Linear State Feedback Control Law Research Articles

Coordinated management of oxygen excess ratio and cathode pressure for PEMFC based on synthesis variable-gain robust predictive control

In this research endeavor, a novel synthesis variable-gain robust model predictive control (SVGRPC) method using the min-max technique with parameter dependent Lyapunov functions is introduced to achieve the desired trajectory tracking of oxygen excess ratio (OER) and cathode pressure in the polymer electrolyte membrane fuel cells (PEMFCs) system. Initially, a simplified control-oriented model of the air supply system is developed and then transformed into a polytopic form to accommodate the inherent uncertainties in the PEMFC. Subsequently, the polytopic model is integrated with the reference trajectory to construct an augmented state-space model for deriving an error state representation. In the framework of robust model predictive control (RPC) utilizing a parameter-dependent Lyapunov function, a series of variable feedback gains are employed to mitigate conservatism. Additionally, the online solution process imposes a significant computational burden, presenting challenges for the real-time implementation of RPC-based control strategy. Therefore, the offline computing is introduced to significantly reduce the computational burden, resulting in the development of the SVGRPC strategy proposed in this paper. Subsequently, the SVGRPC strategy computes explicit linear state-feedback control laws by solving linear matrix inequalities (LMIs) using an offline control algorithm. The effectiveness of the proposed controller is then validated through assessments conducted under three distinct operating conditions of the PEMFC system. The outcomes of this study affirm that the proposed controller improves the requirements of control performance when compared to the online RPC with a quadratic Lyapunov function while significantly alleviating the computational workload.

Optimization of the model predictive control meta-parameters through reinforcement learning

Model predictive control (MPC) is increasingly being considered for control of fast systems and embedded applications. However, MPC has some significant challenges for such systems, such as its high computational complexity. Further, the MPC parameters must be tuned, which is largely a trial-and-error process that affects the control performance, the robustness, and the computational complexity of the controller to a high degree. This paper presents a multivariate optimization method based on reinforcement learning (RL) that automatically tunes the control algorithm’s parameters from data to achieve optimal closed-loop performance. The main contribution of our method is the inclusion of state-dependent optimization of the meta-parameters of MPC, i.e. parameters that are non-differentiable wrt. the MPC solution. Our control algorithm is based on an event-triggered MPC, where we learn when the MPC should be re-computed, and a dual-mode MPC and linear state feedback control law applied in between MPC computations. We formulate a novel mixture-distribution RL policy determining the meta-parameters of our control algorithm and show that with joint optimization we achieve improvements that do not present themselves with univariate optimization of the same parameters. We demonstrate our framework on the inverted pendulum control task, reducing the total computation time of the control system by 36% while also improving the control performance by 18.4%.

Autonomous Landing of an UAV Using H∞ Based Model Predictive Control

Possibly the most critical phase of an Unmanned Air Vehicle (UAV) flight is landing. To reduce the risk due to pilot error, autonomous landing systems can be used. Environmental disturbances such as wind shear can jeopardize safe landing, therefore a well-adjusted and robust control system is required to maintain the performance requirements during landing. The paper proposes a loop-shaping-based Model Predictive Control (MPC) approach for autonomous UAV landings. Instead of conventional MPC plant model augmentation, the input and output weights are designed in the frequency domain to meet the transient and steady-state performance requirements. Then, the H∞ loop shaping design procedure is used to synthesize the state-feedback controller for the shaped plant. This linear state-feedback control law is then used to solve an inverse optimization problem to design the cost function matrices for MPC. The designed MPC inherits the small-signal characteristics of the H∞ controller when constraints are inactive (i.e., perturbation around equilibrium points that keep the system within saturation limits). The H∞ loop shaping synthesis results in an observer plus state feedback structure. This state estimator initializes the MPC problem at each time step. The control law is successfully evaluated in a non-linear simulation environment under moderate and severe wind downburst. It rejects unmeasured disturbances, has good transient performance, provides an excellent stability margin, and enforces input constraints.

Asynchronous Guaranteed Cost Control of 2-D Markov Jump Roesser Systems.

This article is concerned with the problem of guaranteed cost control for 2-D Markov jump Roesser systems with mismatched modes. The hidden Markov model is introduced to describe the asynchronous phenomenon caused by mismatched modes, and an asynchronous linear state-feedback control law is designed based on this model. With the help of the 2-D Lyapunov function and linear matrix inequality (LMI) techniques, sufficient conditions are established to ensure the asymptotic stability of the concerned system with a bound of the predefined guaranteed cost under three different boundary conditions, respectively. Finally, an algorithm that concludes the design processes of the optimal asynchronous guaranteed cost control law is proposed, and a numerical example is provided to verify its effectiveness.

