In this chapter, the eigenstructure synthesis using state variable feedback has been analysed. It is shown that the solution scheme is simple and just involves solving a set of linear equations to synthesise each eigenvector for a specified eigenvalue. The modal characterisation elegantly maps the n*m arbitrary feed back gain parameters to the arbitrary selection of n-eigenvalues and n*(m 1) eigenvector elements (total of n*m parameters). Since the system dynamic response is fully characterised by its eigenstructure, the direct control of the eigenstructure as discussed in this chapter provides a useful basis for feedback control design. The special mode decoupling eigenvector structures assignable, as illustrated in Example 2.1, demonstrates the unique advantage of the direct eigenvector element selection formulation alluded to in Chapter 1.

The eigenstructure assignment using state variable feedback is analysed. It is interesting to examine the extent of eigenstructure assign ment that is possible if only output feedback is employed (number of outputs less than the number of states). At the outset, the pole placement problem with output feedback has received much attention by researchers over the years. In the state feedback case, all system poles can be arbitrarily assigned if the system is controllable. Unfortunately such a definitive statement in case of output feed back continues to be elusive.

In this chapter a unified approach to the design of observers has been detailed. The algorithm developed is applicable to all categories of observers studied in the literature. The key concept of eigenstructure assignment developed in Chapter 2 is used in the construction of the observer. The observer eigenvalues define the observer stability matrix F, and the eigenvectors define the trans formation matrix T. Defining the stability matrix in the modal canonical form facilitates formulation of a computationally simple observer design algorithm. Further this modal canonical observer structure also enjoys advantages in real time implementation since (i) the stability matrix F has a minimum parameter representation and (ii) only a bank of first-order (real eigenvalues) or second-order (complex conjugate eigenvalues) filters needs to be implemented. Existence conditions of the observer with arbitrary eigenvalues are derived using the Kronecker canonical structure properties of the resulting singular rectangular matrix pencils. The computationally stable SCF is used to extract these structural properties. However, construction of the SCF is only required to check the existence of the solution for a specified observer problem and is not needed for design optimisation of the observer.

In this chapter, the basic specifications for design of flight control systems have been outlined. It should be pointed out that historically, flight vehicle HQ guidelines evolved as a basis for the design of a new aircraft with desir able dynamic characteristics using only low authority stability augmentation systems. With the modern full authority high-gain fly-by-wire flight control systems, most of these specifications can easily be achieved. However, other design problems associated with such high-gain/high-bandwidth feedback systems, namely (i) stability margins, (ii) interaction of structural modes with rigid body dynamics and (iii) actuator rate saturation during large-amplitude manoeuvres in the presence of severe atmospheric turbulence, etc. take centre stage in the control law design process. Brief specifications/guidelines to meet these practical control system design requirements have also been outlined. The guidelines detailed in this chapter will be used for the design studies in Chapters 9-11. Additional useful flight control design practices have also been well documented in Reference 17.

In this chapter, the pitch axis controller design of an aircraft is studied. If the aircraft has only one control surface in the pitch axis, eigenstructure synthesis is not possible and the design reduces to a simple eigenvalue assignment problem. Since the aircraft dynamic performance is dictated by the short-period mode,the natural frequency and damping of the mode can be modified by feedback to improve the response characteristics. The Gibson's time and frequency domain criteria are usually satisfied by proper design of the command filter. If the aircraft is equipped with more than one control surface in the pitch axis, some control can be exercised in shaping the eigenvectors. Again since the main interest is in shaping the short-period mode response, the complex conjugate pair of eigenvectors associated with the short-period mode needs to be synthesised. In this chapter, it is shown that the multivariable pitch axis design can be conveniently formulated as a model following control problem since the design objectives can be easily translated into an appropriate dynamic model. Examples of both IMF and EMF control design formulations are included to highlight the utility of eigenstructure assignment algorithms. Thus, for the pitch axis design, using multiple inputs, optimisation techniques play a major role both in constructing ideal models and in the subsequent design of the controllers to match the performance of these ideal models.

This chapter is primarily based on eigenstructure assignment and classical control techniques used in the AFW program, with additional extension to improve upon the results presented therein. In this chapter, problem of stabilising aeroelastic modes has been examined. The study of the flutter mechanism, from a feedback control point of view, reveals that associated with each pair of interacting elastic modes (poles) participating in flutter, there exists a zero called the critical zero. This zero determines the achievable improvement in the damping of the unstable flutter mode. The role of EAC to optimally deploy multiple control effectors for this control problem is also highlighted.

The F-8C aircraft state variable models are used for numerical examples used in the book. The linear perturbation rigid body models of the aircraft in Reference 1 are given in Cartesian (rectangular) co-ordinates. These are converted to spherical (polar) co-ordinates (convenient for stability and control analysis). The flight control system (FCS) hardware elements add phase lags associated with (i) sensors, (ii) actuators, (iii) filters to suppress structural mode response and (iv) digital computer delays. These effects have to be accounted in the assessment of the feedback system performance.

The system matrix pencil plays an important role in characterising many control theoretical properties of multivariable state space system. In particular, the characterisation of multivariable zeros is of interest in the design of observers (Chapter 6). A brief definition of multivariable zeros is included here for reference.