Design Of Multivariable Control Systems Research Articles

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. The methodology is based on the linear parameterization of equivalent loop transfer functions (ELTFs) for centralized control. These functions capture the dynamics of the other loops and, from a prior design, allow solving the design problem at each iteration with linear programming that shapes the Nyquist plot of the ELTFs in the frequency domain, which also avoids the need for approximations. Two optimizations are proposed: (I) maximizing integral gains by fulfilling linear robustness margins in each ELTF and (II) maximizing linear robustness margins by fulfilling minimum bandwidths in each loop. In both optimizations, static decoupling and decoupling at a frequency close to the bandwidth of each loop are included as constraints, which improves the decoupling performance and the procedure convergence. The effectiveness of the method is verified in three simulation examples (square and non-square) and a lab experimental process. The proposed designs achieve a similar or better response when compared to that achieved by other authors.

Sir Alistair G. J. MacFarlane. 9 May 1931—2 November 2021

Sir Alistair MacFarlane was a gifted engineer with a fascination for feedback control systems from his industrial experience on radar systems through to his university research on multivariable control system design. He managed to excel in both practical design and mathematical analysis. He was also exceptionally effective, charismatic and visionary in leadership positions at both Cambridge and Heriot-Watt universities.

Multivariable Fractional-Order Controller Design for a Nonlinear Dual-Tank Device

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual-tank device are precisely formulated by fractional calculus. Using the accurate model, a multivariable fractional-order controller is designed for nonlinear devices. The merits of the fractional-order design include: (1) control of multivariable nonlinearities, (2) compensation of uncertainties, and (3) elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control system design.

Stability Augmentation in Lateral Directional Dynamics: A Multivariable Approach

This paper delves into the concept of stability augmentation in lateral-directional dynamics, focusing on a multivariable approach. In aircraft control systems, ensuring lateral-directional stability is crucial for safe and efficient flight. The primary objective is to examine the feedback control system's role in enhancing stability and how it interacts with the aircraft's inherent dynamics. We begin by exploring the basic augmentation system for lateraldirectional dynamics, which includes the feedback of body-axis roll rate to ailerons and yaw rate to the rudder, commonly referred to as the yaw damper. One of the key challenges addressed in this paper is the need to overcome the interference caused by the yaw damper when coordinating turns. This interference results from the constant nonzero yaw rate present during coordinated turns. To address this issue, the concept of "transient rate feedback" is introduced, which uses a washout filter to differentiate the feedback signal and minimize its effect during steady-state conditions. The paper presents mathematical models and transfer functions that describe the behavior of the lateral-directional augmentation system. It discusses the impact of different parameters, such as the time constants of actuators and washout filters, on the system's performance. The design of the feedback loops for roll and yaw control is elaborated upon, emphasizing the trade-offs between roll response, dutch roll damping, and roll-yaw coupling. Simulation results are used to evaluate the effectiveness of the stability augmentation system in improving the aircraft's roll response and dutch roll damping under varying flight conditions. The paper concludes with insights into the challenges and benefits of multivariable control system design for lateral-directional stability augmentation in aircraf

Decoupling Control Applied to the Smart Grid Power Dispatching Problem

This paper presents controller designs of the decoupling issue dedicated to renewable decentralized generators or new generation grids known as smart grids. The control methods were based on a three-phase voltage source grid representation that integrated wind and photovoltaic generators. The utilized decoupling strategies (Boksenbom and Hood, Zilkind and Luyben, and inverted decoupling) allowed the optimization of energy transfers and costs through the routing grid distribution path. Simulations were conducted in Matlab/Simulink. The trustworthiness of the multivariable control system design in addition to the tuning method was established using three test batches, totally decoupled and stable from input dependencies.

Design of a H∞ Robust Controller for a Small UAV

For Small Unmanned Aerial Vehicles (SUAV), because of its wide flight envelope and its own flight control system has many uncertainties, the aircraft itself is also vulnerable to strong interference such as atmospheric turbulence, so a robust controller is required to meet the specific performance requirements. In this work, a H∞ algorithm, based on a Linear Matrix Inequality (LMI), is used to the design of multivariable flight control system for the longitudinal motion mathematical model of a SUAV in a key laboratory. The simulation result demonstrated that the control system cannot only guarantee the stability of the closed-loop, but also has good robustness for internal and external disturbances.

