Gain-scheduled Output Feedback Research Articles

Integrated torque-vectoring and anti-roll moment distribution strategies based on optimal control: influence of model complexity and road curvature preview

Although the vehicle dynamics effects of variable anti-roll moment distribution actuated through active suspension systems are widely discussed in the literature, their model-based control has only been recently analysed, given the highly nonlinear nature of the involved dynamics. Moreover, the available studies do not discuss the trade-off between internal model complexity and controller performance, nor analyse the opportunities offered by vehicle connectivity, which enables the prediction of the steering angle and reference yaw rate profiles ahead. To address the gap, this paper introduces and assesses three optimal controllers for an electric vehicle with active suspensions, multiple powertrains, and a brake-by-wire system. The formulations are: (a) a gain scheduled output feedback linear quadratic regulator (OFLQR); (b) a nonlinear model predictive controller using a three-degree-of-freedom prediction model, without and with preview of the steering angle and reference yaw rate ahead, respectively referred to as NMPC-3 and NMPC-3-Pre; and (c) a nonlinear model predictive controller based on an eight-degree-of-freedom prediction model, referred to as NMPC-8 and NMPC-8-Pre depending on the absence or presence of preview. The results on an experimentally validated model show that: (i) NMPC-8 provides evident yaw rate tracking benefits with respect to (w.r.t) OFLQR and NMPC-3; and (ii) NMPC-8-Pre can bring ∼20% yaw rate tracking improvement w.r.t. an optimally tuned NMPC-8 configuration.

Robust gain-scheduled output feedback H2 controller synthesis with reduced conservativeness: An application to EMS system

This article investigates the design problem of gain-scheduled output feedback (GSOF) [Formula: see text] controller exploiting uncertain scheduling parameters for continuous-time linear parameter-varying (LPV) systems. The problem of coexistence of absolute and proportional uncertainties on the scheduling parameters is considered to address more practical situations. This challenging issue has been tackled by introducing a novel admissible region for the actual and measured scheduling parameters. Furthermore, all the system matrices of the LPV system are assumed to be polynomially dependent on the scheduling parameters with arbitrary degrees. Both Lyapunov and auxiliary matrices are considered to be parameter-dependent. The merit of the proposed method lies in its less conservativeness in comparison with the available approaches. The design method is presented in terms of solutions to a set of parameter-dependent linear matrix inequalities (LMIs) including parameter searches for two scalar values. The application of the provided method on an electromagnetic suspension (EMS) system is considered to demonstrate the applicability and benefits of the proposed approach for practical systems.

Observer-Based Control of LPV Systems with Input Delay and Saturation and Matched Disturbances via a Generalized Sector Condition

This paper examines the control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints and matched input disturbances. A gain-scheduled dynamic output feedback controller, coupled with a disturbance observer to cancel out input disturbance effects, was augmented with an anti-windup compensator to locally stabilize the input-delay LPV system under saturation, model uncertainty, and exogenous disturbances. Sufficient delay-dependent conditions to asymptotically stabilize the closed-loop system were derived using Lyapunov-Krasovskii functionals and a modified generalized sector condition to address the input saturation nonlinearity. The level of disturbance rejection was characterized via the closed-loop inducedL2-norm of the closed-loop system in the form of linear matrix inequality (LMI) constraints. The results are examined in the context of the mean arterial pressure (MAP) control in the clinical resuscitation of critical hypotensive patients. The MAP variation response to the injection of vasopressor drugs was modeled as an LPV system with a varying input delay and was susceptible to model uncertainty and input/output disturbances. A Bayesian filtering method known as the cubature Kalman filter (CKF) was used to estimate the instantaneous values of the parameters. The varying delay was estimated via a multiple-model approach. The proposed input-delay LPV control was validated in closed-loop simulations to demonstrate its merits and capabilities in the presence of drug administration constraints.

