fuzzified Multi-Objective Transportation Problem (FMOTP) is discussed. For this purpose, some benchmark problems with well-defined membership function were considered and several changes have been made in the execution of Genetic Algorithm with real codes. The performance of the RGA Approach in obtaining the compromised near-to-optimal solution is compared with the traditional methods, namely as Interactive approach and Fuzzy programming approach. The obtained results reveal that, the applied RGA technique is more advantageous and effective after incorporating some changes according to the problem statement. This approach gives more than one compromised near-to-optimal solutions as well as bypasses the allocation rule of (m +n − 1), which is a great advantage in solving FMOTP. Two numerical examples have been considered and discussed to demonstrate this advent.

This paper deals with the reduced order controller design for infinite dimensional port Hamiltonian systems (IDPHS). Firstly, a structure preserving and passive LQG control design equivalent to Control by Interconnection is proposed. Based on this LQG controller, a structure preserving reduction method is used to approximate both the closed loop IDPHS and the LQG controller. This closed loop reduction guarantees that the reduced order controller will ensure acceptable closed loop performances on the infinite dimensional system. The proposed methods is applied to the control of a vibro-acoustic system.