Robust Multivariable Control Research Articles

Designing Decentralized Multi-Variable Robust Controllers: A Multi-Objective Approach Considering Nearly Optimal Solutions

This article presents a new methodology for designing a robust, decentralized control structure that considers stochastic parametric uncertainty and uses a multi-objective approach. This design tunes the loop pairing and controller to be implemented. The proposed approach obtains the optimal and nearly optimal controllers relevant to the nominal scenario. Once obtained, the robustness of these solutions is analyzed. This methodology is compared with a traditional approach for selecting the most robust control pairings. The traditional approach obtains lightly robust controllers, i.e., the most robust controllers with an acceptable performance for the nominal scenario, and it obtains trade-offs between robustness and nominal performance. However, the traditional approach has a high computational cost because it is necessary to consider uncertainty in the optimization stage. The proposed approach mathematically guarantees the acquisition of at least one neighbor controller for each existing lightly robust controller. Therefore, this approach obtains solutions similar to lightly robust solutions with a significantly lower computational cost. Furthermore, the proposed approach provides the designer with more diversity and interesting solutions that are not lightly robust. The different approaches are compared using an example of a multi-variable process with two alternative control structures. The results show the usefulness of the proposed methodology.

Bond graph realizations of state space linear time-invariant multivariable descriptions

Given a state space description of a linear time-invariant multivariable system, a similarity transformation is applied to get a controllability canonical form. This transformation assures a Bond Graph (BG) realization and avoids the use of active bonds. Active or signal bonds do not preserve the continuity of power flows and consequently, energy conservation properties are lost. The state matrix of the system in transformed coordinates contains an antisymmetric matrix associated with the storage field and the rest is associated with the dissipative field. Thus, in general, the dissipative field is implemented with a multiport element, and in order to give physical meaning, the storage field is implemented with one-port elements. The resulting BG model does not have zero-order causal paths, that is, algebraic loops between the dissipative elements. The results are applied to the BG realization of a linear robust multivariable controller that is designed for a two mass system modelled in BG.

Multivariable robust tube-based nonlinear model predictive control of mammalian cell cultures

In this paper, the application of a robust nonlinear model predictive control (NMPC) framework to mammalian cell cultures is proposed, dealing with possible large kinetic parameter uncertainties. Industrial constraints formulated in view of good manufacturing practice and quality-by-design approach are also considered, namely the assurance that all state trajectories are contained within a corridor defined by lower and upper safety bounds. The latter are assimilated to the well-known tube-based paradigm which is used to formulate the corresponding robust NMPC problem. Both classical and tube-based NMPC performances are assessed in numerical simulations where specific key-species are regulated while dealing with an uncertain plant model. The capability of the tube-based method to reduce the impact of the parameter variations on the state trajectories and the violation of the constraints is highlighted, suggesting the transfer of the method on a real pharmaceutical process.

Optimized reduced order ARX modelling and robust control for multivariable uncertain systems

This paper deals with modelling and robust control of linear multivariable uncertain systems based on the new linear multivariable ARX (Auto-Regressive with eXogenous input)-Laguerre model and the loop-shaping design procedure with the relative gain array theory. In fact, to guarantee significant parameter number reduction of the multivariable ARX-Laguerre model compared with the classic multivariable ARX model, we propose the optimization of the Laguerre poles of the model using the genetic algorithm where the Fourier coefficients are identified using the recursive least square method. Later, the optimized multivariable ARX-Laguerre model is exploited to propose a robust control algorithm for linear multivariable uncertain systems. Indeed, we propose to combine the loop-shaping design procedure approach and the relative gain array theory to develop a simplified final robust controller guaranteeing reference tracking and robust stability against parametric uncertainties. This proposition aims for the simplification of the control’s scheme by adjusting the weighting matrix and the final robust controller calculated from the loop-shaping design procedure for a simpler and more experimentally applicable control scheme. The identification of Fourier coefficients and Laguerre poles as well as the robust multivariable control algorithm are experimentally validated on a laboratory coupled two-tank system showing good results in terms of modelling and attending desired control performances.

