Control Synthesis Techniques Research Articles

A game theoretic approach to controller design for hybrid systems

We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and discrete control and disturbance parameters. We translate safety specifications into restrictions on the system's reachable sets of states. Then, using analysis based on optimal control and game theory for automata and continuous dynamical systems, we derive Hamilton-Jacobi equations whose solutions describe the boundaries of reachable sets. These equations are the heart of our general controller synthesis technique for hybrid systems, in which we calculate feedback control laws for the continuous and discrete variables, which guarantee that the hybrid system remains in the safe subset of the reachable set. We discuss issues related to computing solutions to Hamilton-Jacobi equations. Throughout, we demonstrate out techniques on examples of hybrid automata modeling aircraft conflict resolution, autopilot flight mode switching, and vehicle collision avoidance.

Robust variance control for systems with finite-signal-to-noise uncertainty

This paper develops control analysis and synthesis techniques for systems with finite signal-to-noise-ratios (called the finite-signal-to-noise (FSN) models). The system is characterized by an easily computed measure φ. The control synthesis finds output feedback control laws to tolerate finite signal-to-noise ratio uncertainty on an interval. An algorithm to conduct this synthesis is proposed, to achieve locally optimal performance for the closed-loop system.

Moore Automata for the Supervisory Control of Robotic Manufacturing Workcells

The potential of flexible-manufacturing workcells (FMCs) to produce a family of parts in many possible orders of operations and choices of different machines is advantageous. Despite intensive research on the theoretical control of discrete-event systems (DESs), however, current techniques can still only be used for the supervisory control of simple cells. In this paper, a novel modeling and control synthesis technique is presented for FMCs that allow part-routing flexibility. Our proposed methodology combines Extended Moore Automata (EMA) and Controlled-Automata theories to synthesize supervisors for such FMCs.

Automata-based modeling and control synthesis for manufacturing workcells with part-routing flexibility

The utilization of flexible manufacturing workcells (FMCs) to produce families of parts in many possible orders of operations and choices of different machines is advantageous. The modeling and control of such discrete-event systems (DESs) have generally been performed in a hierarchical structure. Despite intensive research on the theoretical control of DESs, however, current techniques such as controlled automata can still primarily be used for the supervisory control of simple cells. In the paper, a modeling and control synthesis technique is presented for FMCs that allow part-routing flexibility. The proposed methodology combines extended Moore automata (EMA) and controlled-automata theories to synthesize supervisors for such FMCs. EMA-based supervisors have the capability to read (receive) multiple pieces of information regarding the behavior of the FMC. Based on this information they can explicitly generate control commands issued to cell devices. In order to significantly reduce the state-space of EMA-based supervisors without affecting the behavior enforced on the (controlled) FMC, a minimization procedure is also outlined.

Synthesis of Discrete-Event Controllers Based on the SignalEnvironment

In this paper, we present the integration of controller synthesis techniques in the environment through the description of a tool dedicated to the incremental construction of reactive controllers. The plant is specified in Signal and the control synthesis is performed on a logical abstraction of this program, named polynomial dynamical system (PDS) over \{-1,0,+1\}. The control of the plant is performed by restricting the controllable input values with respect to the control objectives. These restrictions are obtained by incorporating new algebraic equations into the initial system. This theory sets the basis for the verification and the controller synthesis tool, Signal. Moreover, we present a tool developed around the Signal environment allowing the visualization of the synthesized controller by an interactive simulation of the controlled system. In a first stage, the user specifies in Signal both the physical model and the control objectives to be ensured. A second stage is performed by the Signal compiler which translates the initial Signal program into a PDS, and the control objectives in terms of polynomial relations/operations. The controller is then synthesized using Signal. The result is a controller coded by a polynomial and then by a Ternary Decision Diagram (TDD). Finally, in a third stage, the obtained controller and some simulation processes are automatically included in the initial Signal program. It is then sufficient for the user to compile the resulting Signal program which generates executable code ready for simulation. Different academic examples are used to illustrate the application of the tool.

Selection and care of pumps

This paper describes a technique for synthesizing controllers for hybrid plants. Our modeling framework allows for the efficient online construction of limited lookahead discrete abstractions of the nonlinear continuous dynamics of the plant model. Discrete event supervisory controller synthesis techniques are used to construct a controller based on a DES specification and the abstracted plant model. The controller is advanced in a moving horizon approach. The modeling framework, synthesis techniques and the on-line computational strategy are discussed. A simple illustrative example is presented in detail and a realistic industrial application is outlined. Copyright © 2006 IFAC

Experiences of using formal methods for chemical process control specification

This paper discusses the benefits of adding formal specification in B to existing controller synthesis techniques, and some of the limitations of B for this area of application. Examples from case studies carried out in the “Object-oriented specification of real-time and reactive systems” (ROOS) project are given.