Robust Precision Position Tracking of Planar Motors Using Min-Max Model Predictive Control

In this article, a min-max model predictive control (MPC) method of planar motors is proposed for the first time to achieve robust precision position tracking, which has a low computational burden and strong capability to deal with the problems of stability, robustness, optimization, and input constraints. A state-space model with a homogeneous state equation is built to describe the dynamics of the time-varying reference trajectory. Combining the state-space model of the reference trajectory and that of the planar motor, an augmented state-space model is established to obtain an error state formulation. Then, using the error state formulation, a min-max optimal control problem subject to the constraints on bounded uncertainty, stability, and control input is developed. Moreover, applying the theory of asymptotically stable invariant ellipsoids and employing the nested invariant ellipsoids, the explicitly linear state-feedback control laws are obtained using a linear-matrix-inequalities based offline control algorithm. Finally, the min-max MPC is applied to a planar motor system developed in the laboratory for an experimentally comparative study. The results demonstrate the effectiveness of the proposed min-max MPC of planar motor for robust precision position tracking applications.

On interval observer design for active Fault Tolerant Control of Linear Parameter-Varying systems

This paper proposes an active Fault Tolerant Control (FTC) scheme for polytopic uncertain Linear Parameter-Varying (LPV) systems subject to uncertainties and actuator faults. First, a fault estimation interval observer is designed to estimate the system state and the actuator fault. A novel approach is developed using the L ∞ norm to attenuate the effects of the uncertainties and to improve the accuracy of the proposed observer. Then, based on the fault estimation information, the FTC strategy is designed using a linear state feedback control law and H ∞ technique to compensate actuator faults and maintain system performance and stability, even under faulty conditions. Finally, the effectiveness of the proposed method is demonstrated by its application to a vehicle lateral dynamic nonlinear model. • Fault Tolerant Control using interval state estimation and robust stabilization. • Set-membership framework for the design of Linear Parameter Varying systems. • Fault estimation observer design for descriptor system. • L ∞ norm-based design method to attenuate the effect of fault and uncertainties and to improve the estimation performance.

Distributed Differential Games for Control of Multi-Agent Systems

Motivated by the challenges arising in the field of multi-agent system (MAS) control, we consider linear heterogeneous MAS subject to local communication and investigate the problem of designing distributed controllers for such systems. We provide a game theoretic framework for systematically designing distributed controllers, taking into account individual objectives of the agents and their possibly incomplete knowledge of the MAS. Linear state-feedback control laws are obtained via the introduction of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributed differential game</i> , namely, the combination of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local non-cooperative differential games</i> , which are solved in a decentralized fashion. Conditions for stability of the MAS are provided for the special cases of acyclic and strongly connected communication graph topologies. These results are then exploited to provide stability conditions for general graph topologies. The proposed framework is demonstrated on a tracking synchronization problem associated with the design of a distributed secondary voltage controller for microgrids and on a numerical example.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

Abstract This paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

Analytical guidance for circular orbit transfers with staging of space propulsion systems

This paper considers the combination of an analytical reference trajectory with linear state feedback control to allow for autonomous guidance and control of a spacecraft for coplanar circle-to-circle transfers with a stage-based propulsion system. Staging of electric propulsion components, such as tanks and thrusters, could allow small spacecraft to achieve high-ΔV capabilities with current propulsion technology. In order to utilize these propulsion systems, further developments in guidance and control of such spacecraft are required due to limitations in computational power and communications. Analytical approximations for low-thrust trajectories could allow for computationally simple guidance and control of autonomous spacecraft for circle-to-circle transfers around large central bodies. Many trajectories have been developed for conventional propulsion systems, based either on their shape or input thrust, and applied for preliminary mission design. A previously developed analytical trajectory is extended to account for the effects of staging propulsion system components. In order to stabilize the trajectory in the presence of disturbances, a linear state feedback control law is designed with linear quadratic regulator methods. Finally, a methodology for determining the correct phasing between the spacecraft and a target object is developed and is practical to implement on power-limited computers. The use of the analytical reference trajectory is simulated on an orbit transfer from low-Earth orbit to geostationary orbit.

