Gain-scheduled Controller Synthesis Research Articles

Gain-Scheduling Controller Synthesis for Nested Systems With Full Block Scalings

Gain-Scheduling Controller Synthesis for Nested Systems With Full Block Scalings

Synthesis of gain scheduling controllers for a class of nonlinear systems based on a spatial discretization procedure

A methodology for the synthesis of gain scheduling controllers, capable of stabilising a class of nonlinear systems, is proposed in this paper. The technique is based on the spatial discretization of the state-space, considering only a subset of the states, generating an approximate dynamics dependent on time-varying parameters. The relationship between the stability of both the original and approximation dynamics is shown through a convex condition, which is then used to develop the proposed synthesis methodology. The computed controllers assure the local stability within a known region and can be obtained by the resolution of a set of convex conditions. A series of numerical experiments illustrate the validity of the technique.

Distributed Control Design for Heterogeneous Interconnected Systems

This article presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular, the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the individual subsystems. To solve these decomposed synthesis conditions that are coupled only over neighboring subsystems, we propose a distributed method based on the alternating direction method of multipliers. It only requires nearest-neighbor communication and no central coordination is needed. Then, a new classification of systems is introduced that consists of groups of homogeneous subsystems with different interconnection types. This classification includes heterogeneous systems as the most general and homogeneous systems as the most specific case. Based on this classification, we show how the interconnected system model and the decomposed synthesis conditions can be formulated in a more compact way. The computational scalability of the presented methods with respect to a growing number of subsystems and interconnections is analyzed, and the results are demonstrated in numerical examples.

Synthesis of Memory Gain-Scheduled Controllers for Discrete-Time LPV Systems

This paper considers synthesis of discrete-time gain-scheduled controllers for linear parameter varying systems based on linear matrix inequalities (LMIs). Unlike most of the previous results, gain...

Gain-scheduled H∞ controller synthesis for actively steered longer and heavier commercial vehicles

This paper proposes a gain-scheduled controller synthesis for improving the lateral performance and stability of articulated heavy vehicles by active steering of the selected towed vehicle units. The longitudinal velocity is on-line measurable, and it is thus treated as a scheduling parameter in the gain-scheduled controller synthesis. The lateral performance of four articulated heavy vehicles, including existing Nordic heavy vehicles and prospective longer articulated heavy vehicles, are investigated with and without active steering and compared with a commonly used conventional tractor–semitrailer. The control problem is formulated as an [Formula: see text] static output feedback, which uses only information from articulation angles between the steered vehicle unit and the vehicle unit in front of it. The solution of the problem is obtained within the linear matrix inequality framework, while guaranteeing [Formula: see text] performance objectives. Effectiveness of the designed controller is verified through numerical simulations performed on high-fidelity vehicle models. The results confirm a significant reduction in yaw rate rearward amplification, lateral acceleration rearward amplification, and high-speed transient off-tracking, thereby improving the lateral stability and performance of all studied heavy vehicles at high speeds.

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.

Gain Scheduling Controller Synthesis for Control Moment Gyroscope Using Improved Approximation

This paper presents gain scheduling (GS) control of a variable speed control moment gyroscope (VSCMG) based on sum of squares (SOS). Nonlinear motion equations of the VSCMG are complicated because ...

On exploiting inexact scheduling parameters for gain-scheduled control of linear parameter-varying discrete-time systems

This paper is concerned with the problem of gain-scheduled controller design for parameter-varying discrete-time systems. In practice, the scheduling parameters are only available with limited accuracy due to the measurement errors. In the present paper, these uncertainties are systematically taken into account for the gain-scheduled controller synthesis to achieve improved performance in practical situations. It is assumed that all the matrices of the state-space model of the plant have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameters. The merit of the proposed method is its capability in dealing with the measurement error less conservatively than available approaches while it can also encompass the traditional methods employing the exact scheduling parameters in a less conservative manner. A comprehensive numerical example demonstrates the effectiveness of the proposed method.

