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Abstract
A novel systematic technique for gain-scheduled control based on fixed-structure synthesis is adopted to design the aerial vehicle autopilot. The gain-scheduled design can be transformed into the multi-model control problem with both controller architecture and gain-scheduled architecture defined a priori. Hidden coupling terms naturally arise in the linearized dynamics of the gain-scheduled controller when some of the state variables are also used as scheduling variables. Unlike traditional approaches that do not consider these terms, the proposed method takes the hidden coupling terms directly into account in the synthesis phase. Finally, numerical simulations are carried out to evaluate the effectiveness of the proposed methods.
Since the dynamical system and control system of the missile are typically nonlinear, an effective acceleration tracking autopilot is designed using the dynamic surface control (DSC) technique in order to make the missile control system more robust despite the uncertainty of the dynamical parameters and the presence of disturbances. Firstly, the nonlinear mathematical model of the tail-controlled missile is decomposed into slow acceleration dynamics and fast pitch rate dynamics based on the naturally existing time scale separation. Secondly, the controller based on DSC is designed after obtaining the linear dynamics characteristics of the slow and fast subsystems. An extended state observer is used to detect the uncertainty of the system state variables and aerodynamic parameters to achieve the compensation of the control law. The closed-loop stability of the controller is derived and rigorously analyzed. Finally, the effectiveness and robustness of the design is verified by Monte Carlo simulation considering different initial conditions and parameter uptake. Simulation results illustrate that the missile autopilot based DSC controller achieves better performance and robustness than the other two well-known autopilots. The method proposed in this paper is applied to the design of a missile autopilot, and the results show that the acceleration tracking autopilot based on the DSC controller can ensure accurate tracking of the required commands and has better performance.
This paper presents new MATLAB-based tools for tuning fixed-structure linear control systems using the H-infinity methodology. Unlike traditional H-infinity synthesis, these tools can directly tune arbitrary control architectures consisting of one or more feedback loops and one or more fixed-order, fixed-structure control elements. This makes them ideally suited for deploying H-infinity techniques in real-world applications.
This paper describes an application of nonsmooth optimization to the tuning of fixed-structure gain-scheduled controllers. The gain schedule is tuned over the entire operating range subject to standard frequency-domain requirements at each design point. The result is a smooth, compact scheduling formula that can be either implemented directly or turned into a lookup table. The effectiveness of this approach is illustrated on a gain-scheduled three-loop autopilot for the pitch axis of an airframe. I. INTRODUCTION Gain scheduling is a well established practice in industry with many applications in automotive, aerospace, and indus-trial automation. It is commonly used to control nonlinear systems or linear systems whose dynamics change with time and/or operating condition. Typically, gain-scheduled controllers are fixed single-or multi-loop control structures where lookup tables specify gain values as a function of the scheduling variables. The conventional approach consists of dividing the system's operating range into regions where linear control is adequate, designing a linear controller for each region, and "interpolating" the resulting set of con-trollers in some reasonable way (gain interpolation or control signal blending). This ad-hoc strategy yields satisfactory results as long as the linearized dynamics vary slowly during operation [1]. Alternative approaches based on linear matrix inequalities (LMI) have been proposed in [2]–[6]. While they provide stability and performance guarantees, they come with various degrees of conservatism and also dictate the controller structure and complexity. See [7], [8] for a comprehensive survey of the state of the art.
We develop nonsmooth optimization techniques to solve \Hinf synthesis problems under additional structural constraints on the controller. Our approach avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems. The proposed framework is very versatile and can accommodate a number of challenging design problems including static, fixed-order, fixed-structure, decentralized control, design of PID controllers and simultaneous design and stabilization
problems. Our algorithmic strategy uses generalized gradients and bundling techniques suited for the \Hinf-norm and other nonsmooth performance criteria. Convergence to a critical point from an arbitrary starting point is proved (full version) and numerical tests are included to validate our methods.
The gain-scheduling approach is perhaps one of the most popular non-linear control design approaches which has been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide application of gainscheduling controllers and a diverse academic literature relating to gain-scheduling extending back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in interest in gain-scheduling in the literature with many new results obtained. An extended review of the gain-scheduling literature therefore seems both timely and appropriate. The scope of this paper includes the main theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition of non-linear design into linear sub-problems) control with the aim of providing both a critical overview and a useful entry point into the relevant literature.
This paper presents a gain-scheduled design for a missile longitudinal autopilot. The gain-scheduled design is novel in that it does not involve linearizations about trim conditions of the missile dynamics. Rather, the missile dynamics are brought to a quasilinear parameter varying (LPV) form via a state transformation. An LPV system is defined as a linear system whose dynamics depend on an exogenous variable whose values are unknown a priori but can be measured upon system operation. In this case, the variable is the angle of attack. This is actually an endogenous variable, hence the expression "quasi-LPV." Once in a quasi-LPV form, a robust controller using H synthesis is designed to achieve angle-of-attack control via fin deflections. The final design is an inner/outer- loop structure, with angle-of-attack control being the inner loop and normal acceleration control being the outer loop.
For a general type of nonlinear tracking problem, we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points. A necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented. Using this condition, the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed, and ad hoc approaches to scheduling can be analyzed.
