Lateral Controller Performance

A 5◦ _{roll angle step command, a 1}◦ _{sideslip angle step command, and a 5 m commanded cross-}

track error was exectured to evaluate the lateral controller performance. Roll and Sideslip Angle Steps

Figure 5.57 shows the lateral response of the linear and non-linear model, with only the DPDR law active for lateral-directional control. For a 5◦ _{roll angle step command, the linear and}

non-linear responses match very well, and the response characteristics are summarised in Table 5.3. The peak time for the roll response is well below 10 seconds, with a very small amount of overshoot. The steady-state error in the linear and non-linear model responses is very small (approximately 2%). As desired, the turn co-ordination controller minimised the amount of sideslip during a commanded roll angle to a negligibly small value.

Table 5.3: Comparison of roll response specifications. Specification Desired Linear Non-Linear

Peak Time (s) <10 6.15 6.15

% Overshoot <5 1.94 1.94

Sideslip (deg) 0 -0.116 -0.116

Regarding the sideslip response in Figure 5.57b, for a 1◦ _{sideslip angle step command, the}

linear and non-linear responses match very well. The response characteristics are summarised in Table 5.4. The realised sideslip is only half of the commanded sideslip, exhibiting an overshoot of roughly 20%. Exhibiting a natural response during a sideslip command, the achieved steady- state ratio for a bank angle induced by a sideslip angle command is,

CHAPTER 5. CONVENTIONAL FLIGHT CONTROL SYSTEMS DESIGN 130

φss

βss ≈

−2.1

0.5 =−4.2 (5.101)

Table 5.4: Comparison of sideslip response specifications. Specification Desired Linear Non-Linear

Peak Time (s) <10 1.3 1.3 % Overshoot 20 23.64 23.64 φss/βss -5 -4.2 -4.2 0 5 10 15 20 25 30 35 40 45 50 −1 0 1 2 3 4 5 6

Roll and Sideslip Response of Leader

Time (s) An g le (d eg )

Commanded Roll Angle Roll − Non−Linear Sideslip − Non−Linear Roll − Linear

(a) Lateral Response for a commanded roll

0 5 10 15 20 25 30 35 40 45 50 −2.5 −2 −1.5 −1 −0.5 0 0.5 1

Roll and Sideslip Response of Leader

Time (s) An g le (d eg )

Commanded Sideslip Angle Sideslip − Non−Linear Roll − Non−Linear Sideslip − Linear

(b) Lateral Response for a commanded sideslip

Figure 5.57: The lateral response of the linear and non-linear model with only the DPDR law active for lateral-directional control. As shown, the linear and non-linear models share the same response with good characteristics.

Cross-Track Error Step

Figure 5.58a shows the step response of the cross-track error for a 5 m commanded tracking error. A comparison of the specifications for the desired and realised characteristics is given in Table 5.5. The linear model response characteristics are well within the desired specifications, but the non-linear model exhibits a larger overshoot (almost 10%). In an attempt to decrease the overshoot to below 5%, a rate limiter can be added to the reference input of the cross-track guidance controller. Although the overshoot will improve, the rise and settling time may increase substantially. An acceptable trade-off between overshoot and response time is selected and the focus is given to reducing the overshoot. As such, the response after adding a rate limiter is illustrated in Figure 5.58b.

CHAPTER 5. CONVENTIONAL FLIGHT CONTROL SYSTEMS DESIGN 131

Table 5.5: Comparison of cross-track error tracking response specifications.

Specification Desired Linear Non-Linear Rate Limited

% Overshoot <5% 2.26 8.98 3.32 80% Rise Time (s) <30 17.84 19.9 52.43 2% Settling Time (s) <60 36.93 54.3 86.29 0 20 40 60 80 100 120 140 160 180 200 −1 0 1 2 3 4 5 6

Cross-Track Error Response of Leader

y (m ) Time (s) NL Reference L Reference Non−Linear Linear

(a) No rate limiter at input

0 20 40 60 80 100 120 140 160 180 200 −1 0 1 2 3 4 5 6

Cross-Track Error Response of Leader

y (m ) Time (s) NL Reference L Reference Non−Linear Linear

(b) With rate limiter at input

Figure 5.58: Lateral tracking response for a 5 m step command.

5.6

Conclusions

In this chapter, a representative conventional fly-by-wire architecture and a set of guidance laws were designed, implemented and verified in an integrated simulation. Longitudinal manoeuvres are controlled using: a DQ law with incremental normal load factor control; an autothrust con- troller to command a thrust based on airspeed; and finally the altitude-hold guidance law to obtain a desired altitude with FPA or CR specific control. For lateral-directional control, there was a DPDR law that controls the roll φ and sideslip angle β of the aircraft, using rudder turn co-ordination during roll; and ensuring a natural roll response during sideslip, enclosed by a rudimentary cross-track error guidance law to navigate along a set of waypoints. The stabil- ity and response characteristics of the representative fly-by-wire system as well as the set of guidance laws were evaluated for a conventional isolated aircraft in simulation. Specifications were reasonably achieved with a good match between the linear and non-linear model responses. With the conventional fly-by-wire architecture in place, it was shown by B¨uchner that no changes need to be made to the inner-loop controllers, and only minor changes to the outer-loop guid- ance laws are required for formation flight aircraft [4]. The next chapter focuses on the design, implementation and verification of the extended formation flight specific guidance laws.

Chapter 6

Extended Formation Flight Control

Systems Design

In this chapter, the flight control system architecture will be extended for a formation follower aircraft. The inner-loop fly-by-wire flight control architecture needs to remain representative of that used in modern-day transport aircraft. As such, the inner-loop flight control architecture remains unchanged. At this point, the goal is not to produce an optimal controller for passenger comfort, but instead to create a system that will be successful in ensuring that the follower maintains the formation separations with acceptable performance.

This chapter starts with an overview of the extended formation flight control architecture. This is followed by the design of three formation-specific guidance controllers: an axial guidance controller, required to maintain the desired geometric longitudinal separation ξ by commanding a desired airspeed; a vertical guidance controller, required to maintain the desired geometric vertical separation ζ; and lastly a lateral guidance controller, required to maintain the desired geometric lateral separation η. To evaluate the performance of the extended formation flight guidance laws, extended simulations were performed at different levels of turbulence intensity and geometric lateral separations. The feasible and most practical regions of geometric sep- aration are investigated. The ability to maintain the separations after the leader performs longitudinal manoeuvres is also investigated. Finally, the formation-hold performance of the controllers is evaluated in simulation.

6.1

Extended Formation Flight Control Architecture

Figure 6.1 illustrates the flight control architecture for extended formation flight control. The inner-loop flight controllers are the conventional fly-by-wire flight controllers in the Normal law configuration. The fly-by-wire architecture was not redesigned for the follower aircraft. To command the fly-by-wire flight control, a set of formation-extended guidance laws is required, used to guide the follower aircraft by maintaining the relative geometric separation between the two formation aircraft.

CHAPTER 6. EXTENDED FORMATION FLIGHT CONTROL SYSTEMS DESIGN 133 DQ Control Law DP Control Law DR Control Law ∆Tc δac δrc Autothrust δec Vertical Separation ξRef ζRef ηRef δn_zRef φRef βRef ¯ VRef βRef (FPA/CR Control) Lateral Separation Axial Separation ∆T δe δa δr Conventional Fly-By-Wire Flight Controllers Formation-Extended Guidance Laws Actuators

Figure 6.1: Overview of the extended formation flight control architecture.