Robust Gain-scheduled Controller Research Articles

Robust Gain-scheduling Control of Dynamic Lateral Obstacle Avoidance for Connected and Automated Vehicles

Robust Gain-scheduling Control of Dynamic Lateral Obstacle Avoidance for Connected and Automated Vehicles

Robust Gain-Scheduling Path Following Control of Autonomous Vehicles Considering Stochastic Network-Induced Delay

This paper concerns the robust gain-scheduling control issue for autonomous path following systems with stochastic network-induced delay. Firstly, to effectively approximate the highly nonlinear tire dynamics, the linear fractional transformation formulations are employed to describe the tire cornering stiffness with a norm-bounded uncertainty. Secondly, by taking the data dropout and delay encountered in signal computation and transmission into account, a more generalized lumped delay form is proposed to unify the time-varying data dropout and network-induced delay. Moreover, a Markovian process is presented to describe the lumped delay as a stochastic distribution. Thirdly, to address the issue of varying vehicle velocity, a linear parameter varying model is established to capture vehicle lateral behaviors. Based on the stochastic stability theory, a new robust gain-scheduling path following control method is proposed for the autonomous vehicles. Finally, the experimental study is presented to bridge the gap between the theoretical and practical investigations on path following control of autonomous vehicles, and results validate the superior performance of the proposed method compared with existing works.

Adaptive saturated tracking control for solid launch vehicles in ascending based on differential inclusion stabilization

The large-range uncertainties of specific impulse, mass flow per second, aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles (SLVs) ascending leads to the deviation of the actual trajectory from the reference one. One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer (ESO) and then modify the control commands. However, ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large, which reduces the guidance accuracy. This paper introduces differential inclusion (DI) and designs a controller to solve the large-range parameter uncertainties problem. When above uncertainties have large ranges, it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set. If the DI system is stabilized, all the subsets are stabilized. Different from the traditional controllers, the parameters of the designed controller are calculated by the uncertain boundaries. Therefore, the controller can solve the problem of large-range parameter uncertainties of in ascending. Firstly, the ascent deviation system is obtained by linearization along the reference trajectory. The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation, which is called DI system. A DI adaptive saturation tracking controller (DIAST) is proposed to stabilize the DI system. Secondly, an improved barrier Lyapunov function (named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations. Compared with traditional barrier Lyapunov function, it can dynamically adjust the boundary of deviation convergence, which improve the convergence rate and accuracy of altitude, velocity and LTIA deviation. In addition, the correction amplitudes of angle of attack (AOA) and angle of sideslip (AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight. In this paper, a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate, which eliminates the adverse effects caused by the saturation. Finally, it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller. Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values. The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm. Compared with Robust Gain-Scheduling Control method, the robustness to the engine parameters are greatly improved and the control variable is smoother.

Observer-based robust gain-scheduled control for semi-active air suspension systems subject to uncertainties and external disturbance

In this paper, an observer-based robust gain-scheduled control scheme is designed for a semi-active air suspension (SAAS) system subject to uncertainties and external disturbance. Since the air spring in SAAS system is a highly nonlinear component and its stiffness relies on the spring interior pressure and displacement, an air spring model is constructed based on aerothermodynamics theory. Aiming at comprehensive and simplified expression of air spring nonlinear dynamics, the air spring model is expressed as linear-parameter-varying (LPV) form and further integrated into a quarter car semi-active air suspension model. To identify system states under the noisy condition with lower cost, a LPV-Kalman filter is proposed to estimate the states which are difficult to be measured or physically unmeasurable in the semi-active air suspension. With the proposed observer, a robust gain-scheduled controller is developed to overcome complex nonlinear dynamics, actuator uncertainties and external disturbance. To realize a better transient response, the control law is improved by constraining eigenvalues of the closed-loop system in desired linear matrix inequality (LMI) region. At last, simulations and experiments are conducted to illustrate the effectiveness of proposed control scheme in a quarter car test rig.