Plasma magnetic time-varying nonlinear robust control system for the Globus-M/M2 tokamak

This paper is devoted to the development of the magnetic plasma control system for the Globus-M/M2 spherical tokamak (ST) when minor disruptions occur. The novelty of the research is the design of robust cascade multivariable control systems for time-varying plasma models in the presence of nonlinear thyristor current inverters as actuators for plasma position control. A new architecture of coordinated control of plasma position and shape is proposed. Quantitative Feedback Theory is used for the synthesis of robust Single-Input Single-Output (SISO) controllers for plasma position and PF-currents. Multiple-Input Multiple-Output (MIMO) H∞ control is applied to control the plasma shape. The simulation results of the gaps-based MIMO plasma shape control system with the plasma equilibrium reconstruction code in the feedback are shown. The robust stability of the control system is estimated.

Quantitative-fuzzy Controller Design for Multivariable Systems with Uncertainty

This work serves as a pioneer contribution in terms of application of Quantitative Feedback Theory (QFT) methodology and fuzzy logic method to design a controller for MIMO systems. Due to the presence of uncertainty in multivariable dynamic systems, the application of robust control methods for achieving high accuracy in tracking is inevitable. On the other hand, application of QFT to MIMO uncertain systems still remains to be one of the most difficult control problems for engineers. In this paper, authors attempt to simplify the MIMO control problem by proposing a new algorithm which joins QFT and fuzzy techniques. In order to illustrate the utility of the proposed algorithm, its application on a two degree of freedom link robot manipulator is depicted. Initially, a QFT controller is designed for each link to overcome the track and disturbance rejection problems. Then, a bi-level tuned PD-fuzzy controller is employed as one strategy for curbing probable errors in the previous controller. The controller design was carried in the following stages; first, a linear PD controller independently applied to each actuator. Then, fuzzy rules were developed to design a fuzzy PD controller. Fuzzy controller normalizing parameters were regulated according to maximum PD control errors. In the second stage, named nonlinear tuning, other parameters of the fuzzy controller were tuned using genetic algorithms. Finally, nonlinear simulations of arbitrary path tracking shows that the proposed controller has a consistent tracking ability, and also it can clearly be seen that the mentioned approach is precise and very simple in comparison to other MIMO control techniques.

IMC-PID Fractional Order Filter Multi-loop Controller Design for Multivariable Systems Based on Two Degrees of Freedom Control Scheme

An IMC-PID fractional order filter multi-loop controller design method based on two degrees of freedom paradigm is proposed for Multiple Input-Multiple Output systems with time delays. The interactions among the control loops are considered as disturbances. Thus, a two degrees of freedom control scheme, used for monovariable system to ensure the disturbance rejection, is extended to multivariable systems in order to reduce the effect of the coupling among the control loops. The proposed controller design method requires the control pairing selection with the least interactions and a set-point controller is calculated. An interactions reduction effect controller is calculated for each loop by defining a suitable complementary sensitivity function. The proposed controller design method is simple and systematic in relation with the desired closed loop specifications of each loop. The controllers obtained ensure robustness to process variations. Two illustrative examples are presented to show the merits of the proposed method.

Controller design for multivariable nonlinear control systems based on gradient-based ant colony optimisation

In the present study, a swarm intelligent algorithm called gradient-based continuous ant colony optimisation (GCACO) was utilised for controller design in multi-variable nonlinear control systems. The time domain objectives subject to the frequency domain constraints were considered in the proposed procedure. In order to be able to incorporate the time domain requirements in an overall controller design technique, the appropriate linearisation techniques utilised here was the exponential input describing function (EIDF). Experimental results obtained showed that GCACO technique developed here for controller design of nonlinear multivariable feedback control systems was capable to produce optimal and practical controllers that meet the design requirement in an efficient manner and computationally acceptable amount of time.