Lossless [formula omitted]-synthesis for 2D systems (special issue JCW)

We study 2D systems with a continuous and discrete time axis. We embed known results about the stability and H∞-performance properties of such systems into multiplier theory from robust control. It is shown that this opens the way for applying recently developed gain-scheduled controller synthesis techniques in order to solve the H∞-design problem for 2D systems without any conservatism. This is presented if the discrete-time axis is either one- or two-sided, the latter leading to non-conservative H∞-synthesis result for infinite string interconnections of identical linear time-invariant systems.

Guaranteed Performance State-Feedback Gain-Scheduling Control With Uncertain Scheduling Parameters

State-feedback gain-scheduling controller synthesis with guaranteed performance is considered in this brief. Practical assumption has been considered in the sense that scheduling parameters are assumed to be uncertain. The contribution of this paper is the characterization of the control synthesis that parameterized linear matrix inequalities (PLMIs) to synthesize robust gain-scheduling controllers. Additive uncertainty model has been used to model measurement noise of the scheduling parameters. The resulting controllers not only ensure robustness against scheduling parameters uncertainties but also guarantee closed-loop performance in terms of H2 and H∞ performances as well. Numerical examples and simulations are presented to illustrate the effectiveness of the synthesized controller. Compared to other control design methods from literature, the synthesized controllers achieve less conservative results as measurement noise increases.

Smoothly Gain-Scheduled Control of a Tri-Turbofan Airship

Designing a controller for the full nonlinear model of an aircraft remains a challenging task. The main purpose of this work is to present a new linearization-based gain-scheduled controller synthesis technique that allows the systematic design of compact smoothly interpolated controllers that perform efficiently even for such a complex plant. Another appealing feature of the new approach is that design specifications can be easily translated into synthesis constraints, thus considerably facilitating the design task. The validity of the proposed synthesis technique is corroborated by a challenging case study in which the objective is to design a controller for the coupled six-degree-of-freedom nonlinear model of a low-altitude tri-turbofan airship subject to atmospheric disturbances.

A synthesis framework for robust gain-scheduling controllers

We present a general framework for the systematic synthesis of robust gain-scheduling controllers by convex optimization techniques and for uncertain dynamical systems described by standard linear fractional representations. We distinguish between linear time-varying parameters, which are assumed to be available online as scheduling parameters for the controller, and genuine uncertainties, not necessarily time-varying, parametric or linear, that are not available online. Under the rough hypothesis that the control channel is not affected by the unmeasurable uncertainties and that the properties of the uncertainties and scheduling variables are captured by suitable families of integral quadratic constraints, this paper reveals how controller synthesis can be turned into a genuine semi-definite program. The design framework is shown to encompass a rich class of concrete scenarios.

Gain-scheduled controller synthesis for a nonlinear PDE

Linear parameter-varying (LPV) modelling and control of a nonlinear partial differential equation (PDE) is considered in this article. The one-dimensional viscous Burgers' equation is discretised using a finite difference scheme; the boundary conditions are taken as control inputs and the velocities at two grid points are assumed to be measurable. A nonlinear high-order state space model is generated and proper orthogonal decomposition is used for model order reduction. After assessing the accuracy of the reduced model, a low-order functional observer is designed to estimate the reduced states which are linear combinations of the velocities at all grid points. A discrete-time quasi-LPV model that is affine in scheduling parameters is derived based on the reduced model. A polytopic LPV controller is synthesised based on a generalised plant containing the LPV model and the functional observer. More generally, the proposed method can be used to design an LPV controller for a quasi-LPV system with non-measurable scheduling parameters. Simulation results demonstrate the high tracking performance and disturbance and measurement noise rejection capabilities of the designed LPV controller compared with a linear quadratic Gaussian (LQG) controller based on a linearised model.

Gain Scheduled Control: Switched Polytopic System Approach

Gain Scheduled Control: Switched Polytopic System Approach

重力傾度安定方式を用いた人工衛星の構造系と制御系の同時最適設計

In general, small satellites must achieve relatively high performance in spite of their restricted resources. To contribute such developments of small satellites, in this paper, we propose a new method of attitude controller synthesis of small satellites. This method is developed by a strategic use of gain-scheduled controller synthesis from the viewpoint of simultaneous optimization of structural and control systems. It also includes some modification of the existing gain-scheduled controller synthesis to achieve fixed closed-loop property. A numerical example of a gravity-gradient stabilized satellite illustrates the effectiveness of the proposed method in a practical application.