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

Aeroengine Robust Gain-Scheduling Control Based on Performance Degradation

This study was conducted to develop a novel tracking control strategy for aeroengines with strong nonlinearity and uncertainty. Compared to existing robust gain-scheduling control strategies, the proposed control strategy has relatively low conservatism and can markedly improve engine performance. An improved on-board adaptive aeroengine model was established to estimate engine performance degradation and eliminate the degradation term contained in the perturbation block of the engine uncertain model in the design process. Robust controllers under engine normal and performance degradation states were designed at a set of operating points and scheduled according to relevant scheduling and health parameters. A desired robust gain-scheduling controller, which works based on performance degradation, can be precisely constructed via this approach. Simulation results are given to demonstrate the effectiveness of the proposed method, where the response speed of engine is improved by 38%.

LPV Robust Controller Design with Regional Pole Assignment for an Aero-Engine

The aerodynamic characteristics of aero-engine, which have a wide range of flight envelopes, vary drastically, so its controller is required to be able to adapt to a large range of parameter variations and have good robustness. To solve the above problem, based on the regional pole assignment, a new aero-engine multi-variable robust gain scheduled LPV control algorithm was proposed. Firstly, the Jacobian linearization method was used to obtain polynomial LPV model of aero-engine, which can describe its dynamic performance under certain conditions. Further, aiming at the polynomial LPV model, a LPV output feedback controller with the closed-loop system pole placement in a given region, which satisfied robust H∞ performance requirement, is designed using the LMI method. Then the grid method is used to transform the Lyapunov functional which depend on the scheduling parameters into a single Lyapunov function, which can guarantee the system has good steady performance. Finally, simulation studies have carried out based on a certain turbofan engine. The simulation results show that the designed controller can realize the accurate tracking of control commands with response time less than 1.6 s, over shoot less than 1% and steady-state tracking error less than 0.1%. The control system can guarantee the global stability and has good robustness in the design envelope.

Parameter-Space Based Robust Gain-Scheduling Design of Automated Vehicle Lateral Control

This paper presents a robust gain-scheduling controller design based on the parameter-space approach. The gain-scheduling control is of interest for systems with varying dynamics at different operating conditions. Requirements of robustness of stability and performance are also necessary if the system is subject to other parametric or model uncertainties. The parameter space approach is capable of projecting these requirements to the space of design parameters and facilitate the design of robust gain-scheduling control. This method is applied to automated vehicle lateral control to ensure its tracking accuracy and stability subject to uncertainties in vehicle load, speed and tire saturation. The proportional feedback gain and look-ahead distance are scheduled with respect to speed while sustaining robust stability, mixed sensitivity bound constraint and satisfaction of performance indices. Realistic hardware-in-the-loop (HIL) simulation with a validated vehicle model and road tests are conducted to demonstrate the robust performance of the designed gain-scheduling control in the presence of model uncertainty and disturbances. Another general robust gain-scheduling approach, the linear-matrix-inequality- (LMI-) design is also conducted for benchmarking purposes and the comparisons are discussed.

LMI relaxations for robust gain‐scheduled control of uncertain linear parameter varying systems

This study deals with the problem of robust gain-scheduled dynamic output feedback control for uncertain discrete-time linear parameter varying systems. The obtained controller guarantees an upper bound on the induced $l_2$l 2 -gain performance of the closed-loop system. The system matrices are assumed to depend polynomially on both the scheduling and uncertain parameters which are supposed to belong to intervals with a priori known bounds. To formulate the design problem in a linear matrix inequality (LMI) setting, a required auxiliary matrix is initially determined using a necessary condition for finding a gain-scheduled controller by the proposed method. Then, a robust gain-scheduled controller is designed by LMI conditions combined with a scalar search using the obtained auxiliary matrix. The method is applied to an inverted pendulum on a cart to illustrate the benefits and applicability of the proposed method.

