Dynamic Gain Scheduling Research Articles

Robust consensus tracking of linear multiagent systems with input saturation and input‐additive uncertainties

SummaryThe problem of robust global consensus tracking of linear multiagent systems with input saturation and input‐additive uncertainties is investigated in this paper. By using the parametric Lyapunov equation approach and an existing dynamic gain scheduling technique, a new distributed nonlinear‐gain scheduling consensus‐trackining algorithm is developed to solve this problem. Under the assumption that each agent is asymptotically null controllable with bounded control, it is shown that the robust global consensus tracking can be achieved under the undirected graph provided that its generated graph contains a directed spanning tree. Compared with the existing algebraic Riccati equation approach, which requires the online solution of a parameterized algebraic Riccati equation, all the parameters in the proposed nonlinear algorithm are offline determined a priori. Finally, numerical examples are provided to validate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

Dynamic gain-scheduled control and extended linearisation: extensions, explicit formulae and stability

A controller designed for linearisations at various trim/operating points of a nonlinear system using linear approaches is not necessarily performing well or stable once scheduled with a state under dynamic conditions; the key idea of using this scheduled control law design is to retain states close to the current, usually dynamically varying, operating point. Dynamic gain scheduling (DGS) is a technique aimed to resolve this controller scheduling issue for rapidly changing dynamics and states. It entails scheduling the control law gains with a fast-varying state variable rather than with a slowly varying state. It has been successfully applied to the aircraft system models, allowing also for nested loops. The aim of this paper is to extend DGS to a more general setting allowing for more complex multi-input dynamics incorporating the more simple static scheduling within the same controller. Hence, given a linear design, suitable transformations are provided which allow fast scheduling of multi-variable controllers. Important parallels to the approach of extended linearisation are drawn. Theoretical results are shown, providing explicit formulae related to nonlinear dynamic inversion control. Several examples of varying nonlinear complexity are presented in order to emphasise the characteristics of the approach.

Gain Scheduled Control of Linear Systems Subject to Actuator Saturation With Application to Spacecraft Rendezvous

This brief is concerned with gain scheduled approaches to the stabilization of linear systems with actuator saturation. For linear systems that are polynomially unstable, using the parametric Lyapunov equation-based and Riccati equation-based design, we propose gain scheduling approaches to increase the design parameter online so as to increase the convergence rates of the closed-loop systems. To apply the proposed gain scheduling approaches, only a scalar differential equation whose right-hand side is a function of the state vector is required to be integrated online. The closed-loop system is proven to be exponentially stable provided some parameters in the scheduling law are properly chosen. The established gain scheduling approaches are also extended to exponentially unstable linear systems with actuator saturation. As applications of the proposed dynamic gain scheduling approaches, the controller design of spacecraft rendezvous systems is revisited. Numerical simulation with the nonlinear model of a spacecraft rendezvous system shows the effectiveness of the proposed gain scheduling approaches.

Mixed ${\cal H}_{2}/{\cal H}_{\infty}$ Observer-Based LPV Control of a Hydraulic Engine Cam Phasing Actuator

In this paper, a family of linear models previously obtained from a series of closed-loop system identification tests for a variable valve timing cam phaser system is used to design a dynamic gain-scheduling controller. Using engine speed and oil pressure as the scheduling parameters, the family of linear models was translated into a linear parameter varying (LPV) system. An observer-based gain-scheduling controller for the LPV system is then designed based on the linear matrix inequality technique. A discussion on weighting function selection for mixed H2/H∞ controller synthesis is presented, with an emphasis placed on examining various frequency responses of the system. Test bench results show the effectiveness of the proposed scheme.

Modeling and Identification for Lightweight High-Speed Machines with Loads Variation

The positioning performance of high-speed, high-accuracy light-weight motion control systems is usually restricted by the structure flexibility and model parameter-varying caused by load mass variation. It needs to develop novel motion control algorithm to eliminate the residual vibration in the end-effectors, as well as to be robust over the load mass variation. This paper addresses the first and crucial step of this problem, modeling and identification technique. The linear parameter-varying model of the system is constructed and analyzed. The parameters and affine function identification method based on nonlinear least-squares and principle component analysis technique is proposed. The validity of the proposed method is demonstrated through a lightweight machine experimental setup. It is general enough to be applicable to the dynamic behaviors analysis and gain-scheduling robust control design for industrial lightweight vibration suppression and motion control systems that possess flexible elements and variable loads.

