Linear Robust Control Research Articles

Vehicle Motion Control for Overactuated Vehicles to Enhance Controllability and Path Tracking

The motion control of vehicles poses distinct challenges for both vehicle stability and path tracking, especially under critical environmental and driving conditions. Overactuated vehicles can effectively utilize the available tyre–road friction potential by leveraging additional actuators, thus enhancing their stability and controllability even in challenging scenarios. This paper introduces a novel modular upstream control architecture for overactuated vehicles, integrating a fast and robust linear time-varying model predictive path and speed tracking controller with a model following approach and nonlinear control allocation to form a holistic vehicle motion controller. The architecture decouples the path and speed tracking task from the actuator allocation, where torque vectoring and rear-wheel steering are applied to achieve linear understeer reference vehicle behavior. It allows for the use of a simpler path tracking controller, enabling long preview horizons and enhanced computational efficiency. Nonlinearities, such as the mutual influence of lateral and longitudinal tyre forces, are accounted for within the control allocation. The simulation results demonstrate that the proposed control architecture and overactuation improve vehicle stability in critical driving conditions and reduce path tracking errors compared to a dual-motor vehicle.

Robust Bumpless Transfer Control for Switched Systems with Unmatched Uncertainties Based on the Common Robust Integral Sliding Mode Under Arbitrary Switching Rules

In this paper, a robust bumpless transfer control scheme for tracking control is proposed to avoid large jumps in the control signals for a switched system (SS) with unmatched uncertainty and disturbance. The robust bumpless controller comprises a robust linear feedback control (RLFC) and a continuous sliding mode control (CSMC) based on the given robust integral sliding mode (RISM). The RLFC meets the requirement of bumpless indices, and the CSMC suppresses the unmatched uncertainty and disturbance. First, the RLFC design is proposed, and the linear feedback coefficients satisfy the bumpless indices, despite the uncertainty and disturbance. Then, a RISM surface design is proposed, in which the uncertain SS satisfies the given H-infinity robust performance index, and can resist the unmatched uncertainty. Consequently, the CSMC ensures that the RISM surface can be reached in finite time from the initial time instant. By composing the CSMC with the RLFC, the control scheme achieves the robust trajectory tracking and the suppression of the control signal bumps during switching. Finally, the proposed robust bumpless transfer control scheme was applied to the different examples, and the simulation results verified its effectiveness.

Robust Controller Design Ensuring the Desired Aperiodic Stability Degree of a Control System with Affine Uncertainty

This paper considers a system whose characteristic polynomial coefficients are linear combinations of the interval parameters of a plant forming a parametric polytope. A linear robust controller is parametrically designed to place a dominant pole of the system within the desired interval of the negative real semi-axis and ensure an aperiodic transient in the system. The parametric design procedure involves a low-order controller with dependent and free parameters: the former serve to place the dominant pole within the desired interval on the complex plane whereas the latter to shift the other poles to some localization regions beyond a given bound (to the left of the dominant pole to satisfy the pole dominance principle). To evaluate the dependent parameters of the controller, the originals of the interval bounds of the dominant pole are determined for the plant’s parametric polytope based on a corresponding theorem (see below). The free parameters of the controller are chosen using the robust vertex or edge D-partition method, depending on the boundary edge branches of the localization regions of the free poles. A numerical example of the parametric design procedure is provided: a PID controller is built to ensure an acceptable aperiodic transient time in a load-lifting mechanism with interval values of cable length and load weight.

Robust Linear Discrete Control for a Hexacopter: Experimental Results

This paper presents a discrete-time robust linear control method for tracking a hexacopter's trajectory in the presence of external disturbances. The control of multi-rotor type unmanned aerial vehicles (UAVs) has gained considerable attention recently due to their various applications, such as crop spraying in precision agriculture. The control of UAVs requires robustness to reject disturbances and accommodate dynamic uncertainties. To achieve this goal, the robust discrete-time control action is designed in two stages. The first stage utilizes the solution of a difference Riccati-equation to guarantee system stability in an optimal sense. The second stage provides system robustness against external disturbances and uncertain dynamics. Furthermore, the Lyapunov stability theory for discrete linear systems is used to derive system asymptotic stability. Finally, experimental results of the hexacopter flight are provided to illustrate the effectiveness of the presented control law.

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.