Interval methods for robust gain scheduling controllers

A novel interval-based approach for a gain-scheduled controller synthesis is presented in this paper which aims at stabilizing continuous-time dynamic systems of finite dimension in a guaranteed manner over predefined finitely long time horizons. The fundamental aim of the design is the temporal adaptation of the feedback gain in combination with a reduction of the interval widths which characterize outer enclosures of the states that are reachable in the worst case at a certain time instant while ensuring asymptotic stability of the closed-loop dynamics. For that purpose, feedback gains are computed first for an initial state enclosure. Second, they are tested for validity in such a way that the parameterization of the controller shall be applicable over the whole time discretization step. In case of the verification failing, the gain is modified after determining a bounding box for those states that can be reached over the considered prediction window. That means, an offline calculation of controller gains is possible so that prespecified performance indicators with respect to the closed-loop dynamics are guaranteed to be satisfied. The robust and/or optimal control problem is solved efficiently using linear matrix inequality (LMI) techniques, while methods from interval analysis are furthermore employed during the underlying reachability analysis. Additionally, efficient approaches are presented which reduce overestimation due to the unavoidable wrapping effect. Hence, the proposed design method aims, simultaneously, at the reduction of overestimation and a guaranteed stability verification. To conclude this paper, the resulting control strategy is verified numerically for an inverted pendulum as a prototypical benchmark application.

H∞Optimization-based robust decoupling control algorithm in linear parameter varying systems using Hadamard weighting

This article proposes a novel gain scheduled control technique for a class of linear parameter varying (LPV) systems with main emphasis on reducing the cross coupling interaction in dynamics using the Hadamard weight. By employing the Hadamard and the conventional [Formula: see text] performance weighting, an extended [Formula: see text] closed loop norm LPV theorem is derived that involves traditional [Formula: see text] weights for input output shaping control and Hadamard weight for decoupling control. Furthermore, a robust dynamic output feedback gain scheduled control law is designed to solve the control optimization problem in the proposed theorem using the linear matrix inequality (LMI) approach. It is shown that the proposed theorem is suitable for the multivariable control of multiple input multiple output (MIMO) coupled non-linear systems. In particular, in presence of cross coupled dynamics, external disturbances, changing operating conditions and time varying parameters. The effectiveness of the proposed technique is demonstrated in simulation as well as validated with experiments.

Design of robust gain scheduled controller using $L_2$ gain performance

Design of robust gain scheduled controller using $L_2$ gain performance

Static output-feedback robust gain-scheduling control with guaranteed [formula omitted] performance

This paper develops synthesis conditions for Static Output-Feedback (SOF) Gain-Scheduling (GS) control with guaranteed upper bound of H2 performance for continuous-time Linear Parameter Varying (LPV) systems, where measurements of scheduling parameters are affected by uncertainties or measurement noise. The control problem is solved through an iterative two-stage design procedure. In the first stage, parameter-dependent state-feedback controller is obtained to minimize upper-bound of the H2 performance. Then, this controller is used as input to the second stage to synthesize Robust Gain-Scheduling (RGS) static output-feedback gain with minimal H2 performance. In both stages, the synthesis conditions are given in terms of Parametrized Linear Matrix Inequalities (PLMIs). Robust SOF (parameter-independent) controller can be synthesized as special case of the developed synthesis conditions. Two examples have been presented to illustrate the benefit of the proposed approach. One is an academic numerical example from literature and the other one is a realistic LPV model of Electric Variable Valve Timing (EVVT) actuator for automotive engines that utilizes engine speed and vehicle battery voltage as time-varying scheduling parameters.

Robust Gain-scheduled Controller Design with a Hierarchical Structure

Abstract In the LFT framework, we propose an exact state-space solution for the problem of designing a robust gain-scheduled controller with a hierarchical structure and based on semi-definite programming. Under the hypothesis of adopting general dynamic multipliers for robustness and static D-scalings for gain-scheduling, our technique enriches the class of structured controller design problems that are tractable by convex optimization.

Trajectory tracking using robust gain-scheduling control with a new independent variable

To reduce the expenditure, a low-performance guidance and control system is usually employed in the design of guided artillery rockets, which however will induce great difficulties in trajectory tracking because the rocket's parameters vary fast over a large operation range. The traditional time invariant control approaches for trajectory tracking cannot guarantee the adaptability of controller. On the other hand, since time is routinely considered as the independent variable, the dynamic error system varies sharply, resulting in a weak anti-jamming capability. To address these issues, a new trajectory tracking approach for guided rockets is developed by using the robust gain-scheduling control technique based on the linear parameter varying system, in conjunction with a new coordinate transformation that considers the arc length of reference trajectory as the independent variable. Through comparative studies, it is observed that the proposed method outperforms the existing ones in trajectory tracking during the whole flight trajectory, which demonstrates its effectiveness and advantages.