Evolutionary design of marginally robust multivariable PID controller

Two Margin-based design methods for tuning of decentralized PI controllers for multivariable systems are presented. The first method is predefined marginally robust controller (PMR) which is based on solving a constrained optimization problem to satisfy the desired values of the multivariable phase and gain margins that are set based on the designer’s knowledge of the working condition of the plant. The second method is self-setting marginally robust (SMR) that is an automatic controller design procedure. This method, by solving a many-objective optimization problem (MaOP), sets controller coefficients and finds optimum gain and phase margins. It offers a trade-off between tracking, interaction, and robustness. Evolutionary algorithm is applied to solve the problems and disk margin to define the multivariable stability margins. Proposed methods by combining the simplicity of margin-based design and effectiveness of optimization problems offer a practical solution in tuning the industrial multivariable controllers. Simulation results show that these methods are simple, practical, and at the same time, comparable with other robust multivariable controllers.

Quantitative feedback theory-based multi-variable robust control for soil quality improvement in a drip irrigated field

This article presents the control of Soil moisture, Nitrogen, and Salt content in soil using a robust control technique to maintain a desired quality of soil in a drip irrigated field. The control of this multi-variable system is accomplished by adopting two possible control structures namely (i) a decentralized controller backed by a feed-forward controller (ii) a diagonal centralized de-coupler along with a diagonal controller. The controllers are designed using quantitative feedback theory. The efficacy of the proposed techniques is validated through numerical simulations. A comparative study among the two methods reveals that the former performs better than the later. Another comparative study shows that the proposed controller outperforms some of the reported works.

LQ optimal robust multivariable PID control for dynamic positioning of ships with norm-bounded parametric uncertainties

The design of a suitable controller for dynamic positioning (DP) of ships is a challenging task keeping the hydrodynamic uncertainties in mind. The magnitude and rate constraints on the actuators make the problem more difficult. The present work employs a two-degree-of-freedom (2-DOF), multivariable, proportional–integral–derivative (PID) control for DP of a ship. To design the controller, first, the ship dynamics with hydrodynamic parameter uncertainties is represented in an uncertain state-space descriptor form. Then, the design of feedback gains of 2-DOF PID controller for the uncertain descriptor plant is converted into a state feedback design for an augmented uncertain descriptor plant. Next, a linear matrix inequality-based condition is obtained to solve this state feedback problem in order to ensure a desired linear quadratic (LQ) performance, even in presence of uncertainties. Finally, to further improve the tracking performance, the feedforward gain of the 2-DOF PID controller is designed using H∞ approach. The DP performance of the proposed controller is tested for the considered ship model along with uncertainties, actuator constraints, and environmental disturbances. A comparison with the existing PID controllers is also carried out to show superiority of the proposed controller.

Robust multimodel control for uncertain nonlinear MIMO systems based on ARX-Laguerre multimodel and LSDP approach

In this paper, we propose a new alternative for the robust control of nonlinear MIMO (multiple-input multiple-output) systems based on the multimodel approach and LSDP (Loop-Shaping Design Procedure)approach in the discrete case. First, the multimodel approach is exploited by representing each linear sub-model in the form of the recent linear MIMO ARX (Auto-Regressive with eXogenous inputs) -Laguerre model which guarantees a significant parameters number reduction compared with the MIMO ARX model. Thus, the resulting multivariable multimodel, entitled MIMO ARX-Laguerre multimodel, ensures a reduction of the parametric complexity with a simple recursive vector representation. However, this reduction is conditioned by an optimal choice of the pole characterising each Laguerre base. To deal with this, we propose the identification, using the genetic algorithm, of the Laguerre poles as well as the weighting function parameters of the MIMO ARX-Laguerre multimodel. This latter allows to generate a set of linear MIMO ARX-Laguerre sub-models which are exploited to propose a robust multimodel control for uncertain nonlinear MIMO systems. In fact, for each identified sub-model, we combine the LSDP approach and the RGA (Relative Gain Array) theory to develop a local robust controller. Then, a multivariable roust multimodel control algorithm is developed where the overall control strategy by multimodel approach amounts to incorporating the same weighting functions used in the considered multivariable multimodel in order to interpolate the control laws calculated from each local robust controller. The optimisation of Laguerre poles and weighting functions parameters as well as the proposed multivariable robust multimodel control algorithm are validated on the experimental prototype Quanser Aero system.

