Multivariable Control Design Research Articles

A Multivariable Adaptive Control Design with Applications to Air-heat Tunnel Using Delta Models

The article describes the design of adaptive controller for autonomous and non-autonomous control of nonlinear laboratory model hot-air tunnel using delta models. Synthesis of the controller is based on a matrix approach and polynomial theory. Autonomous control is solved using compensators. The controller was verified by simulation and the real-time experiment on nonlinear laboratory model hot-air tunnel. The recursive least squares method in delta domain is used in identification part of the proposed controller.

Design and experimental evaluation of a data-oriented multivariable PID controller

PID control has been applied in many real systems. The control performance strongly depends on PID parameters. Although, some schemes for tuning PID parameters have been proposed, these schemes require system parameters which are estimated by system identification in order to calculate PID parameters. Moreover, most process systems are multivaliable systems which have interference of each respective inputs. On the other hand, data-oriented controller design schemes represented by VRFT or FRIT have received much attention in the last few years. These methods can calculate control parameters using closed loop data, and are expected to reduce computational costs. However, these methods have not been extended for MIMO systems. In this paper, a type of data-oriented multivariable PID controller using closed loop data is proposed. According to the proposed method, full matrices PID parameters which suppress mutual interference are calculated based on the implicit GMVC. Moreover, the control performance can be suitably adjusted by user-specified parameters. The effectiveness of the proposed method is numerically and experimentally evaluated.

Boiler Combustion System of Multivariable Internal Model Control Application Research

In the industrial process of common multivariable time delay input/output system, a multivariable decoupling internal model controller design method is put forward based on the internal model control structure, the method for the design of internal model controller has the function of decoupling and controller. The advantage has the ability to achieve approximate or complete decoupling in nominal system output response, the method is used on the multivariable strong coupling of the boiler combustion control system to design and simulation study, the simulation results prove the effectiveness of the method. And in the process model and process mismatch showed strong robustness and anti jamming ability.

PEMODELAN SISTEM DAN ANALISIS KESTABILAN DINAMIK PESAWAT UAV (MODELING SYSTEM AND DYNAMIC STABILITY ANALYSIS OF UAV)

Mission of Unmanned Aerial Vehicle (UAV) “Elang Avionik” is surveillance and aerial photographs. Therefore the flight of UAV must be stable and controlable, and first step activity is dynamic modelling and stability analisys. The problems of UAV system is disturbance, noise of sensor, MIMO and uncertainty dynamic model. For good result using the multivariable robust control, with some step research that is: (1)modeling and stability analysis, (2) design and implementation of PID control system, (3) flight dynamic parameter identification, (4) design and implementation of hardware in the loop simulation, (5) design and implementation of multivariable robust control, (6) test and evaluation of system. Simulation result show that the eigen value in longitudinal is: phugoid mode = –0,061293±0,40526i and non-oscillation mode = –6,1121±4,9253. In lateral directional is:dutch roll mode = –0,91089±5,7994i, spiral mode= –0,036563, and roll subsidence mode = –12,7181. Location of poles system on the left of imaginary axis, the means that the character of system is dynamic stable. But settling time to steady state condition is very long and improved by control system design.
 Key word: State space, Longitudinal, Lateral, Stable static, Stable dynamic

Multivariable PID controller design for chemical processes by frequency response approximation

In this paper we propose a systematic approach to designing low order controllers for chemical processes using frequency response approximation. The method consists of four major steps: (i) the desired behavior for the closed-loop system in the time domain is specified. The achievable performance of the closed loop is determined to ensure internal stability because of process inherent characteristics, i.e., non-minimum phase elements; (ii) the frequency response of the “ideal” controller, which is usually high order and too complex to be realized, is algebraically determined; (iii) this response is approximated in the frequency domain through a structured low order controller with PID parameters; and finally (iv) a closed loop simulation provides design evaluation. This novel design procedure is demonstrated through two case studies. These successful applications demonstrate its efficiency and applicability to the design of low order multivariable controllers for complex industrial processes.