Implementation of Linear Controllers via Active Disturbance Rejection Control Structure

Linear active disturbance rejection control (LADRC) takes the controlled plant as a cascaded integral model and treats all other plant information and external disturbances as a generalized disturbance, and uses an linear extended state observer (ESO) to estimate the generalized disturbance and incorporates it in a linear state feedback control law to reject it quickly. This ESO-based LADRC controller is a fixed-structure controller as long as the (relative) order of the controlled system is specified. This article shows that any linear finite-dimensional controller can be implemented via the LADRC structure; thus, it is a general-purposed control structure in that it can be applied to any control system where linear control is sufficient. Case study shows that the implementation not only retains the disturbance rejection performance of the original linear controller but also improves its tracking performance due to the two-freedom-of-degree property of LADRC.

Semi-global containment control of discrete-time linear systems with actuator position and rate saturation

In this paper, we study semi-global containment control problem for a multi-agent system in the presence of multiple leader agents. We describe the dynamics of each follower agent in multi-agent system by a general discrete-time linear system subject to both actuator position and rate saturation. By using low gain approach, we construct both a linear state feedback control law and an observer-based output feedback control law for each follower agent. Under some standard assumptions, we provide a sufficient condition to guarantee that the states of follower agents converge to the convex hull formed by the leader agents asymptotically. Finally, we illustrate the theoretical results by numerical simulation results.

Analytical solution to motion planning and modal-based tracking control for dynamic positioning of subsea equipment

One of the challenges of the installation of subsea equipment is the precise positioning of the equipment in a desired location on the seabed. This positioning procedure is still commonly performed manually by an operator. This article presents a trajectory tracking control system design for the positioning of a subsea equipment. This work will be done in two stages. First, a motion planning for dynamic positioning system of platform is presented. For this, an analytical solution of motion equation of the riser, which is modeled as a damped cable, is detailed. This analytical solution when compared to numerical solutions has the advantage of generating more precise and smooth trajectories for the system input and output. Second, we propose a tracking control system to ensure that the subsea equipment follows the desired trajectory in the presence of disturbances. More precisely, a linear state-feedback control law is proposed using a reduced model, which is obtained from a modal reduction with delay insertion. This delay insertion provides a high precision low order model. This fact highly increase the robustness of the control system to the measurement noise. Numerical simulations and experimental tests are presented to evaluated the proposed control strategy.

Optimal Periodic-Gain Fractional Delayed State Feedback Control for Linear Fractional Periodic Time-Delayed Systems

This paper develops the fundamentals of optimal-tuning periodic-gain fractional delayed state feedback control for a class of linear fractional-order periodic time-delayed systems. Although there exist techniques for the state feedback control of linear periodic time-delayed systems by discretization of the monodromy operator, there is no systematic method to design state feedback control for linear fractional periodic time-delayed (FPTD) systems. This paper is devoted to defining and approximating the monodromy operator for a steady-state solution of FPTD systems. It is shown that the monodromy operator cannot be achieved in a closed form for FPTD systems, and hence, the short-memory principle along with the fractional Chebyshev collocation method is used to approximate the monodromy operator. The proposed method guarantees a near-optimal solution for FPTD systems with fractional orders close to unity. The proposed technique is illustrated in examples, specifically in finding optimal linear periodic-gain fractional delayed state feedback control laws for the fractional damped Mathieu equation and a double inverted pendulum subjected to a periodic retarded follower force with fractional dampers, in which it is demonstrated that the use of time-periodic control gains in the fractional feedback control generally leads to a faster response.

Disturbance Observer-Based Integral Sliding Mode Control for Singularly Perturbed Systems With Mismatched Disturbances

This paper presents a disturbance observer-based integral sliding mode control (ISMC) for singularly perturbed systems (SPSs) with mismatched disturbances. First, a linear state feedback control law for the slow subsystem of the SPS is designed, and the fast subsystem is established. Second, a disturbance observer and an ISMC incorporating the disturbance estimate are constructed. The gain of ISMC is obtained by applying the ${H_\infty }$ control theory, and the resulting ISMC can effectively attenuate the mismatched disturbances. Finally, the proposed method is applied to an electric system, which illustrates the effectiveness and feasibility. The proposed design methods are based on the reduced-order subsystems and thus free of the high dimensionality and possible numerical ill-conditioned problems.

Proportional Retarded Controller to Stabilize Underactuated Systems with Measurement Delays: Furuta Pendulum Case Study

The design and tuning of a simple feedback strategy with delay to stabilize a class of underactuated mechanical systems with dead time are presented. A linear time-invariant (LTI) model with time delay of fourth order and a Proportional Retarded (PR) controller are considered. The PR controller is shown as an appealing alternative to the application of observer-based controllers. This paper gives a step forward to obtain a better understanding of the effect of output delays and related phenomena in mechatronic systems, making it possible to design resilient control laws under the presence of uncertain time delays in measurements and obtain an acceptable performance without using a derivative action. The Furuta pendulum is a standard two-degrees-of-freedom benchmark example from the class of underactuated mechanical systems. The configuration under study includes an inherent output delay due to wireless communication used to transmit measurements of the pendulum’s angular position. Our approach offers a constructive design and a procedure based on a combination of root loci and Mikhailov methods for the analysis of stability. Experiments over a laboratory platform are reported and a comparison with a standard linear state feedback control law shows the advantages of the proposed scheme.