Robust multi-variable control of continuous yeast drying

This work considers robust moisture content and activity control in a continuous convective drying for particulate bio-materials. The major process uncertainty is in the kinetics of the second (falling-rate) drying period. Robust feedback controllers in the multi-variable and de-central case are designed to guarantee desired product specifications. The advantages of the robust controllers are discussed in comparison with a conventional PI controller. The case study presented is the drying of baker’s yeast in a fluidized bed dryer. The results show constant performances concerning the uncertainty of the drying kinetics and disturbance rejection at different operating points.

Robust multivariable control design for HVDC systems considering AC grid impedance uncertainties

High-voltage direct current (HVDC) transmission system based on modular multilevel converter (MMC) technology is considered as an attractive solution for the interconnection of two AC grids to enhance the security of supply. Several studies have concluded that the AC grid impedance is a key parameter for the control system design of the MMC. Such important design parameter, however, is subject to wide variations due to the time-varying nature of AC grid and the future modifications and expansions. Therefore, the grid impedance has to be considered as an uncertain parameter during control design stage. To this end, this paper suggests a robust multivariable controller which is able to maintain system stability and performance for an extended range of grid impedance uncertainties. To ensure that the controller operates robustly in a wide range of grid impedances, structured singular value of the system (known as μ) is minimized via an iterative procedure. In such procedure, the uncertainties are separated from the nominal linear model of the system and the weighing functions are tuned to fulfill the robustness criteria defined by the small-gain theorem. The effectiveness of the suggested controller and the design procedure is validated by means of simulation results.

Adaptive robust multivariable control of noninvertible memoryless systems with bounded disturbances: a generalization

The discrete-time robust adaptive control for some classes of the uncertain multivariable memoryless (static) systems in the presence of unmeasurable bounded disturbances, whose bounds are assumed to be known is addressed. The systems where the number of the control inputs do not exceed the number of their outputs are considered. The main feature of plants to be controlled is that their gain matrices are noninvertible. The assumption that the elements of these matrices are unknown a priori but there is information about possible bounds on these elements. The problem stated and solvesd here is to design a feedback controller to be capable to cope with the noninvertibility of the gain matrices and also with the parametric uncertainty in order to reject the external disturbances and to ensure the boun­dedness of all the control and output system signals. To solve the problem above mentioned, the robust adaptive approach together with the so-called pseudoinverse or inverse model-based concept is used. Three different cases are studied. In the first case, the robust adaptive controller applicable to the uncertain plant with the square singular gain matrix is designed. The robust method employing the pseudoinverse model-based controllers whose parameters are estimated via a standard recursive adaptation procedure is proposed in the second case to deal with the unknown nonsquare gain matrices having the full rank. The approach proposed in first case is extended to the third case dealing with the control of the unknown plants the gain matrices of which represent the nonsquare matrices of not full rank. Asymptotic properties of the robustly-adaptive controllers proposed in this paper are established. Results of numerical examples given to support the theoretic study.

Flight Testing Automatic Landing Control for Unmanned Aircraft Including Curved Approaches

Automatic landing of aircraft is a challenging guidance and control task that requires multiple feedback loops and a precise sequence of actions. Increasing operational flexibility and reducing the dependence on external infrastructure are key challenges for future unmanned aircraft. Usually, an aircraft performs the final approach on a straight line. This paper contributes a complete automatic landing controller capable of using three-dimensional curved approach paths all the way until touchdown. The controller consists of a nonlinear guidance law that steers the aircraft along a predefined spline path, various single-input–single-output control loops for rate and attitude control, and a robust multivariable flare controller. This flare controller ensures a three-point landing, i.e., simultaneous touchdown of all three wheels. Further, practical issues such as bumpless mode transfer and anti-windup compensation are considered. The controller is evaluated in multiple flight test experiments. Both the crabbed approach and the sideslip technique are demonstrated on several different approach paths, such as a steep curve and a helix. These paths are particularly challenging, because the flare maneuver is performed while the aircraft is in a turn. The controller is shown to reliably land the aircraft on an unpaved runway with high precision.