Design of a New Nonlinear Excitation Controller Combined Differential Geometry with PID Theory

This paper presents a nonlinear excitation controller for transient stability combined differential geometry theory with PID technology. The controller ties the output of linear multi-variable excitation controller with the output of PID. Exact feedback linearization theory of differential geometry is applied to the design of linear multi-variable excitation controller for the single machine infinite system. Simulation results show that, compared with the general differential geometric controller, the proposed controller has the better control effect on power system and which remarkably improves the terminal voltage deficiencies in the control of generator.

Multi-variable Fuzzy Controller for Water Tank Temperature Control System

Due to the contradiction between high precision control with complexity of fuzzy controller design, an method for multi-variable fuzzy controller design is presented. A dynamic compensation model for the fuzzy controller is introduced, which simplify the analysis and design of multi-variable fuzzy controller, and improve control performance. The method is applied to high precision water tank temperature control system, and experience show that the multi-variable fuzzy controller with dynamic compensation model has excellent control effects.

Non-iterative direct data-driven controller tuning for multivariable systems: theory and application

In this study, a data-driven technique is proposed to deal with multivariable fixed-order controller design. The method is based on the virtual reference feedback tuning (VRFT) philosophy and thus does not require any model of the plant. Unlike standard VRFT for SISO systems, extended instrumental variables and variance weighting are used to counteract the effect of noise and achieve consistent controller estimate with a single set of input-output data. The proposed strategy is numerically compared to other existing direct and indirect techniques on a benchmark simulation example. The effectiveness of the method is finally tested on the airpath control of a real diesel engine.

MODELING OF A NEW STRUCTURE OF PRECISION AIR CONDITIONING SYSTEM USING SECONDARY CONDENSER FOR RH REGULATION

A dynamic mathematical model for a new structure of precision air conditioning (PAC) has been developed. The proposed PAC uses an additional secondary condenser for relative humidity regulation compared to a basic refrigeration system. The work mechanism for this system and a vapour-compression cycle process of the system are illustrated using psychrometric chart and pressure-enthalpy diagram. A non-linear system model is derived based on the conservation of mass and energy balance principles and then linearized at steady state operating point for developing a 8th-order state space model suited for multivariable controller design. The quality of linearized model is analyzed in terms of transient response, controllability, observability, and interaction between input-output variables. The developed model is verified through simulation showing its ability for imitating the nonlinear behavior and the interaction of input-output variables.

The design of nonovershooting and nonundershooting multivariable state feedback tracking controllers

We consider the use of linear multivariable feedback control to achieve a nonovershooting and nonundershooting step response. Recently, Schmid and Ntogramatzidis (2010) [13] introduced a linear state feedback controller design method to avoid overshoot. In this paper, we describe conditions under which the design method may be modified to avoid undershoot. The method is applicable to square and nonsquare systems, minimum and nonminimum phase systems, and also strictly proper and bi-proper systems.

Nonlinear MPC of a multi-zone multi-feed LDPE autoclave reactor

This paper discusses the design of a model-based multivariable nonlinear model predictive control (NMPC) formulation for the control of a multi-zone multi-feed LDPE autoclave reactor. Unscented Kalman filtering (UKF) state estimation was employed for online estimation of the plant states and disturbances. In addition to structural plant-model mismatch and noisy process measurements, the closed-loop performance of the UKF based NMPC scheme was investigated under parametric uncertainty in the kinetic rate constants. The closed-loop NMPC performance was also assessed for polymer grade changes, and for disturbance rejection at both open-loop stable and unstable operating regions.

Design of Dual-Range Linear Multivariable Controllers for Nonlinear Systems with Application to UAV Control

In this research, the previous design procedure for single-variable dual-range linear controllers for highly nonlinear systems is extended to the multivariable case. The procedure is based on generating the sinusoidal input describing function models of the plant followed by selection of two of these models for optimization of the dual-range linear controller. A single multivariable controller is designed by optimization to achieve a stable closed-loop system that satisfies a set of user-defined performance measures. Finally, the design is verified by digital simulation of the nonlinear plant and linear controller. Stability is demonstrated by successful generation of the sinusoidal input describing function models of the final closed-loop system. The procedure developed and the associated software are applied to bank-angle control of an unmanned aerial vehicle (UAV) with a discontinuous nonlinear term. It is shown that performance of a dual-range linear controller is superior to that of both a single-range and a multirange linear controller, and it competes with two other nonlinear controllers.

