Controller Design for Lateral Dynamics of Reusable Launch Vehicle by H- infinity Mixed Sensitivity approach Gopal Jee *, AkashYalagach**, V. Brinda***, V. R. Lalithambika + , M. V. Dhekane † Vikram Sarabhai Space Centre, Thiruvananthapuram, India, 695022; e-mail: *gopaljee@gmail.com. ** yalagach_akash@sify.com, ***v_brinda@vssc.gov.in., + vr_lalithambika@vssc.gov.in., † mv_dhekane@vssc.gov.in. Abstract: During reentry flight regime of a typical Reusable Launch Vehicle (RLV), there is rise in dynamic pressure which increases the coupling between yaw (directional) and roll (lateral) dynamics. High uncertainty on aerodynamic coefficients due to less number of wind tunnel tests, makes it essential to use robust control design techniques to design a controller for any new aerodynamic configuration of RLV. Control system design during critical flight regime of RLV using ‘H-infinity Mixed Sensitivity’ approach is addressed in this paper. The main bottle neck in using H-infinity approach is the lack of guidelines in finding weighting functions to achieve required time and frequency domain specifications. It is seen that the solution process becomes easier if the coupling and damping requirements are first addressed by designing the aileron to rudder interconnect (ARI) gain and roll-yaw rate gains using classical approach and then applying the H-infinity procedure on the plant model, updated with the designed ARI and rate gains, to shape the sensitivity and complementary sensitivity functions. This is the main contribution of our paper. This approach has resulted in highly robust controller against plant parameter perturbations. The yaw-roll coupling, which is the main problem, could also be eliminated to a greater extent. Keywords: H-infinity control, robust control, aerospace control, linear systems, computer-aided control system design 1. INTRODUCTION After atmospheric re-entry, during the descent phase of RLV there is high angle of attack, Mach no. and dynamic pressure, leading to difficulty in control law design meeting both stability and performance specifications. High dynamic pressure causes increase in all aerodynamic moments specially the coupling moment between yaw and roll which is undesirable. High angle of attack reduces rudder effectiveness due to blocking of airflow by the fuselage. The challenge is to design a controller which reduces the coupling and tolerate large perturbations of plant parameters (in some of the aerodynamic coefficients, perturbation is as high as 75% of nominal value). Design must also achieve the prescribed stability margins for nominal plant and should be robust against plant parameter variations. Reduction in dependency on rudder deflection is also desirable. H-infinity design approach is a powerful technique which can handle large plant uncertainties and achieve stability and performance robustness. In H ∞ control we optimize over the space of transfer functions based on their H ∞ norm. H ∞ norm of a transfer function G(s) can be defined as the largest of all maximum singular values over frequency, and is given by [ ] sup ) ω G σ G(j ω ∞ = (1) Consider the standard 2 port block diagram of Fig. 1, taken from Xue et. al. (2007), where P(s) is the plant and K(s) is the controller, U(s) consists of exogenous signals (reference inputs and disturbances), Y(s) consists of regulated outputs or the performance variables of our interest, Y c (s) consists of measurements used for feedback purposes, and U c (s) consists of the control signals generated by the controller K(s). Fig. 1. Standard two port block diagram The closed loop relationship from y to u can be obtained as, ( ) 1 11 12 22 21 yu T P PK I PK P - = + - (2) where P ij is the transfer function between i th input and j th output of the plant P(s). The above expression is also known as the linear fractional transformation (LFT) of the interconnected system. The standard H ∞ problem is to find an internally stabilizing controller K(s) which is proper and minimizes the infinity norm of the transfer function T yu to a particular value. A stabilizing controller achieving minimum closed loop norm yu opt T γ ∞ = is said to be optimal. A stabilizing controller achieving ɀ >ɀ opt is called a sub-optimal controller. Third International Conference on Advances in Control and Optimization of Dynamical Systems March 13-15, 2014. Kanpur, India 978-3-902823-60-1 © 2014 IFAC 171 10.3182/20140313-3-IN-3024.00160