Robust H2 output-feedback bumpless transfer control of polytopic uncertain LPV systems

The problem of Robust Switching Gain-Scheduled Output-Feedback (RSGSOF) H2 controller synthesis with control bumps limitation is tackled in this paper for polytopic uncertain continuous-time linear parameter varying (LPV) systems. The presented robust switching gain-scheduled control design scheme overcomes the limitation of existing methods based on single quadratic Lyapunov function. However, in practice, RSGSOF controller leads to expressive discontinuities at switching instants. Hence, we aim to investigate of H2 output-feedback Bumpless Transfer Controller (BTC) design problem. In this study, not only stability and an upper bound on the H2-norm performance of the closed-loop system can be guaranteed but also solvability conditions are incorporated in the synthesis procedure to reduce control bumps. The proposed BTC composes multiple LPV controllers with the bumps limitation objective and a Lyapunov-based min-switching rule governing the switching among these controllers. Numerical studies demonstrate the effectiveness of the proposed approach.

Causal Gain-scheduled output feedback controllers using parameter-dependent Lyapunov Functions

This paper addresses the design problem of Gain-Scheduled Output Feedback (GSOF) controllers, in which causality with respect to (w.r.t) scheduling parameters in the GSOF controllers is kept, for continuous-/discrete-time Linear Parameter-Varying (LPV) systems using Parameter-Dependent Lyapunov Functions (PDLFs). In general, continuous-time GSOF controllers designed by conventional methods, i.e. so-called change-of-variables using PDLFs, depend on the derivatives of scheduling parameters, and discrete-time GSOF controllers designed by conventional methods or extended Linear Matrix Inequality (LMI) technique using parameter-dependent auxiliary matrices both depend on the one-step-ahead scheduling parameters. These mean that the designed GSOF controllers are not implementable to practical systems due to the non-causality w.r.t. scheduling parameters. On this issue, we propose a formulation which circumvents the causality problem by replacing the term that introduces the causality issue with another term via the reverse use of the Elimination lemma which is also known as “S-variable” approach. A toy example and a practical example (lateral-directional motion control around wing level flight of JAXA’s research airplane MuPAL-α) are included to demonstrate the effectiveness compared to the existing methods.

Dual formulation of causal gain-scheduled output feedback controller design using parameter-dependent Lyapunov functions

This paper is concerned with the design problem of causal gain-scheduled output feedback controllers for linear parameter-varying systems using parameter-dependent Lyapunov functions. This research topic has already been addressed by several researchers, and several effective methods have been correspondingly proposed in terms of parametrically dependent matrix inequalities. This paper addresses the dual formulation of one of the methods, and successfully derives the counterpart result in continuous-time case but points out the intractability of deriving the counterpart result in discrete-time case. It is also shown, in discrete-time case, that the intractability disappears and a design method similar to an existing method is successfully derived if the causality with respect to scheduling parameters is abandoned, namely, if one-step ahead scheduling parameters are available. A toy example is introduced to confirm that, in continuous-time case, the derived dual formulation gives the same performance as the previously proposed method for the dual state-space representation of the example.

Gain-scheduled control for morphing aircraft via switching polytopic linear parameter-varying systems

This paper addresses the gain-scheduled output feedback control for morphing aircraft (MA) in full envelope using switching polytopic linear parameter-varying (SPLPV) theory. The SPLPV model of MA is derived by scheduled parameter interval division and convex decomposition. Considering average dwell time (ADT) and mode-dependent average dwell time (MDADT) switching logics, sufficient conditions to ensure that the SPLPV systems are exponential stable with weighted disturbance attenuation indexes are presented based on the multiple parameter-dependent Lyapunov functions (MPDLFs) technique, and the comprehensive algorithm for the controller solution is obtained. To reduce the computational burden and ease controller implementation, a finite number of linear matrix inequalities (LMIs) are developed for solving controller by proposing the intermediate controller variables are depend affinely on the scheduled parameter. In addition, the control matrix of linear parameter-varying (LPV) system is not limited to be constant, which greatly expands the application scope of the proposed method. The simulation validation is carried out on the SPLPV control for MA.

Gain Scheduling Output Feedback Control for Vehicle Path Tracking Considering Input Saturation

This paper presents a gain scheduling output feedback control method to reduce driver workload and improve driving performance by considering input saturation. The driver–vehicle system model is developed by considering tire cornering stiffness uncertainties and different driver parameter uncertainties. Meanwhile, the input saturation is also considered in the driver-vehicle system. A quadratic Lyapunov function is designed to solve the optimization problem with uncertainties and input saturation. The results, which are based on the MATLAB-CarSim co-simulation platform, indicate that the robust controller not only improves the convergence rate of the state but also reduces the steering workload of the driver.