A novel multivariable nonlinear robust control design for turbofan engines

Traditional steady-state control methods are applied to turbofan engines operating in the small region near certain operating conditions, which need to switch controllers for operating in the large region and then may lead to instability and performance degradation of the closed-loop system. In this paper, a novel multivariable nonlinear robust control method for turbofan engines is proposed to improve the control performance within the large region. To enlarge the controllable region, a polynomial state-space model describes the nonlinear characteristics of turbofan engines. Based on the analysis of the closed-loop control system, by using the Lyapunov function theorems, a polynomial robust controller is designed to ensure the stability and desired nonlinear control performance of turbofan engines. Compared with the classical PI, mixed sensitivity, and H∞ control, simulation results show that the proposed method has better transient responses, disturbance rejection, and other control performance for the turbofan engine within the large region.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

Decentralized Robust Control of Nonlinear Uncertain Multivariable Systems

In this paper, we propose the development of a new strategy for the synthesis of a decentralized robust control for multiple-input–multiple-output (MIMO) nonlinear systems. The proposed method takes into account system’s loop interactions to synthesize a MIMO robust control stabilizing the system facing parametric uncertainties. The use of RGA theory is proposed to define the structure of the robust controller, synthesized by the loop shaping design procedure (LSDP), with the most effective input/output pairing. Then, an extension of an existing transition technique to the nonlinear multivariable case is proposed to decide the equilibrium points. The transition from an equilibrium point to another is ensured by the variation in the scheduling parameter (SP) while monitoring the variation in the gap metric compared to the maximum stability margin of the LSDP. We note that the new developed transition approach exploits during its execution the RGA theory whose purpose is to impose a common input/output pairing. Furthermore, for each equilibrium point a local full-order robust controller is obtained based on the LSDP approach, whose configuration is simplified also by exploiting RGA theory by proposing a selection matrix to deduce a local final robust controller. In this case, the overall decentralized robust control system is obtained by switching between local final robust controllers, where the maximum stability margin is used as an indicator of robustness in terms of stability and precision against parametric uncertainties. The proposed algorithm, for the synthesis of the decentralized robust multivariable control of uncertain nonlinear MIMO systems, is validated for the regulation of a benchmark of type continuous stirred tank reactor in the presence of parametric uncertainties. Moreover, the efficiency of the proposed decentralized robust control is validated on an experimental communicating two tank system.

Multi-Variable H∞ Control Approach for Voltage Ancillary Service in Autonomous Microgrids: Modelling, Design, and Sensitivity Analysis

This paper proposes a multi-variable robust control scheme for voltage regulation in a diesel-photovoltaic-supercapacitor hybrid power generation system operating in stand-alone mode. First, we study the influence of system parameters on the dynamic behavior of open-loop system measured outputs by means of a stability analysis method based on Monte Carlo simulation. Next, by applying $\mathcal {H}_{\infty }$ control theory, an $\mathcal {H}_{\infty }$ -based voltage controller is proposed to robustly force the voltage magnitude of a point of common coupling such as to satisfy design specifications. A cascaded two-level control architecture, where this controller acts as an upper control level and provides references to classical PI-based current tracking controllers placed on a lower level, is developed. A comprehensive methodology that casts the specific engineering demands of microgrid operation into an $\mathcal {H}_{\infty }$ control formalism is detailed. Effectiveness of the proposed voltage robust control strategy is validated via MATLAB®/Simulink® closed-loop time-domain simulations. Finally, we perform a sensitivity analysis of robust performance of the designed $\mathcal {H}_{\infty }$ controller in the presence of various load disturbances and model uncertainties through a series of closed-loop time-domain simulations carried out in MATLAB®/Simulink®.