Fuzzy multivariable control of domestic heat pumps

Poor control has been identified as one of the reasons why recent field trials of domestic heat pumps in the UK have produced disappointing results. Most of the technology in use today uses a thermostatically-controlled fixed speed compressor with a mechanical expansion device. This article investigates improved control of these heat pumps through the design and evaluation of a new multivariable fuzzy logic control system utilising a variable speed compressor drive with capacity control linked through to evaporator superheat control. A new dynamic thermal model of a domestic heat pump validated using experimental data forms the basis of the work. The proposed control system is evaluated using median and extreme daily heating demand profiles for a typical UK house compared with a basic thermostatically-controlled alternative. Results show good tracking of the heating temperature and superheat control variables, reduced cycling and an improvement in performance averaging 20%.

Multivariable disturbance observer-based H2 analytical decoupling control design for multivariable systems

In this paper, an H2 analytical decoupling control scheme with multivariable disturbance observer for both stable and unstable multi-input/multi-output (MIMO) systems with multiple time delays is proposed. Compared with conventional control strategies, the main merit is that the proposed control scheme can improve the system performances effectively when the MIMO processes with severe model mismatches and strong external disturbances. Besides, the design method has three additional advantages. First, the derived controller and observer are given in analytical forms, the design procedure is simple. Second, the orders of the designed controller and observer are low, they can be implemented easily in practice. Finally, the performance and robustness can be adjusted easily by tuning the parameters in the designed controller and observer. It is useful for practical application. Simulations are provided to illustrate the effectiveness of the proposed control scheme.

Bond-graph-based controller design for the quadruple-tank process

The quadruple-tank process has been proposed as a benchmark for multivariable control system design. This paper addresses the design in the bond-graph domain of a robust controller having the volumetric flows of two pumps as manipulated variables and the level of the two lower tanks as the regulated outputs. The basic control objectives are expressed in terms of desired closed-loop energy and power-dissipation functions and captured in the bond-graph domain by means of a so-called target bond-graph. A basic controller design performed via bond-graph prototyping yields a primary control law which is further robustified against parameter uncertainties, measurement deviations and faults using the diagnostic bond-graph concept. This results in an additional closed-loop consisting of a PI-law which is represented by a physically meaningful bond-graph subsystem. The design methodology is first developed on a simpler two-tank SISO-control problem and then straightforwardly extended to the multivariable problem with the help of some causal manipulations on the four-tank bond-graph model.

Analytical Design of Multivariable Control Systems by Dynamical Decomposition Method

Design of multivariable control systems for complex technical plants with several interrelated channels and controlled variables is difficult problem. Usually here it is necessary to provide either independent (autonomous, unrelated) or coherent control of output variables. This design problem can be solved by using the analytical method implying exact, dynamical decomposition of the multivariable plant to the set of an independent single input–single output channels. The dynamic decomposition method is based on decomposing property of the adjunct matrix and provides realized of control action as function of output variables, reference input and measured disturbances (control on output and inputs) of the system. The efficiency of this analytical method is shown by the numerical example of control system design for the turbojet engine of the gas-pumping station with three interrelated channels.

The Modified Quadruple-Tanks Process: A Flexible Mathematical Model with an Adjustable Simulink Block

This paper presents the modified quadruple-tanks process, a flexible laboratory process with an adjustable Simulink block, which is multivariable system consisting of four interconnected water tanks included with lower interacting valve. The new general form of modified quadruple-tanks mathematic model and Simulink block is developed for the advantage of control system analysis and design which can make practical use for many styles of multivariable process by adjusting the value of connected valve resistance, inlet and outlet valve ratio. In this paper described clearly about physical properties of modified quadruple-tanks process, mathematical modeling, transformation of modified quadruple-tanks process, analysis of right half-plane zeros characteristic and controller design for multivariable system. By the several models of transformed modified quadruple-tanks, they can be used to teach students in the skills of multivariable control system analysis and design, understanding control limitation due to interactions, model uncertainties, non-minimum phase behavior, and unpredictable time variations, design decentralized controllers, Implementing decouples to reduce the effect of interactions, and understanding their limitations.