Simultaneous Damping and Frequency Control in AC Microgrid Using Coordinated Control Considering Time Delay and Noise

The incorporation of converter-based generating sources in utility-scale microgrids causes frequency instability and low-frequency oscillations (LFOs), which is also a reason for degeneration in system stability. Damping frequency control is an essential part of alternating current (AC) microgrid system operation and control. Sudden changes in load, variations in renewable power outputs due to changes in solar insolation or wind speed, and so on factors cause the system frequency to deviate from the nominal value. Therefore, the role of a frequency controller is to maintain the dynamic stability in an AC microgrid by retaining the system frequency at the nominal value. Again, AC microgrids with high renewable power penetration face even more difficulty in maintaining frequency stability because of their poor inertial response. The research presented here proposes a novel approach for grid-connected AC microgrid oscillation damping and frequency control that simultaneously takes into consideration time delay and noise. To improve the frequency response and dampen LFOs by providing the voltage and frequency within the specified range, a coordinated technique-based control approach is adopted. In the developed hybrid control, the frequency controller relies on active power modulation, while the power oscillation damping controller is dependent on reactive power modulation. To improve stability and reduce communication consequences such as noise and signal latency (time delay), the developed power oscillation damping controller and frequency controller are coordinated along with the robust linear quadratic Gaussian controller. The comparative investigation of the effectiveness of the coordinated control technique is employed in the software of MATLAB/Simulink for grid-connected AC microgrid. The outcome of the simulation illustrates the superior effectiveness of the suggested controller over the traditional droop controller for huge power flows under disturbance with various operating conditions, under/overfrequency events, time delay, and noise. This grid encouragement capability for AC microgrids is anticipated to lead to novel possibilities for generating revenue.

Robust Space Launcher Control with Time-Varying Objectives

This paper presents a novel approach to robust linear time-varying control design for space launchers. It allows the controller to explicitly account for the launcher’s time-varying dynamics and changing control objectives along the ascent trajectory. The latter are readily incorporated via time-varying weighting functions into a mixed sensitivity design. For a traceable and transparent control design, a physically motivated weighting scheme is applied, which requires little tuning effort. The controller is obtained via a novel observer-based finite horizon linear time-varying synthesis approach. It provides a transparent structure which is easy to implement. The approach is used to design a pitch controller for a flexible expendable launch vehicle in atmospheric ascent tracking the open-loop guidance reference signal.

Graph-based conditions for feedback stabilization of switched and LPV systems

This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: (i) the robust case, in which the active mode is completely unknown and unobservable, and (ii) the mode-dependent case, in which the controller depends on the current active switching mode. The technical developments are based on graph-theory tools, relying in particular on the path-complete Lyapunov functions framework. The main idea is to use directed and labeled graphs to encode Lyapunov inequalities to design robust and mode-dependent piecewise linear state-feedback controllers. This results in novel and flexible conditions, with the particular feature of being in the form of linear matrix inequalities (LMIs). Our technique thus provides a first controller-design strategy allowing piecewise linear feedback maps and piecewise quadratic (control) Lyapunov functions by means of semidefinite programming. Numerical examples illustrate the application of the proposed techniques, the relations between the graph order, the robustness, and the performance of the closed loop.

Reduced-order Koopman modeling and predictive control of nonlinear processes

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to select lifting functions for Koopman identification. The selected lifting functions are used to project the original nonlinear state–space into a higher-dimensional linear function space, in which Koopman-based linear models can be constructed for the underlying nonlinear process. To curb the significant increase in the dimensionality of the resulting full-order Koopman models caused by the use of lifting functions, we propose a reduced-order Koopman modeling approach based on proper orthogonal decomposition. A computationally efficient linear robust predictive control scheme is established based on the reduced-order Koopman model. A case study on a benchmark chemical process is conducted to illustrate the effectiveness of the proposed method. Comprehensive comparisons are conducted to demonstrate the advantage of the proposed method.

Dynamic event-triggered fuzzy non-fragile control of DC microgrids

This paper studies the event-triggered fuzzy non-fragile control of uncertain DC microgrids subject to false data injection (FDI) attacks, controller saturation, network delays and premise mismatching. Firstly, a dynamic event-triggered mechanism (ETM) is proposed, which can save more communication bandwidth than the static ETMs, and remove the complex Zeno-free computation required by the continuous-time ETMs. Secondly, a fuzzy time-delay closed-loop system model is established, which provides a unified framework to study the effects of the dynamic ETM, FDI attacks, uncertainties, saturation, delays and premise mismatching. Thirdly, mean-square exponential stability criteria are established, and co-design method for the saturated fuzzy non-fragile (SFNF) controller and the dynamic ETM is presented. Simulation results confirm that the SFNF controller can stabilize the unstable DC microgrid, while the dynamic ETM significantly reduces the triggering rate by 84.98%. Comparisons show that the proposed controller performs better than the non-fragile controller, fuzzy controller and robust linear controller, and the dynamic ETM achieves a lower triggering rate than the static ETMs.