Design and implementation of multi-variable [formula omitted] robust control for the underground coal gasification project Thar

The energy per unit time is an important performance indicator in determining the performance of an underground coal gasification (UCG) site to produce electricity. In literature, model-based strategies are employed by considering UCG as a single input single output (SISO) system, in which only the heating value of syngas is maintained at the desired level by varying inlet gas flow rate. However, the energy per unit time is also dependent on the flow rate of the produced gas mixture. Therefore, in this work, a model-based multi-variable robust control design, based on H∞ technique is proposed for the UCG process. The actual nonlinear model of UCG is very complex due to its 3D axisymmetric geometry, which makes the model-based control design a formidable task. Thus, a simple linear model with two inputs (flow rate and composition of inlet gas) and two outputs (flow rate and heating value of syngas) is identified by using subspace-based (N4SID) system identification technique. The linear model is then employed to design the H∞ (S/KS mixed sensitivity) multi-variable robust controller. The simulation results show that the designed controller has achieved both robust stability and performance in the presence of modeling inaccuracies and external disturbance. Furthermore, the designed controller is also implemented on the actual nonlinear cavity simulator (CAVSIM) for the UCG process. The controller exhibits an adequate performance by tracking the desired set points for the heating value and flow rate of the syngas.

Design of a new steerable in-pipe inspection robot and its robust control in presence of pipeline flow

Robust multivariable control of an in-pipe inspection robot with variable pitch rate is performed in this paper which moves through the pipelines while fluid is flowing. Most of the traditional inpipe robots have two challenges which make difficulty for investigating the pipe line. The necessity of blocking the flow and difficulty toward bypassing the probable obstacles in the pipes. Here a new mechanism of inpipe robot is proposed which can bypass the obstacles as a result of its mechanism modification and also is able to work in presence of flow by the aid of its designed robust controlled. To meet this goal, the proper mechanism is designed and its related model is derived. Afterwards a nonlinear robust controller is designed and implemented on the proposed robot based on Sliding Mode Control (SMC). The efficiency of the designed robot for bypassing the obstacles and also the robustness of its corresponding controller in presence of flow are investigated by the aid of MATLAB simulation. These simulations are validated by modeling the system in ADAMS and comparing the response of the proposed SMC and Feedback Linearization (FL). It is proved that the designed robot is able to move with controllable velocity through full pipelines while the designed controller can successfully cancel the fluid flow disturbances with a good accuracy of order 10-2.

Multivariable robust MPC design for neutralisation plant: Experimental analysis

The paper provides an extensive experimental analysis of offset-free multivariable robust model predictive control (MPC) of a neutralisation plant. The behaviour of the neutralisation plant was nonlinear and asymmetric. The controlled variable was a pH value of the outlet stream, and the manipulated variables were the inlet volumetric flow rates of the acid and base. The observer was designed to estimate the system states. Operating conditions make the tuning of the robust controller a challenging task. First, the conventional robust MPC was designed. The control setup was tuned and experimentally analysed in various operating conditions. Based on the measured data, the novel approach of the real-time compensation of the asymmetric behavior was investigated. Implementation of the proposed control strategy leads to improved control performance. The real-time compensation of asymmetric behaviour can be considered for the control of other systems with nonlinear behaviour.

A Robust $H_\infty$ Multivariable Stabilizer Design for Droop Based Autonomous AC Microgrid

The autonomous microgrid (MG) with multiple voltage source inverters (VSI) is operated in droop mode to share the load proportionally. These VSI controllers require higher droop constants if the feeder lines connecting the VSI to microgrid has a low X/R ratio. The higher droop gains and large loading conditions in the microgrid may exhibit instability with the low frequency power modes (LFPM). This paper details a systematic multivariable plant model of the MG using dynamic phasor modeling of power flow transfer functions to analyze the LFPM. Further, a robust supplementary multivariable controller is developed to stabilize the developed plant model, damp LFPM and improve transient power sharing performance of VSIs without affecting their steady-state power sharing. This stabilizer is developed based on Glover-McFarlane H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> loop shaping robust stabilization technique with an additional pole placement constraints formulated in linear matrix inequality framework. A laboratory scale experimental validation is presented to evaluate the performance of proposed stabilizer under various operating conditions and uncertainties in the autonomous MG. Moreover, the transient power sharing performance of DGs with proposed controller was compared with that of widely used derivative droop controller.