Multivariable Control System Design and Application for Energy Saving of Temperature and Humidity Chamber

This paper reports the development of a multivariable control system for the energy saving of a thermo-hygrostat. The thermo-hygrostat is used to inspect various products and to create the desired atmosphere by controlling the temperature and humidity in the chamber. The controlled values are those of temperature and humidity, and manipulated values are those of the heater, humidifier and refrigerator. A conventional multi-loop PID controller is known to have sometimes caused energy loss owing to the canceling out of the manipulated values because the system gains of both the heater and the refrigerator are opposite. In this study, the proposed control system was able to achieve a reduction in the energy consumption by also controlling the output of the refrigerator; the experimental results show this decrease.

Combined Nonlinear Tokamak Plasma Current Profile Control System Design and Simulation with Input Constraints

AbstractThe paper presents the design and simulation results of the combined multivariable control system with the plant input constraints for a plasma current profile in a tokamak. The plasma kinetic model was used in terms of the Grad-Shafranov plasma equilibrium equation and the poloidal magnetic flux diffusion equation. The model is square specifically contains 5 inputs and 5 outputs. Actuators are external current drive sources. Output is plasma current density measured at five points of the minor radius. A set of linear models for controller design was obtained by a state subspace identification approach. A set of H∞ controllers was synthesized by a loop shaping methodology at various values of the plasma electron temperature on the magnetic axis. Controllers designed were applied by the numerical simulation to the original model to change the current profile from one state to another. In the presence of plant input constraints a special logic block was developed in addition to the linear robust controller and used when plant inputs saturated. The plasma current profile control system designed showed its operability in the tokamak plasma electron temperature range on the magnetic axis from 0.1 to 18 keV.

PID controller design of TITO system based on ideal decoupler

The proposed method for designing multivariable controller is based on ideal decoupler D( s) and PID controller optimization under constraints on the robustness and sensitivity to measurement noise. The high closed-loop system performance and robustness are obtained using the same controller in all loops. The method is effective despite the values and positions of the right half plane zeros and dead-times in the process transfer function matrix G p( s). The validity of the proposed multivariable control system design and tuning method is confirmed using a test batch consisting of Two-Input Two-Output (TITO) stable, integrating and unstable processes, and one Three-Input Three-Output (TITO) stable process.

A Design of Discrete-Time Multivariable Iterative Learning Control Systems with Interactor Matrix

In this paper, it is proposed a discrete-time multivariable iterative learning control (ILC) algorithm which guarantees the monotonic convergence of the tracking error norms along with the number of the trials. It is pointed out that an interactor matrix plays an important role in the iterative learning control. Since ILC is a design method not requiring plant parameters explicitly, the information on the interactor matrix should be treated same manner as in an adaptive control systems. In this paper, it is presented a design of ILC using G-interactor which is derived not requiring the plant parameters. It is also presented a design of ILC using a diagonal precompensator which will make the interactor of the compensated plant be diagonal. Numerical simulations are presented to confirm the validity of the proposed design.

Fundamental Analysis of the Static VAr Compensator Performance Using Individual Channel Analysis and Design

In this paper the performance of a synchronous generator – SVC system is evaluated using Individual Channel Analysis and Design (ICAD), a control-oriented framework suitable for small-signal stability assessments. The SVC is already a mature piece of technology, which has become very popular for providing fast-acting reactive power support. The great benefits of ICAD in control system design tasks are elucidated. Fundamental analysis is carried out explaining the generator dynamic behavior as affected by the SVC. A multivariable control system design for the system is presented, with particular emphasis in the closed-loop performance and stability and structural robustness assessment. It is formally shown in the paper that although the addition of the SVC with no damping control loop does not improve the dynamic of the system, its inclusion is very effective in enhancing voltage stability. Moreover, ICAD analysis shows that with the use of the SVC the dynamical structure of the system is preserved and no considerable coupling or adverse dynamics are added to the plant.