Design of optimal-robust control of step motors with partially unknown parameters and disturbances

The paper describes the design of a novel control law for step motor under participially unknown parameters and bounded external disturbances. The unknown parameters and disturbances are related to the motor torque, the rotor moment of inertia, the viscous friction, the resistance and the load torque. The design of a novel control law is based on feedback linearization and linear robust control. The gain of a linear control law is calculated by solving the linear matrix inequality and some optimization problems. The simulations illustrate the efficiency of the proposed scheme in comparison with classical PID-controller and adaptive control law.

A multivariable super‐twisting‐based fault‐tolerant control with control allocation for uncertain systems

SummaryThis article contributes with a fault‐tolerant control (FTC) for uncertain systems under the effect of some possible time‐ and state‐dependent actuator faults and/or failures, and component faults, which are zero at the initial time. The proposed scheme is based on a continuous integral sliding‐mode control approach and a fixed control allocation technique. The integral sliding‐mode control strategy allows us to design a robust linear controller and a multivariable Super‐Twisting algorithm, which deals with the faults. The proposed scheme guarantees the fulfilment of an output regulation task, with an arbitrarily small regulation error, and does not require a fault diagnosis stage but full‐state availability. The performance of the proposed FTC is illustrated through some simulations on a benchmark B747 aircraft model.

Robust servo linear quadratic regulator controller based on state compensation and velocity feedforward of the spherical robot: Theory and experimental verification

There are few studies on the lateral motion of spherical robots. In this article, a new algorithm is proposed to solve the problem of low control accuracy of the lateral motion. A single lateral motion model is established, and the optimal solution of the linear quadratic regulator in infinite time domain is obtained. Aiming at the problems of longitudinal velocity and lateral angle coupling and low control precision, state compensation and velocity feedforward are carried out, and an improved robust servo linear quadratic regulator control algorithm is proposed. Experiments show that the proposed lateral control algorithm has strong adaptability and robustness to changing speeds and lateral angles, and the control effect is stable and reliable.

LMI-based Data-Driven Robust Model Predictive Control

Predictive control, which is widely used currently, bases on a model of the system to compute the applied input optimizing the future system behavior. If the nominal models are not given or are uncertain, data-driven model predictive control approaches can be employed, where control input is directly obtained from past measured trajectories. Using a data informativity framework and Finsler's lemma, we propose a data-driven robust linear matrix inequality-based model predictive control scheme that considers input and state constraints for linear parameter-varying systems and Lur'e-type nonlinear systems. Using these data, we formulate the problem as a semi-definite optimization problem, whose solution provides the matrix gain for the linear feedback, while the decisive variables are independent of the length of the measurement data. The designed controller stabilizes the closed-loop system asymptotically and guarantees constraint satisfaction. Numerical examples are conducted to illustrate the method.

Stability analysis of robust control problems in linear descriptor systems with matching conditions

We investigate the optimal control equivalent and state feedback approach to linear time-invariant descriptor systems with norm-bounded uncertainty in matrix A(q). The goal is to find a controller that can stabilize the system even in the presence of random perturbations and to study the effect of initial conditions on the system’s stability. The systems with matching conditions and also linear algebraic equations with the full rank of the algebraic coefficient matrix are investigated. The solution to the optimal control problem (OCP) for the linear descriptor system (LDS) is the solution to the robust linear descriptor control problem provided. We will show that with theorems and examples.

Fractional Transformation-Based Intelligent H-Infinity Controller of a Direct Current Servo Motor

Direct current (DC) servo motors are central to many complex systems, such as electrical, electro-mechanical, and electro-hydraulic frameworks. In practice, these systems can have nonlinear characteristics and parameter variations. Accurate model representation and position tracking of DC motors are the main issues in many real systems, such as twin rotors, aircraft, airships, and robot manipulators. The precise position tracking of these systems has already been achieved using conventional H-infinity (H∞) controllers. However, the order and structure become more intricate when employing complex weights to shape the closed-loop system, which limits the current proposals. To overcome the above-mentioned limitations, in this article, we provide a precise angular position tracking of a DC servo motor utilizing an intelligent, robust linear controller based on a fixed-structure linear fractional transformation. The conventional H∞ controllers are based on the minimization of an unstructured linear fractional transformation objective function that leads to a complex design of these controllers. The main advantage of the proposed intelligent H∞ synthesis is the fixed and simple structure that increases its practical implementation. The methodology is formulated in the MATLAB software for the robust design of the proposed synthesis based on an intelligent fixed-structure H∞ optimization. Simulation results are compared with conventional H∞ and proportional-integral-derivative controllers. The results are also validated experimentally.

