Control Of Linear Parameter-varying Systems Research Articles

Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems

Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

In control of aerospace systems with large operating envelopes, it is often necessary to adjust the desired dynamics according to operating conditions. This paper presents a robust adaptive control architecture for linear parameter-varying (LPV) systems that allows for the desired dynamics to be systematically scheduled, while being able to handle a broad class of uncertainties, both matched and unmatched, which can depend on both time and states. The proposed controller adopts an L1 adaptive control architecture for designing the adaptive control law and peak-to-peak gain (PPG) minimization for designing the robust control law to mitigate the effect of unmatched uncertainties. Leveraging the PPG bound of a LPV system, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system with respect to a nominal system. The proposed control architecture is applied to control the longitudinal motion of an F-16 aircraft operating within a large envelope. Simulation results using both LPV and fully nonlinear models validate the efficacy of the proposed method.

Design of a mixed ℋ2/ℋ∞ gain scheduling state derivative feedback controller for linear parameter-varying systems

In this paper, the mixed guaranteed cost for continuous-time linear parameter-varying (LPV) systems is proposed. In addition, the gain scheduling (GS) strategy and the state derivative feedback (SDF) were considered. The time-varying parameter is assumed to be available for online measurement, and the conditions are based on linear matrix inequalities (LMIs). To improve the behaviour of the system, the -stability is used. Examples show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and a mixed guaranteed cost minimisation.

Fault-Tolerant Control of Wind Turbine System Using Linear Parameter-Varying Model

This paper proposes a fault-tolerant control scheme for WTS with actuator faults and disturbance, based on a linear parameter-varying (LPV) model. First, a LPV model of WTS subject to disturbances and actuator fault is obtained. Using this model, unknown input observer (UIO) is developed to estimate the WTS fault and state variables. Then, an integral tracking controller for LPV systems is developed. Based on the Lyapunov and H ∞ theory, the convergence of UIO and the stability of the closed-loop system are analyzed and ensured. The proposed fault-tolerant controller is applied to a wind turbine system with pitch and torque actuator faults, and its performances are compared with those of controller without integral action.

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.

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.

Interval observer-based methodology for passive fault tolerant control of linear parameter-varying systems

The paper deals with passive fault tolerant control for linear parameter varying systems subject to component faults. Under the assumption that the faults magnitudes are considered unknown but bounded, a novel methodology is proposed using interval observer with an [Formula: see text] formalism to attenuate the effects of the uncertainties and to improve the accuracy of the proposed observer. The necessary and sufficient conditions of the control system stability are developed in terms of matrix inequalities constraints using Lyapunov stability theory. Based on a linear state feedback, a fault tolerant control strategy is designed to handle component faults effect as well as external disturbances and preserve the system closed-loop stability for both fault-free and component faulty cases. Two simulation examples are presented to demonstrate the effectiveness of the proposed method.

Design of an gain scheduling state derivative feedback controller for linear parameter-varying systems

ABSTRACT This paper is devoted to the guaranteed cost of continuous-time linear parameter-varying (LPV) systems, considering the gain scheduling (GS) strategy and the state derivative feedback (SDF). The main contribution of the paper is to derive linear matrix inequalities (LMIs) conditions for the -SDF problem for LPV systems, taking into account the GS controller. For the good behaviour of the controller, we assume that the time-varying parameters are available for online measurement. In some cases, the -GS-SDF controller obtained high control signals, and as we intend to apply the proposed method in practical situations, we introduce the concept of -stability in the problem approach. Examples and a practical implementation show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and guaranteed cost minimisation.

Interval observer-based finite-time control for linear parameter-varying systems

The paper is concerned with the finite-time control of linear parameter-varying systems by means of the interval observer method. An unknown input observer framework is utilized to construct the interval observer to avoid the cooperativity constraint in estimation error dynamics. The corresponding control scheme composed of upper-lower bounds of the controller is established to treat the time-varying parameter in control input channel. Sufficient conditions are formulated as LMIs to guarantee the finite-time boundedness of error systems. The effectiveness of the proposed strategy is evaluated by numerical simulations.