Robust decentralized power system controller design: Integrated approach

Abstract A unique approach to the design of gain scheduled controller (GSC) is presented. The proposed design procedure is based on the Bellman-Lyapunov equation, guaranteed cost and robust stability conditions using the parameter dependent quadratic stability approach. The obtained feasible design procedures for robust GSC design are in the form of BMI with guaranteed convex stability conditions. The obtained design results and their properties are illustrated in the simultaneously design of controllers for simple model (6-order) turbogenerator. The results of the obtained design procedure are a PI automatic voltage regulator (AVR) for synchronous generator, a PI governor controller and a power system stabilizer for excitation system.

Robust gain-scheduled control of variable stiffness actuators

Abstract Variable stiffness actuators were introduced to decouple an otherwise stiff actuator from the load by an adjustable elasticity. This variable elastic element can be used as torque sensor, acts as an energy storage, decouples the actuator for exogenous high frequency excitation inputs and contributes towards shock resistance and safety in human-robot interaction scenarios. However, the variable element complicates the design of torque and impedance controllers which have to be synthesized by employing contradicting design objectives, such as minimisation of the output impedance, robust stability and performance. Moreover, the system to be controlled consists of an additional control-loop to set-up the stiffness of the elastic element in real-time. To overcome these synthesis problems, we present a new controller design procedure that imposes a positive-real constraint on the load output port function to guarantee a stable interaction with respect to a passive, yet otherwise unknown environments. Additional design requirements are subsequently cast into a generalised plant. Ultimately, a H∞ - nonsmooth design procedure is employed to design a torque controller under these constraints and is tested in in silico experiments with the Mechanical Rotational Impedance Actuator (MeRIA).

Reliable Robust Control for the System with Input Saturation Based on Gain Scheduling

In this paper, a reliable robust discrete gain scheduling controller is designed based on the linear matrix inequalities (LMIs) and gain scheduling technology for the systems with the input saturation, system uncertainty, external disturbance and actuator failures. By the designed discrete gain scheduling controller, we can use a series of nesting ellipsoid invariant sets to strengthen the disturbance attenuation ability as strong as possible. It means that the innermost invariant ellipsoid set needs to be minimized to strengthen the disturbance attenuation ability. The dynamic performance of the closed-loop system is improved by introducing a parameter. By the Lyapunov approach, the existing conditions for the admissible controller can be formulated in the form of LMIs. The numerical simulation illustrates the effectiveness of the proposed method.

Improved synthesis conditions for mixed gain-scheduling control subject to uncertain scheduling parameters

ABSTRACTThe vast majority of the existing work in gain-scheduling (GS) control literature assumes perfect knowledge of scheduling parameters. Generally, this assumption is not realistic since for practical control applications measurement noises are unavoidable. In this paper, novel synthesis conditions are derived to synthesise robust GS controllers with mixed performance subject to uncertain scheduling parameters. The conditions are formulated in terms of parameterised bilinear matrix inequalities (PBMIs) that depend on varying parameters inside multi-simplex domain. The conditions provide practical GS controllers independent of the derivatives of scheduling parameters. That is, the designed controllers are feasible for implementation. Since bilinear matrix inequality problems are intractable, an iterative PBMI algorithm is developed to solve the developed synthesis conditions. By the virtue of this algorithm, conservativeness reduction is achieved with few iterations. Examples are presented to illustrate the effectiveness of the developed conditions. Compared to other design methods from literature, the developed conditions achieve better performance.

Robust gain-scheduled control for unmanned aerial vehicles

The flight dynamics of a modern aircraft are highly nonlinear and vary over the wide flightenvelope of the aircraft. This fact makes it difficult for a single controller to achieve the desired closedloopspecifications. This paper considers gain-scheduling successive loop control design for linear parameter-varying system in terms of linear matrix inequalities. The obtained controller guarantees an efficientunmanned aerial vehicle’s control under external disturbances within the flight envelope. The designprocedure is illustrated by a case study of unmanned aerial vehicle lateral channel control