Experimental Results for Sensor Selection and Multivariable Controller Design for a Heavy-Duty Diesel Engine

In this paper we consider the issues facing the design of a practical multivariable controller for a heavy duty engine equipped with an exhaust gas recirculation (EGR) valve and variable geometry turbocharger (VGT). Issues facing the selection of sensors are considered, and a combination of physical as well as practical implementation requirements are treated in the choice and design of a model predictive controller. The nonlinearities and the multivariable nature of the system are investigated in order to coordinate both actuators such that the the emission and torque response requirements of the system are met. The process of modeling the engine, development of the controller, the hardware set-up that was utilized in running the controller validation work and, the results of utilizing the proposed system over transient cycles (e.g., FTP) and other certification cycles (e.g., RMCSET cycle) are presented.

Real/binary co-operative and co-evolving swarms based multivariable PID controller design of ball mill pulverizing system

In this paper, multivariable PID controller design based on cooperative and coevolving multiple swarms is demonstrated. A simplified multi-variable MIMO process model of a ball mill pulverizing system with steady state decoupler is considered. In order to formulate computational models of cooperative and coevolving multiple swarms three different algorithms like real coded PSO, discrete binary PSO (DBPSO) and probability based discrete binary PSO (PBPSO) are employed. Simulations are carried out on three composite functions simultaneously considering multiple objectives. The cooperative and coevolving multiple swarms based results are compared with the results obtained through single swarm based methods like real coded particle swarm optimization (PSO), discrete binary PSO (DBPSO), and probability based discrete binary PSO (PBPSO) algorithms. The cooperative and coevolving swarms based techniques outperform the real coded PSO, PBPSO, and the standard discrete binary PSO (DBPSO) algorithm in escaping from local optima. Furthermore, statistical analysis of the simulation results is performed to calculate the comparative reliability of various techniques. All of the techniques employed are suitable for controller tuning, however, the multiple cooperative and coevolving swarms based results are considerably better in terms of mean fitness, variance of fitness, and success rate in finding a feasible solution in comparison to those obtained using single swarm based methods.

Comparative performance analysis of various binary coded PSO algorithms in multivariable PID controller design

In this paper, comparative performance analysis of various binary coded PSO algorithms on optimal PI and PID controller design for multiple inputs multiple outputs (MIMO) process is stated. Four algorithms such as modified particle swarm optimization (MPSO), discrete binary PSO (DBPSO), modified discrete binary PSO (MBPSO) and probability based binary PSO (PBPSO) are independently realized using MATLAB. The MIMO process of binary distillation column plant, described by Wood and Berry, with and without a decoupler having two inputs and two outputs is considered. Simulations are carried out to minimize two objective functions, that is, time integral of absolute error (ITAE) and integral of absolute error (IAE) with single stopping criterion for each algorithm called maximum number of fitness evaluations. The simulation experiments are repeated 20 times with each algorithm in each case. The performance measures for comparison of various algorithms such as mean fitness, variance of fitness, and best fitness are computed. The transient performance indicators and computation time are also recorded. The inferences are made based on analysis of statistical data obtained from 20 trials of each algorithm and after having comparison with some recently reported results about same MIMO controller design employing real coded genetic algorithm (RGA) with SBX and multi-crossover approaches, covariance matrix adaptation evolution strategy (CMAES), differential evolution (DE), modified continuous PSO (MPSO) and biggest log modulus tuning (BLT). On the basis of simulation results PBPSO is identified as a comparatively better method in terms of its simplicity, consistency, search and computational efficiency.