Robust gain-scheduled control of linear parameter-varying systems with uncertain scheduling parameters in the presence of the time-invariant uncertainties

Robust gain-scheduled control of linear parameter-varying systems with uncertain scheduling parameters in the presence of the time-invariant uncertainties

Adaptive control for linear parameter-varying systems with application to a VTOL aircraft

As a systematic method for gain-scheduling, the linear parameter-varying (LPV) system framework has been widely used for the design of aerospace control systems with large operating envelopes. This paper presents design and analysis of an adaptive control architecture for LPV systems subject to time-varying parametric uncertainties and external disturbances, with both transient and steady-state performance guarantees. We introduce new tools relying on parameter-dependent Lyapunov functions and linear matrix inequality techniques for stability and performance analysis. These tools – limited to linear systems – potentially yield less conservative results than the approach employed for this architecture in previous adaptive control literature based on the small-gain theorem. The transient and steady-state performance of the adaptive closed-loop system, in terms of input and output signals, is quantified with respect to a non-adaptive reference system that depends on the true values of the uncertainties and represents the best achievable performance. It is shown that the transient performance bounds can be made arbitrarily small in the case of zero initialization error for the state predictor and will include additional exponentially decaying terms in the presence of non-zero initialization error. The approach can be used to design an adaptive augmentation of a baseline LPV control system. A simulation example of the longitudinal dynamics of a conceptual Urban Air Mobility aircraft is used to illustrate the efficacy of the proposed framework.

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.

Dynamic Output Feedback H∞ Control for Linear Parameter-varying Systems with Time-delay

In this paper, we address a synthesis problem of the parameter-dependent output feedback H∞ control for linear parameter-varying systems with time-delay. The scheme adopts the parameter-dependent past state information to construct the dynamic output feedback controller. In this case, on basis of the quadratic Lyapunov functional with parameter-dependence, we analyze the parameter-dependent H∞ stability conditions for the closed-loop time-delayed linear parameter-varying system in terms of linear matrix inequalities. However, this stability condition is of an infinite-dimension. To derive computationally tractable criteria for the dynamic output feedback controller, several slack variables and a convex relaxation technique are employed to have the infinite-dimensional condition of linear matrix inequalities cast into a finite dimensional convex optimization problem. By solving the convex optimization problem, we harvest the dynamic output feedback controller with memory for the time-delayed linear parameter-varying system. Finally, two examples are included to illustrate the effectiveness of the proposed approach.

Control Design of Antenna Servo Systems with Velocity Tracking Using LMIs

This paper considers controller design of large antenna servo systems, which is given by a new integral-type servo controller with gain-scheduled control for linear parameter-varying systems, while expanding to type-2 control with velocity tracking. An example of application is provided to demonstrate the effectiveness of the proposed method.

H∞ Control Using Linear Parameter Varying Approach for Motion Control Systems Under Communication Delays: Application to PMSM

Over the past decades, various control methodologies have been studied to improve the performance of motion control systems. However, such methods have no general guidelines for controller gain tuning or performance optimization in the presence of nonlinearities and/or uncertainties. Linear parameter-varying (LPV) control methods have recently been studied to improve the performance of motion control systems by treating the nonlinearities as parameter variations. By contrast, with motion control systems, the plant, microprocessors, controllers, actuators, and sensors are interconnected using a communication network, where the network inherently induces communication delays while sending and receiving information. Hence, when designing an LPV control system, it is necessary to consider both communication delays and nonlinearities. In this study, we address an LPV-approach based H∞ control problem for motion control systems under communication delays between the actuator and plant, and between the sensor and plant. We obtained a linear matrix inequality (LMI) condition under which a closed-loop system using the proposed controller satisfies the H∞ control performance and stability when subjected to a communication delay. The main technique applied to obtain the corresponding LMI condition for an LPV system is interpolating the scheduling variables of the nonlinear parameter variations at each vertex. Finally, we applied the proposed control method to the driver set of a permanent magnet synchronous motor and verified the H∞ control performance under a communication delay.