Controller synthesis technique for systems with affine linear uncertainty

The paper deals with the design of compensators that provide a guaranteed level of performance, in the sense of gain and phase margins, for systems with affine linear uncertainty. To achieve this goal, powerful procedures for computing the Bode, Nyquist and Nichols envelopes of a transfer function, whose numerator and denominator polynomials are polytopic polynomials, are first developed by using the convex parpolygonal value set of polynomials with affine linear uncertainty. Using these frequency envelopes, a controller design strategy is then presented with two illustrative examples.

Uncertainty Modeling for Multivariable-Control Robustness Analysis of Elastic High-Speed Vehicles

High-speed (supersonic or hypersonic ) atmospheric e ight vehicles are typically characterized by a signie cant degree of interaction between the highly elastic airframe and the propulsion system. To achieve adequate stability and performance requirements, robust, integrated multivariable control laws will be required. But to apply robust-control analysis or synthesis techniques such as structured-singular-value techniques (π) or quantitative feedbacktheory,theuncertaintyintheplantdynamicsmustbecharacterized inspecialways.Furthermore,certain assumptions regarding the uncertainties present are frequently made in the application of these techniques. The focus of this research is the development of uncertainty models for this class of e ight vehicle that are derived from the physics of the system, yet are compatible with the cited control synthesis techniques. The potential sources of uncertainty for this class of vehicle are discussed, and three forms of uncertainty models are developed: real parameter,unstructured,and structured. Weareespecially interestedinhowtheusualsourcesofuncertaintymanifest themselves in this context. It will be shown that for this class of vehicle care is required in making the usual assumptions regarding the uncertainty. It is also shown that the e exible degrees of freedom must be considered in the e ight-control synthesis for this class of vehicle.

Experiences of Using Formal Methods for Chemical Process Control Specification

This paper discusses the benefits of adding fonnal specification in B to existing controller synthesis techniques, and some of the limitations of B for this area of application. Examples from case studies carried out in the “Object-oriented specification of Real-time and Reactive Systems” (ROOS) project are given

Parametric robust H2control design with generalized multipliers via LMI synthesis

A new combined analysis and synthesis procedure that provides a less conservative robust control design technique for systems with real parametric uncertainty is presented. The robust stability for these systems is analysed by the passivity theorem with generalized multipliers, and the worst case H2 performance is investigated using an upper bound on the total output energy. The dynamics of the multipliers are systematically chosen using knowledge from the linear part of the uncertain systems. This approach provides additional degrees of freedom in the synthesis that lead to a reduction of the conservatism in the worst-case H2 per formance and achieved robustness bounds. However, the formulation of the control design problem is very complicated and it is difficult to solve directly. This paper presents an iterative algorithm, which in an H2 equivalent of the D-K iteration for the u/Km synthesis, to account for the complicated couplings in the synthesis problem. We use a simple beam system with an uncertain modal frequency to illustrate that this synthesis technique with generalized multipliers results in less conservative controllers than previously published Popov controller synthesis techniques. In the process, we demonstrate that this design approach is very effective and simple to implement numerically.

Comparative Study of H ∞ Robust Control Methods in Missile Autopilot Design

Several controller synthesis techniques in the H methodology in an application to missile autopilot designs are investigated. The designs investigate performance and robustness characteristics of the controllers in the range Mach 1.6-2.6 covering the sustained phase of a missile with non minimum phase characteristics. The first synthesis concerns the use of a mixed-sensitivity approach at different flight conditions. Adaptation of the performance and robustness filters leads to a single satisfactory controller for the entire range. The second and third approaches focus on pole-zero cancellation problem and also improve the design objectives. Further approaches are concerned with third and four terms in the optimization in order to account for uncertainty in the controller and-or to account specifically for output measurements uncertainties.

Model matching controller design for disturbance rejection

A new model matching controller design technique is presented to facilitate direct specification of the disturbance response of a closed-loop system. The desired disturbance response characteristics are implicated through an appropriately chosen reference model. This approach substantially reduces the trial-and-error iterations necessary to meet the design requirements. A simple reference model specification procedure allows arbitrary choice for the reference Transfer Function poles (to control response time) while guaranteeing the physical realizability of the controller and asymptotic rejection of various types of disturbances such as step, ramp, etc. The Frequency Domain Controller Synthesis Techniques produce low-order, practically implementable controllers. The power of the design approach is demonstrated by several illustrative examples. It is shown that ensuring good disturbance rejection characteristics is sufficient to guarantee satisfactory set-point response, and not vice versa.