Missile Autopilot Design: Gain-Scheduling and the Gap Metric

This paper presents a systematic methodology for the synthesis of global gain-scheduled controllers for nonlinear time-varying systems. A controller of this type is used to compute the pitch-axis autopilot of an air-air missile. The missile model used is considered a benchmark for testing autopilot controllers in the academic and industrial communities. The missile's dynamics are linearized at a small set of operating points for which proportional― integral/proportional-type controllers are designed, to shape the frequency response of the linear plants' dynamics. A new set of operating points is computed afterward using the connection between the gap metric and the H ∞ loop-shaping theory. Then, reduced-order, static, H ∞ loop-shaping controllers are designed for this set of points using linear matrix inequality optimization techniques. Finally, the global gain-scheduled controller is obtained by interpolating the proportional―integral/proportional and the loop-shaping controllers' gains over the missile's flight envelope. The simulation results given show the generality and effectiveness ofthe proposed control strategy in terms of the operating point selection, stability, performance and robustness, of the closed loop.

A synthesis of reduced-order gain scheduling controllers for active flutter suppression

This paper presents a synthesis of reduced-order gain scheduling (GS) controllers based on the balanced truncation (BT) method. A polytopic plant model is first reduced by the modified BT method in which the state transformation matrix is obtained by balancing the weighted average controllability and observability Gramians over the entire range of the varying parameter. Using the reduced-order polytopic models, GS controllers are then designed in the frame of a linear matrix inequality technique. The proposed synthesis is applied to the GS controller design for the active flutter suppression of a high-aspect-ratio aeroelastic wing. The effectiveness of the proposed technique is demonstrated by numerical simulation.

Gain-Scheduled Controller Synthesis Based on New LMIs for Dissipativity of Descriptor LPV Systems

This paper is concerned with synthesis of gain-scheduled controllers by representing LPV systems in the descriptor form. Based on a recent algebraic criterion characterizing dissipativity of descriptor systems, an improved synthesis method is proposed with removing limitations of descriptor representation in existing results. Specifications of exponential decay are also considered. A numerical example illustrates the procedure of the proposed synthesis method.

Pointing Control of Mobile Antenna on Vehicle

This paper describes a pointing control of a mobile antenna mounted on a vehicle. For precise pointing, the antenna must be controlled to point to a target under the influence of continuous disturbances acting on the vehicle. For this purpose, we propose an optimal controller design method in a framework of the H∞ gain-scheduled controller synthesis. By this synthesis, the optimal controller is obtained by using parameter varying notch-filter in order to attenuate the various frequency disturbances. We apply this design method to an automobile model having a rotating antenna.

Gain-scheduling Control of Rotary Inverted Pendulum by Weight Optimization and H.INF. Loop Shaping Procedure

Gain-scheduling control is one of effective methods for plants whose dynamics changes significantly according to its operating point. A frozen parameter method is known to be a practical gain-scheduling controller synthesis, which interpolates the controllers designed at the prespecified (frozen) operating points according to the current operation point. Hyde et al. proposed a gain-scheduling control that H∞ loop shaping procedure is adopted as a controller synthesis at each operating point. H∞ loop shaping procedure is based on loop shaping of an open loop characteristic by frequency weights and is known to be effective for plants with bad condition number. However, weight selection satisfying control specifications is hard job for a designer. This paper describes the design of a suboptimal weight and a controller by means of algorithm that maximizes the robust stability margin and shapes the open loop characteristic into the desired shape at each operating point. Moreover, we formulate a weight optimization problem as a generalized eigenvalue minimization problem, which reduces the designer's burden of weight selection. Finally, we realize robust and high performance control system by scheduling both weights and controllers. The effectiveness of the proposed control system is verified in terms of the achieved robust stability margin and experimental time responses of a rotary inverted pendulum which involves strong nonlinear dynamics.