Two-state dynamic gain scheduling control applied to an F16 aircraft model

The feasibility and benefits of applying a novel multi-variable dynamic gain scheduling (DGS) approach to a complex ‘industry-scale’ aircraft model are investigated; the latter model being a non-linear representation of the intrinsically unstable F16 aircraft incorporating detailed aerodynamic data. DGS is a novel control approach, which involves scheduling controller gains with one (or more) of the system states whilst accounting for the ‘hidden coupling terms’ ensuring a near-ideal response. It is effective for non-linear systems exhibiting rapid dynamic changes between operating points. Recently, this approach has been extended to a multi-variable and multi-input context. Hence, unlike previous DGS work on realistic aircraft models, relevant feedback gains are to be scheduled with all (i.e. two) state variables in order to demonstrate the ability of the approach to compensate for non-linearity during rapid manoeuvres and consequently achieving better flying qualities over a range of conditions than standard gain scheduling. Time history simulations are used to draw comparisons with the more traditional ‘static’ gain scheduling and input gain scheduling methods.

Robust global stabilization of linear systems with input saturation via gain scheduling

AbstractThe problem of robust global stabilization of linear systems subject to input saturation and input‐additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation‐based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing ℋ2‐type gain scheduling controller, which requires the online solution of a state‐dependent nonlinear optimization problem and a state‐dependent ℋ2 algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input‐additive uncertainties, the proposed controller also partially recovers Teel's ℋ∞‐type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The ℋ∞‐type scheduling approach achieves robustness not only with non‐input‐additive uncertainties but also requires the closed‐form solution to an ℋ∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the ℋ∞‐type scheduling approach in the absence of non‐input‐additive uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.

Dynamic gain scheduled control of a Hawk scale model

AbstractWhen designing flight control laws using linearisations of an aircraft model about different flight conditions, some form of scheduling of the resultant gains will often be required to implement the controller over wide operating regions. In practice, the controller gains are often scheduled against relatively slowly-varying system states such as altitude or velocity. However, it may also be desirable to schedule gains against rapidly-varying states such as angle-of-attack, thereby generating a cyclic dependence through hidden coupling terms. Previous published work at Bristol has developed a numerical method of accounting for this dependence when scheduling state feedback gains against coupled states. The resulting ‘dynamic gain schedule’ is shown to significantly improve the transient response of the aircraft model during rapid manoeuvring and to reduce the chances of control surface actuator position limit saturation. In this paper, the novel design process, using eigenstructure assignment, is applied to a mathematical second-order longitudinal aircraft model which represents an approximate BAe Hawk wind-tunnel model. The dynamic gain scheduled controller is shown to work extremely well in practice when applied to the closed-loop experimental rig. Despite the highly nonlinear characteristics of the model aerodynamics and tailplane actuation system, as well as unmodelled high turbulence levels, dynamic gain scheduling demonstrates stable closed loop control even in regions where the nonlinearities are such that conventional gain scheduling fails to produce a stable response.

Dynamic gain scheduled process control

Gain scheduled control techniques are widely used in the chemical and aerospace industries but suffer from the limitation to slowly changing scheduling variable ( ξ). A dynamic gain scheduling (DGS) algorithm is proposed to specifically address this constraint. The control synthesis is based on algebraic transformations of the composite nonlinear controller obtained using the input–output linearization (IOL) and internal model control (IMC) formalisms. The controller is reduced to linear form and implemented in a dynamic gain scheduling approach, scheduled in the two-dimensional ξ and ξ ̇ space. In this fashion, the time variation of the scheduling variable is explicitly accounted for. The algorithm is demonstrated on a simple isothermal continuous stirred tank reactor and a complex, highly nonlinear low-density polyethylene polymerization reactor. Simulation results for the polymerizer case study show that the DGS controller provides satisfactory control during polymer grade changes, outperforms IOL control for disturbance rejection, and is stable under noisy measurements. Performance under parametric uncertainty as well as uncertainty with respect to unmodeled dynamics is also evaluated. Structured singular value analysis for nonlinear and time-varying uncertainty facilitated the determination of theoretical stability of the DGS loop. Finally, extensions to multiple-input–multiple-output systems and systems with higher relative degrees are discussed.