Global robust output regulation of multivariable systems with nonlinear exosystem

Summary It is well known that multi-input, multi-output nature of nonlinear system and generalized exosystem have posed some challenges to output regulation theory. Recently, the global robust output regulation problem for a class of multivariable nonlinear system subject to a linear neutrally stable exosystem has been studied. It has been shown that a linear internal model-based state feedback control law can lead to the solution of previous problem. In this paper, we will further study the global robust output regulation problem of the system subject to a nonlinear exosystem. By utilizing nonlinear internal model design and decomposing the multi-input control problem into several single-input control problems, we will solve the problem by recursive control law design. The theoretical result is applied to the non-harmonic load torque disturbance rejection problem of a surface-mounted permanent magnet synchronous motor. Copyright © 2016 John Wiley & Sons, Ltd.

State Feedback Linearization of a Non-linear Permanent Magnet Synchronous Motor Drive

Control system design for inverter fed drives previously used the classical transfer function approach for single-input singleoutput (SISO) systems. Proportional plus Integral (PI) controllers were designed for individual control loops.It is found that the transient response of a PI controller is slow and is improved by pole placement through state feedback. However, the effective gains of the PI controller are substantially decreased as a function of the increase of motor speed. A control system is generally characterized by the hierarchy of the control loops, where the outer loop controls the inner loops. The inner loops are designed to execute progressively faster. The speed controller (PI controller) processes the speed error and generates the reference torque. In the inner loop, firstly a non-linear controller is designed for the system by which the system nonlinearity is canceled using state or exact feedback linearization. In addition, a linear state feedback control law based on pole placement technique including the integral of output error (IOE) is used in order to achieve zero steady state error with respect to reference current specification, while at the same time improving the dynamic response.The proposed scheme has been validated through extensive simulation using MATLAB.

Dynamic IQC-Based Control of Uncertain LFT Systems With Time-Varying State Delay.

This paper presents a new exact-memory delay control scheme for a class of uncertain systems with time-varying state delay under the integral quadratic constraint (IQC) framework. The uncertain system is described as a linear fractional transformation model including a state-delayed linear time-invariant (LTI) system and time-varying structured uncertainties. The proposed exact-memory delay controller consists of a linear state-feedback control law and an additional term that captures the delay behavior of the plant. We first explore the delay stability and the L2 -gain performance using dynamic IQCs incorporated with quadratic Lyapunov functions. Then, the design of exact-memory controllers that guarantee desired L2 -gain performance is examined. The resulting delay control synthesis conditions are formulated in terms of linear matrix inequalities, which are convex on all design variables including the scaling matrices associated with the IQC multipliers. The IQC-based exact-memory control scheme provides a novel approach for delay control designs via convex optimization, and advances existing control methods in two important ways: 1) better controlled performance and 2) simplified design procedure with less computational cost. The effectiveness and advantages of the proposed approach have been demonstrated through numerical studies.

Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks

In this paper, stabilization control of fractional-order bidirectional associative memory neural networks is formulated and studied. By estimating Mittag-Leffler function and some novel analysis techniques of fractional calculation, a generalized Gronwall-like inequality of Caputo fractional derivative is established. Then by applying Lyapunov approach, linear state feedback control law and partial state feedback control law are presented to stabilize the fractional-order bidirectional associative memory neural networks. This analysis framework can be applied to closed-loop control of fractional-order systems. A numerical example is given to show the effectiveness of the derived results via computer simulations.

Optimal control for rail vehicle pantograph systems with actuator delays

This study exploits an optimal control approach for solving the general robust control problem of active pantograph suspension systems with actuator delays and time-varying contact force such that both the stabilisation and optimal performance are achieved. On the basis of Bellman's optimality principle and Razumikhin theorem, the general robust control design problem can be equivalently transformed into an optimal control problem with the amount of matched uncertainties involved in the performance index. A stability criterion has been developed under which the time varying stiffness of contact force and time-delayed actuation force can not only achieve stability, but also acquire the guaranteed level of performance for regulation. A suitable linear state feedback control law is characterised via Lyapunov stability theory to ensure quadratic stability and performance robustness of the closed-loop systems. The effectiveness of the proposed design is demonstrated through simulation studies.