Tube-based model predictive control for linear parameter-varying systems with bounded rate of parameter variation

This paper introduces a tube-based model predictive control (MPC) for linear parameter-varying (LPV) systems which exploits knowledge about bounds on the parameters’ rate of change to extrapolate its admissible values over the prediction horizon. This information is used to construct state tubes to which the future trajectories of the state are confined. The tubes are consequently used for constraint tightening. Then, an MPC optimization problem subject to tightened sets for the state and control constraints is solved for only a nominal system corresponding to a nominal trajectory of the scheduling parameter starting from its current value. Recursive feasibility and asymptotic stability are proven and two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Discrete-time H∞ control of linear parameter-varying systems

ABSTRACTWe introduce new conditions for the H∞ synthesis of discrete-time linear parameter-varying systems in the form of linear matrix inequalities. A distinctive feature of the proposed conditions is the ability to handle variation in both the dynamics and the input matrices without resorting to dynamic augmentation or iterative procedures. We show that this new condition contains the existing poly-quadratic H∞ synthesis result as a particular case. We also derive a corollary which shows improvement even in the stronger case of quadratic H∞ synthesis. Additionally, we show that, surprisingly, a dynamic gain-scheduled quadratic H∞ controller can result in inferior performance compared to a static robust controller. Numerical examples illustrate our results.

Set theoretic approach to fault-tolerant control of linear parameter-varying systems with sensor reintegration

ABSTRACTIn this paper, we present a fault-tolerant control scheme for linear parameter-varying systems that utilises multiple sensor switching to compensate for sensor faults. The closed-loop scheme consists of an estimator-based feedback tracking controller and sensor-estimate switching strategy which allows for the reintegration of previously faulty sensors. The switching mechanism tracks the transitions from faulty to healthy behaviour by means of set separation and pre-computed transition times. The sensor-estimate pairings are then reconfigured based on available healthy sensors. Under the proposed scheme, preservation of closed-loop system boundedness is guaranteed for a wide range of sensor fault situations. An example is presented to illustrate the performance of the fault-tolerant control strategy.

Finite‐time control for LPV systems with parameter‐varying time delays and exogenous disturbances

SummaryIn this paper, we consider the stability analysis and control synthesis of finite‐time boundedness problems for linear parameter‐varying (LPV) systems subject to parameter‐varying time delays and external disturbances. First, the concepts of uniform finite‐time stability and uniform finite‐time boundedness are introduced to LPV systems. Then, sufficient conditions, which guarantee LPV systems with parameter‐varying time delays finite‐time bounded, are presented by using parameter‐dependent Lyapunov–Krasovskii functionals and free‐weight matrix technologies. Moreover, on the basis of the results on the uniform finite‐time boundedness, the parameter‐dependent state feedback controllers are designed to finite‐time stabilize LPV systems. Both analysis and synthesis conditions are delay‐dependent, and they are formulated in terms of linear matrix inequalities by using efficient interior‐point algorithms. Finally, results obtained in simulation demonstrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.

IFT-LPV: Data-Based Tuning of Fixed Structure Controllers for LPV Systems

Fixed structure controllers are widely used, however the tuning thereof can be cumbersome and gives no guarantee of optimality, especially when the system is Linear Parameter-Varying (LPV). Iterative Feedback Tuning (IFT) is a technique for the optimisation of a parameterised controller based on closed-loop experiments. This paper extends the applicability of IFT to LPV systems for the case where the LPV scheduling parameters are measurable but cannot be controlled. The closed-loop LPV system matrices are factorised such that the effect of the scheduling parameter on the IFT gradient estimates can be compensated. A suffcient number of IFT experiments are performed to estimate the cost gradient and tune the parameters. The method is validated successfully via a simulation study for a special case with an LPV system.