Comparative Performance Analysis of the DC-AC Converter Control System Based on Linear Robust or Nonlinear PCH Controllers and Reinforcement Learning Agent

Starting from the general topology and the main elements that connect a microgrid represented by a DC power source to the main grid, this article presents the performance of the control system of a DC-AC converter. The main elements of this topology are the voltage source inverter represented by a DC-AC converter and the network filters. The active Insulated Gate Bipolar Transistor (IGBT) or Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) elements of the DC-AC converter are controlled by robust linear or nonlinear Port Controlled Hamiltonian (PCH) controllers. The outputs of these controllers are modulation indices which are inputs to a Pulse-Width Modulation (PWM) system that provides the switching signals for the active elements of the DC-AC converter. The purpose of the DC-AC converter control system is to maintain ud and uq voltages to the prescribed reference values where there is a variation of the three-phase load, which may be of balanced/unbalanced or nonlinear type. The controllers are classic PI, robust or nonlinear PCH, and their performance is improved by the use of a properly trained Reinforcement Learning-Twin Delayed Deep Deterministic Policy Gradient (RL-TD3) agent. The performance of the DC-AC converter control systems is compared using performance indices such as steady-state error, error ripple and Total Harmonic Distortion (THD) current value. Numerical simulations are performed in Matlab/Simulink and conclude the superior performance of the nonlinear PCH controller and the improvement of the performance of each controller presented by using an RL-TD3 agent, which provides correction signals to improve the performance of the DC-AC converter control systems when it is properly trained.

Robust constrained tension control for high-precision roll-to-roll processes

Tension control is critical for maintaining good product quality in most roll-to-roll (R2R) production systems. Previous work has primarily focused on improving the disturbance rejection performance of tension controllers. Here, a robust linear parameter-varying model predictive control (LPV-MPC) scheme is designed to enhance the tension tracking performance of a pilot R2R system for deposition of materials used in flexible thin film applications. The performance of a tension controller may degrade due to disturbances associated with model uncertainties and the slowly-changing dynamics in R2R systems. We introduce a method that separately treats these two sources of disturbance. The controller utilizes an incremental model to eliminate the errors caused by the mismatch between the nominal model and the actual system. A tube-based MPC formulation combined with scheduled parameters adequately updates models and corrects for the time-varying dynamics. Constraints on the rated motor torque are incorporated in the MPC to maintain the controller reliability and avoid machine failures. We illustrate the operation of our control algorithm through simulation of an actual R2R system. The controller outperforms the benchmarks in terms of fast transient response and offset-free tension tracking. It also demonstrates immunity from variations due to parametric uncertainties.

A linear hybrid active disturbance rejection controller design to extenuate powerline bushfires in resonant grounded distribution power systems

This paper proposes a robust linear hybrid controller by combining the active disturbance rejection and proportional–integral controllers (ADRC+PI) for inverter-based arc suppression coils (ASCs) in resonant grounded distribution power systems (RGDPSs). Resonant grounding techniques are used in real power distribution networks for reducing the fault current in order to reduce the severity of powerline bushfires in the presence of single line-to-ground (SLG) faults. The severity of bushfire hazards due to these SLG faults depends on environmental conditions (e.g., wet or dry grounds) that define the behavior of the system. With respect to these conditions, the fault resistance will be lower for wet grounds for which the system model comprises one dominant pole while dry grounds force the system to have one dominant zero with two dominant poles. By considering the circumstances of such groundings, the behavior of power distribution systems changes when there are SLG faults. This paper investigates a detailed analysis in frequency- and time-domains to design a robust arc mitigator based on the hybrid ADRC+PI controller. Furthermore, the robustness of the proposed hybrid controller against the input disturbances is explored in terms of transient and steady-state stability analysis and the results are compared with the ADRC and PI controllers. In addition, the performance of the proposed hybrid ADRC+PI controller is justified by utilizing virtual- and real-time implementations in a digital signal processor (DSP) through MATLAB/SIMULINK platform on a 22 kV (line-to-line) RGDPS under distinctive grounding conditions.

Robust Integral Linear Quadratic Control for Improving PV System Based on Four Leg Interleaved Boost Converter

In this paper, a new robust integral linear quadratic controller (ILQC) is proposed for Four Leg interleaved boost converters (FLIBCs) uses in the photovoltaic systems. Compared to classical boost converters (CBC), IBCs are used in the high power and voltage application. Therefore, the IBC can convert a high-current low-voltage input to a low-current high-voltage output and presents higher efficiency, lower current ripple, and better reliability. In order to enhance the photovoltaic system robust performances as reliability and efficiency of the converter, the proposed robust ILQC is calculating with the consideration of equal current sharing. Results of the proposed technical are compared with those of a classical boost converter (CBC) and FLIBC based on PI control. Performances of FLIBC based on proposed ILQC are tested in several simulations using Sim Power Systems and S-Function of MATLAB/SIMULINK. It is observed that the ILQC based FLIBC is maximizes the conversion efficiency of photovoltaic systems, improving the response time, reduce the overshoot of the waveforms, and decrease the current ripple. Compared to classical PI control, the proposed robust ILQC can increase the efficiency of conversion under different irradiance levels.