One-shot design of performance scaling matrices and observer-based gain-scheduled controllers depending on inexact scheduling parameters

This paper addresses the design problem of continuous-/discrete-time observer-based Gain-Scheduled Output Feedback (GSOF) controllers for Linear Parameter-Varying (LPV) systems, in which some of the state-space matrices are multi-affine with respect to parameters, with the simultaneous design of scaling matrices for multiple uncertainty blocks under the supposition that inexact scheduling parameters are available. In the design of GSOF controllers for practical systems in induced L2∕l2-norm control framework, the following features are to be incorporated; i) structured and easily-understandable controllers are preferable to enhance the practicality, ii) the scaling matrices related to multiple uncertainty blocks which represent various design specifications are also to be designed to reduce conservatism, and iii) one-shot design is preferable to prevent numerical problems in iterative algorithm. However, in general, neither the design problems of the structured controllers nor the simultaneous design of controllers and the performance scaling matrices are formulated in terms of Linear Matrix Inequalities (LMIs). Under the supposition that the uncertainties in the provided scheduling parameters are bounded (this supposition holds true for proportional uncertainties and for absolute uncertainties as well as for the mixed ones of them), we derive a new tractable one-shot multi-affine condition for our problem via dilated/extended LMI technique under some mild assumptions for LPV systems. A numerical example well illustrates the effectiveness of our method.

Gain-Scheduled Flight Controller Using Bounded Inexact Scheduling Parameters

This brief designs gain-scheduled output-feedback (GSOF) model-matching controllers for the lateral-directional motions of an airplane. In our design, equivalent airspeed is used as the scheduling parameter, but its values are affected by measurement errors due to the location of the airplane's Pitot tube (so-called “position error”) and the finite resolution of the measurement system. Furthermore, the generalized plant for our problem has structured exogenous inputs and performance outputs to represent model-matching performance as well as actuator modeling errors. In order to accommodate these two different kinds of uncertainties, we propose a design method for GSOF controllers in which inexact but bounded scheduling parameters are supposed to be provided. We design two GSOF flight controllers: one using our proposed method, and the other using a conventional design method incorporating constant scaling matrices without consideration of the uncertainties in provided scheduling parameters. We demonstrate the effectiveness of our method by comparing the control performance of these two GSOF controllers in a posteriori analysis and in flight tests.

Robust Gain-Scheduled Flight Controller via A New Formulation for Over-Bounding Scheduling Parameter Errors

Abstract This note addresses Gain-Scheduled (GS) flight controller design for the lateral-directional motions of an In-Flight Simulator (IFS) in a certain speed range. The design requirements for the GS flight controller are twofold: Model-matching and gust alleviation under some plant uncertainties as well as bounded errors in the provided scheduling parameters. We design a GS Output Feedback (GSOF) controller which meets the afore-mentioned design requirements via a new formulation for over-bounding the errors between actual scheduling parameters and inexactly provided ones. Control performance comparison between our new controller and the controller designed with an existing method in literature confirms that the former has less conservatism than the latter in synthesis as well as a posteriori analysis.

Robust gain-scheduled output feedback yaw stability control for in-wheel-motor-driven electric vehicles with external yaw-moment

This paper presents a robust gain-scheduled output feedback yaw stability H∞ controller design to improve vehicle yaw stability and handling performance for in-wheel-motor-driven electric vehicles. The main control objective is to track the desired yaw references by managing the external yaw moment. Since vehicle lateral states are difficult to obtain, the state feedback controller normally requires vehicle full-state feedback is a critical challenge for vehicle lateral dynamics control. To deal with the challenge, the robust gain-scheduled output feedback controller design only uses measurements from standard sensors in modern cars as feedback signals. Meanwhile, parameter uncertainties in vehicle lateral dynamics such as tire cornering stiffness and vehicle inertial parameters are considered and handled via the norm-bounded uncertainty, and linear parameter-varying polytope vehicle model with finite vertices is established through reducing conservative. The resulting robust gain-scheduled output feedback yaw stability controller is finally designed, and solved in term of a set of linear matrix inequalities. Simulations for single lane and double lane change maneuvers are implemented to verify the effectiveness of developed approach with a high-fidelity, CarSim®, full-vehicle model. It is confirmed from the results that the proposed controller can effectively preserve vehicle yaw stability and lateral handling performance.