다변수 슬라이딩 모드 제어에 의한 부정합조건 불확실성을 갖는 다입출력 비선형 시스템의 강인그로벌 지수 안정화

In this paper, a systematic design of a robust nonlinear multivariable variable structure controller based on state dependent nonlinear form is presented for the control of MIMO uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After a MIMO uncertain affine nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding diagonalized control input is proposed to satisfy the closed loop global exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

LMI-Based Multivariable PID Controller Design and its Application to the Control of the Surface Shape of Magnetic Fluid Deformable Mirrors

In this paper, the design of multivariable proportional-integral-derivative (PID) controllers for discrete-time systems based on linear matrix inequalities (LMIs) is studied. First the stability problem of the closed-loop system with the multivariable PID controller is investigated. To adjust the transient response of the resulting closed-loop system, the design method is extended to account for a pole clustering constraint. PID controller design methods that yield closed-loop systems with H∞ and H2 performance specifications are then investigated. Algorithms based on properly formulated LMIs are developed for the above different cases. Finally, the performance of the proposed controllers is experimentally evaluated in an adaptive optics system where it is desired to control the shape of a magnetic fluid deformable mirror. The experimental results indicate the proposed controllers can successfully provide the desired shape tracking performance in the closed-loop adaptive optics system.

Nonlinear EGR and VGT Control with Integral Action for Diesel Engines

Nonlinear EGR and VGT Control with Integral Action for Diesel Engines - A nonlinear multivariable control design with integral action is proposed and investigated for control of Exhaust Gas Recirculation (EGR) and Variable Geometry Turbine (VGT) in heavy duty Diesel engines. The main control goal is to regulate oxygen/fuel ratio and intake manifold EGR-fraction, and they are specified in an outer loop. These are chosen as main performance variables since they are strongly coupled to the emissions. An existing nonlinear control design based on feedback linearization is extended with integral action. In particular; the control design method utilizes a control Lyapunov function, inverse optimal control, and a nonlinear input transformation. Comparisons between different control structures are performed in simulations showing the following four points. Firstly, integral action is necessary to handle model errors so that the controller can track the performance variables specified in the outer loop. Secondly the proposed control design handles the nonlinear effects in the Diesel engine that results in less control errors compared to a control structure with PID controllers. Thirdly, it is important to use the input transformation and it is sufficient to use a control structure with PID controllers and input transformation to handle the nonlinear effects. Fourthly, the proposed control design is sensitive to model errors in the input transformation while a control structure with PID controllers and input transformation handles these model errors.

Multivariable Control Designs for Piezoelectric tubes

AbstractMost AFMs use piezoelectric tube nanopositioners for scanning. Fast actuation of piezoelectric tubes are restricted due to the presence of low mechanical resonant modes. These resonances, when excited, set off vibrations that cause loss of precision and repeatability of the scans. Thereby restricting the scanning frequencies to less than 1% of the first resonance frequency. Here, an innovative multivariable control design methodology for damping the resonant modes of the tube is presented. This methodology exploits the symmetry present in transfer-functions relating the input and output, and converts the multivariable control design problem into independent SISO designs. This methodology in conjunction with Integral Resonant control is used for damping the first resonant mode of the tube, and enables scans upto 10% of the first resonant mode. The proposed methodology can be applied to a large class of parallel kinematics nanopositioners used in scanning probe microscopes and probe-based data storage systems.

Necessary and sufficient condition for generalized passivity, passification and application to multivariable adaptive systems

AbstractRecently, a generalized passivity concept for linear multivariable systems was obtained which allows circumventing the restrictiveness of the usual passivity concept. The latter is associated with the classical SPR (Strictly Positive Real) condition whereas the new concept of passivity is associated with the so called WSPR condition and its advantage in multivariable systems is that it does not require a restrictive symmetry condition of SPR systems. As a result, it allows the design of multivariable adaptive control that, unlike some existing factorization approaches, does not imply in additional overparameterization of the adaptive controller. In this paper, we complete a previously established WSPR sufficient condition and prove that it is also necessary. We also propose some methods of passification by either premultiplying the system output tracking error vector or the system input vector by an adequate passifying matrix multiplier, so that the resulting input/output transfer function becomes WSPR. The efficiency of our proposals are illustrated by simulation utilizing a well known robotics adaptive visual servoing problem.