Observer-Based Feedback Linearizing Control of an Electromagnetic Suspension

This paper develops a stabilizing observer-based feedback linearizing controller for a single-axis electromagnetic suspension. The controller uses only the measured output of the system, and is shown to be robust with respect to parameter uncertainty. The controller differs from other robust feedback linearizing controllers that have appeared in recent literature, because it is continuous, and non-adaptive. Lyapunov’s second method is used to prove stability and robustness of the controller. The controller has a simple structure and its gains are determined by solving two weakly coupled Riccati equations. Numerical simulations are performed to compare a linear feedback controller and the observer-based feedback linearizing controller. Results obtained demonstrate that the nonlinear controller yields superior performance when compared with the linear feedback controller. The controller synthesis technique developed in this paper is applicable to other fully feedback linearizable systems, not just electromagnetic suspensions.

Discrete-time, mixed-norm control synthesis applied to aircraft terrain following

A fixed-order, mixed-norm control synthesis technique for discrete-time linear systems is demonstrated. The method allows the control-system designer to combine the H2, /i, and //oo norms of dissimilar transfer functions into a single constrained optimization problem. Any number or combination of constraints can be added to the problem, and the method constrains the norms directly without reliance on upper bounds to the norms. The method is applied to a terrain-following problem involving a multi-input multi-output model of a fighter aircraft. An H2-l problem is formulated and solved to provide altitude and flight-path angle tracking in the presence of wind gusts and sensor noise. Finally, an H^ constraint on output complementary sensitivity is added to improve robust stability.

Analysis and synthesis of concurrent digital circuits using control-flow expressions

In this paper, we present a novel modeling style and control synthesis technique for system-level specifications that are better described as a set of concurrent descriptions, their synchronizations, and constraints. The proposed synthesis procedure considers the degrees of freedom introduced by the concurrent models and by the environment in order to satisfy the design constraints. Synthesis is divided into two phases. In the first phase, the original specification is translated into an algebraic system, for which complex control-flow constraints and quantifiers of the design are introduced. In the second phase, we translate the algebraic formulation into a finite-state representation, and we derive an optimal control-unit implementation for each individual concurrent part. In the implementation of the controllers from the finite-state representation, we use flexible objective functions, which allow designers to better control the goals of the synthesis tool, and thus incorporate as much as possible their knowledge about the environment and the design.

Application of H∞ Control and Lqg with Frequency-Dependent Weight Syntheses to a Multivariable Active Flutter Suppression System

This paper describes the effectiveness of three robust control synthesis techniques applied to a multivariable active flutter suppression system using numerical simulations. These techniques are the mixed-sensitivity reduction in H∞ (H∞-mix), the normalized left coprime factorization robust stabilization in H∞ (H∞-normalized), and LQG with frequency-dependent weights (FWLQG), which are proposed in this paper. Although the plant is an unstable multi-input and multi-output system with large parameter variation, the FWLQG technique is superior to both H∞ synthesis techniques from the viewpoint of the increment of the flutter velocity, the time response and the solubility of control problems.

On the supremal controllable sublanguage in the discrete-event model of nondeterministic hybrid control systems

This paper is concerned with the logical control of hybrid control systems (HCS). It is assumed that a discrete-event system (DES) plant model has already been extracted from the continuous-time plant. The problem of hybrid control system design can then be solved by applying logical DES controller synthesis techniques to the extracted DES plant. Traditional DES synthesis methods, however, are not always applicable since the extracted plant DES will often exhibit nondeterministic transitions. This paper presents an extension of certain DES controller synthesis techniques to the nondeterministic control automaton found in HCS. In particular, this paper derives a formula computing the supremal controllable sublanguage of a given specification language under the assumption that the DES plant exhibits nondeterministic transitions.

Theory and Weighting Strategies of Mixed Sensitivity H∞ Synthesis on a Class of Aerospace Applications

This paper presents a vital design concept commonly used in the robust H∞ control synthesis technique – theMixed Sensitivity H∞ optimization. The underlying theory is also explained in a straightforwardfashion. Several real world aerospace design problems are solved via this particular problem formulation. This simple approach provides control engineer a clean first cut of many complicated aerospace control design issues, e.g., stability, performance and robustness against frequency domain bounded unstructured uncertainty, etc. Only with this first cut result in hand, one can then move on tomore advanced synthesis technique such as Km-Synthesis to imprese the system parametric robustness, if necessary.

Multivariable Active Flutter Suppression Tems using H∞ Control and LQG with Frequency Dependent Weight Syntheses

This paper describes the effectiveness of three robust control synthesis techniques applied to a multivariable active flutter suppression system using numerical simulations. These techniques are the mixed-sensitivity reduction in H∞(H∞-mix), the normalized left coprirne factorization robust stabilization in H∞ (H∞-normalized), and LQG with frequency-dependent weights (FWLQG), which is proposed in this paper. Although the plant is an unstable multi-input and multi-output system with large parameter variation, the FWLQG technique is superior to both H∞ synthesis techniques from viewpoints of the increment of the flutter velocity, the time response and the solubility of control problems.