Explicit hidden coupling terms handling in gain-scheduling control design via eigenstructure assignment

This paper presents a novel method for the design of gain-scheduled output feedback controllers in the presence of hidden coupling terms, which naturally arise when endogenous signals are used as scheduling parameters. In this case, the controller gains vary with respect to system variables, leading to inner loops between the system and the linearized gain-scheduled controller dynamics. Such effects, also known as parasitic feedbacks, are inherently difficult to handle in classic gain-scheduling control design and are often omitted, which might result in performance degradations or even destabilization of the closed-loop system. This paper shows how such a pitfall can be avoided through the application of self-scheduling and eigenstructure assignment techniques. In this context, the main contribution of the present work is the extension of eigenstructure assignment-based self-scheduling techniques for explicit hidden coupling terms handling. The viability of the proposed method is illustrated through a pitch-axis missile autopilot benchmark problem.

Output feedback control of linear fractional transformation systems subject to actuator saturation

ABSTRACTIn this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.

Gain scheduling output feedback control of linear plants with actuator saturation

From a gain-scheduling perspective, we will study the output feedback control problem for linear systems with some of control channels subject to actuator saturation. This includes the scenario of all actuator saturation as a special case. A feedback controller, expressed in the form of linear fractional transformation, is proposed to guarantee regional stability of the closed-loop system and provide disturbance/error attenuation measured in L2 gain. The resulting synthesis condition is formulated as linear matrix inequalities (LMIs) and can be solved efficiently. Moreover, explicit formulas are derived to calculate controller gains, which reduces the computational cost compared to the method of directly solving the LMI-based condition. Numerical examples are provided to demonstrate the proposed saturation control approach.

Gain Scheduling Output Feedback Control of Linear Plants with Partial Actuator Saturation

From a gain-scheduling control perspective, we will study the output feedback control problem for linear systems with some of control channels subject to actuator saturation. This includes the scenario of all actuator saturation as a special case. A feedback controller, expressed in the form of linear fractional transformation, is proposed to guarantee regional stability of the closed-loop system and minimizes disturbance/error effect measured in ***L2 gain. The resulting synthesis condition is formulated as linear matrix inequalities (LMIs) and can be solved efficiently. A modified inverted pendulum is utilized to demonstrate the proposed approach.

不確かなスケジューリングパラメータの使用を前提とした離散時間Gain-scheduled出力フィードバック制御器設計と飛行制御則設計例

不確かなスケジューリングパラメータの使用を前提とした離散時間Gain-scheduled出力フィードバック制御器設計と飛行制御則設計例

Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques.

Gain-scheduled output-feedback controllers using inexact scheduling parameters for continuous-time LPV systems

This paper addresses the design problem of Gain-Scheduled Output-Feedback (GSOF) controllers for continuous-time Linear Parameter-Varying (LPV) systems. In contrast to the conventional problem setting, scheduling parameters are supposed to be provided with bounded absolute/proportional uncertainties. H∞-type problem is tackled and a sufficient condition for our problem is given in terms of Parameter-Dependent Linear Matrix Inequalities (PDLMIs) with a single line search parameter. It is also proved that, our method is no more conservative than an existing method in proportional uncertainty case.

Gain-scheduled output-feedback controllers depending solely on scheduling parameters via parameter-dependent Lyapunov functions

In this paper, we propose a new design method for Gain-Scheduled Output Feedback (GSOF) controllers for continuous-time Linear Parameter-Varying (LPV) systems via Parameter-Dependent Lyapunov Functions (PDLFs). The GSOF controllers depend solely on scheduling parameters. Although our method requires a line search to obtain suboptimal controllers, it produces practical GSOF controllers, being independent of the derivatives of scheduling parameters. Our method is proved to be no more conservative than conventional design methods via constant Lyapunov functions as well as particularly structured PDLFs.