The large inertia and long delay characteristics of main steam temperature control system in thermal power plants will reduce the system control performance. In order to improve the system control performance, a generalized predictive PID control for main steam temperature strategy based on improved particle swarm optimization algorithm is proposed. The performance index of incremental PID controller of main control loop and PD controller of auxiliary control loop based on generalized predictive control algorithm is established. An improved particle swarm optimization algorithm with better fitness and faster convergence speed is proposed for online parameters optimization of performance index. The optimal control value of PID controller and PD controller can be obtained. The simulation experiment compared with fuzzy PID and fuzzy neural network is carried out. Simulation results show that proposed control method has faster response speed, smaller overshoot and control error, better tracking performance, and reduces the lag effect of the control system.
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.
This paper presents a new procedure for the integrated plant and flight control system design in the presence of parametric uncertainties. The proposed approach is based on a design procedure consisting in casting gain-scheduling and robustness requirements into the framework of structured design. As both controller architecture and gain-scheduling structure are defined a priori, the scheduled gains can be tuned by the newly available MATLAB-based tool systune to minimize constraints related to performance requirements over both operating and uncertain domains. It is shown that this technique allows for optimization and adjustment of plant's physical parameters while satisfying closed-loop performance requirements. The proposed procedure is applied to the F-16 Fighting Falcon flight control system design under mass and center of gravity uncertainties by adjusting the location of an additional accelerometer to optimize the closed-loop performance while minimizing the horizontal tail area. Numerical studies are carried out to evaluate the effectiveness of the proposed approach.
The application of a recently developed methodology for gain scheduled control system synthesis to the design of a pitch channel missile autopilot is described. A control signal interpolation strategy is used to generate a family of linear autopilots from a collection of point designs. Conditions are given under which a nonlinear gain scheduled autopilot exists that linearizes to the family of linear autopilots and the interpolation scheme plays an important role in satisfying these conditions. Nonlinear simulation results indicate satisfactory performance over the specified flight envelope.
A new approach to gain-scheduling of linear controllers is proposed. Traditionally, gain scheduling is done a posteriori by interpolation of gains computed for several operating points within the parameter space. The method proposed here which is based on guardian maps does not require the design of linear controllers for several points. Rather, it attempts to extend the performance of an initial design obtained for a single arbitrary point to the whole linearized domain while ensuring generalized stability all along the process. The method is successfully applied on a missile autopilot benchmark problem. © 2008 by the American Institute of Aeronautics and Astronautics, Inc.
This paper presents a new application of structured H∞ synthesis to tune self-scheduled controllers. Newly available MATLAB-based tools allow to tune fixed-structure linear controllers while satisfying H∞ constraints. Moreover multi-model synthesis capabilities can extend their application to self-scheduled controllers. This technique is successfully applied to the attitude control of a launch vehicle in atmospheric ascent phase.
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(infinity) loop-shaping theory. Then, reduced-order, static, H(infinity) 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 of the proposed control strategy in terms of the operating point selection, stability, performance and robustness, of the closed loop.
Multiband frequency domain synthesis consists in the minimization of a finite family of closed-loop transfer functions on prescribed frequency intervals. This is an algorithmically difficult problem due to its inherent nonsmoothness and nonconvexity. We extend our previous work on nonsmooth H∞ synthesis to develop a nonsmooth optimization technique to compute local solutions to multiband synthesis problems. The proposed method is shown to perform well on illustrative examples.
Nonsmooth optimization is used to design feedback controllers subject to closed-loop performance specifications both in time and frequency-domains. In time domain the nonlinear plant is submitted to a set of test input signals and the closed-loop responses so generated are called scenarios. A design technique is proposed which computes a controller with a prescribed structure that satisfies performance specifications for a given set of scenarios in tandem with robustness constraints in the frequency-domain, and is locally optimal among other controllers with these properties.
This final technical report provides a summary and documentation of research accomplishments on methods to improve the performance of gain scheduled controller designs. The main topics involve use of information about scheduling signals, in addition to their current values, to improve performance, the establishment of an optimization framework for the analysis and design of gain scheduled systems, and the development of controller interpolation methods. A list of journal publications is included.
A new approach to gain scheduling linear dynamic controllers is
illustrated for a pitch-axis autopilot design problem. In this
application the linear controllers are designed at distinct operating
conditions by H ∞ methods. The gain scheduling
procedure uses particular features of both the linear dynamic
controllers and the controller configuration to remove so-called hidden
coupling terms that can occur in scheduled controllers. Potential
performance improvement is demonstrated by comparing simulation results
to those for a naive gain scheduled controller that ignores the coupling
terms
The gain scheduling approach to the control of nonlinear systems is explained, and its characteristics are examined. On the basis of this framework questions are raised, and implications are drawn for practical design situations. The relationship between the gain scheduling formulation and the extended-linearization approach for nonlinear control design is considered.< >
Gain scheduling has proven to be a successful design methodology
in many engineering applications. In the absence of a sound theoretical
analysis, these designs come with no guarantees of the robustness,
performance, or even nominal stability of the overall gain-scheduled
design. An analysis is presented for two types of nonlinear
gain-scheduled control systems: (1) scheduling on a reference
trajectory, and (2) scheduling on the plant output. Conditions which
guarantee stability, robustness, and performance properties of the
global gain schedule designs are given. These conditions confirm and
formalize popular notions regarding gain scheduled designs, such as that
the scheduling variable should vary slowly, and capture the plant's
nonlinearities
Dynamic Scheduling of Modern-Robust-Control
- R T Reichert