Longitudinal Control Law Design and Handling Qualities Optimization for a Business Jet Flight Control System

Abstract

A comprehensive set of stability, handling qualities, and performance specifications was used to drive the optimization of commonly used fixed-wing longitudinal control laws applied to a business jet. The specifications were divided into two tiers. The first were the key flight control and handling qualities requirements and were used directly for optimization, while the second were used as a check afterwards. Similarities between the commonly used longitudinal control laws investigated in this study and a model following controller were exploited to explicitly set feed-forward gains to provide good handling qualities. A linear-quadratic regulator method was employed for preliminary design as a way to initialize the control law feedback gain values for optimization. A multi-objective parametric optimization approach was then used to arrive at feedback gains that concurrently satisfy all specifications. Using this optimization approach, the trade-offs of increased crossover frequency were investigated. In addition, a smooth gain schedule was generated by optimizing the control law parameters of different flight conditions to meet the same requirements. This paper describes the control law architecture used as well as the optimization approach, the specifications used, and the design results. Nomenclature α Angle-of-attack [deg, rad] α cmd Angle-of-attack command [rad] α nz Steady state angle-of-attack per normal load factor [rad/g] q Dynamic pressure [psf] δ act Actuator position [deg] δ stk Stick force [lb] α Angle-of-attack rate [deg/sec, rad/sec] α cmd Angle-of-attack rate command [rad/sec] δ act Actuator rate [deg/sec] n z cmd Commanded normal load factor rate [g/sec] q Pitch acceleration [rad/sec 2 ] ω c Crossover frequency [rad/sec] ω n Natural frequency [rad/sec] ω α LQR output shaping function frequency of complex-pair target zeros [rad/sec] ω cmd Command model frequency [rad/sec] ω inv Inverse model frequency [rad/sec] ω sp Short-period frequency [rad/sec] φ Bank angle [rad] τ Time delay [sec] τ n Normal acceleration transfer function equivalent time delay [sec] τ q Pitch rate transfer function equivalent time delay [sec] τ cmd Command time delay [sec] θ Pitch attitude [deg, rad] θ DB Pitch attitude dropback [deg] ζ Damping ratio [-] ζ α LQR output shaping function damping of complex-pair target zeros [-] ζ cmd Command model damping [-] ζ inv Inverse model damping [-] ζ sp Short-period damping [-] a LQR output shaping function real zero [rad/sec] g Acceleration due to gravity [ft/sec 2 ] J LOES LOES fit cost J M F Model following cost K Control law gain K n Normal acceleration transfer function gain [g/deg-elev] K q Pitch rate transfer function gain [rad/sec/deg-elev] K stk Stick gain [g/lb] K u Speed error gain [g/kt] M α Dimensional pitch stiffness derivative [1/sec] M δe Dimensional pitch rate control derivative [rad/sec 2 /deg − elev] n/α Steady-state normal acceleration change per unit change of angle-of-attack [g/rad] n z Normal acceleration [g] n z Normal load factor at the ICR [g] n z u, n z +u No...

Piloted Simulation Handling Qualities Assessment of a Business Jet Fly-By-Wire Flight Control System

“…The filled in symbols are from the analysis model. 1 There is a bit of a spread in the points in Figure 22 because the pilots sometimes shaped their inputs differently to try different capture strategies. However, the points all lie within the Level 1 region of the specification, and show consistent trends with the analysis model.…”

“…For the model following control laws used here, the pitch attitude bandwidth of the aircraft is set by the second-order command model frequency. 1 Using the design approach of setting the command model frequency to match the bare-airframe's short period frequency, ω sp , resulted in pitch attitude bandwidth values well above the minimum pitch attitude bandwidth requirement of ω BW ≥ 1.25 rad/sec. 6 For this flight condition for example, the installed aircraft pitch attitude bandwidth is ω BW = 4.33 rad/sec, which is well in excess of the PVS crossover frequencies.…”

Lateral/Directional Control Law Design and Handling Qualities Optimization for a Business Jet Flight Control System

“…All models are for a flaps-up, gear-up cruise configurations, and are the same models used in the previous development of longitudinal control laws. 1 Figure 2(a) shows the different Mach and altitude combinations, as well as the aircraft flight envelope. 6 Figure 2(b) shows the different weight and CG combinations, as well as the aircraft weight-CG envelope.…”

“…The benefits of these delays are described in detail in the previous longitudinal control laws paper. 1 The remainder of this section will be broken down into the Design Parameters and Set Parameters of the block diagram. Design parameters are those that are determined either by hand tuning or through optimization, and are different for each flight condition.…”

“…1 The optimization was driven by a comprehensive set of specification divided into two tiers. This approach was motivated by several comprehensive compendiums of flight control design experience and lessons learned, which emphasize the importance of meeting multi-tier handling qualities and flight control criteria for improved safety (e.g.…”