S. Mathavaraj

Bio: S. Mathavaraj is an academic researcher from Indian Space Research Organisation. The author has contributed to research in topics: Optimal control & Adaptive control. The author has an hindex of 4, co-authored 18 publications receiving 60 citations. Previous affiliations of S. Mathavaraj include Indian Institute of Science.

Robust Control of a Reusable Launch Vehicle in Reentry Phase Using Model Following Neuro-Adaptive Design

Abstract: Using a model-following neuro-adaptive approach, a nonlinear controller has been designed in this paper for a practical reusable launch vehicle that assures robust tracking of guidance commands despite having uncertainties in the plant model. The overall control design is carrie d out in two steps. First a nominal design is carried out based on the philosophy of dynamic inversion (for RCS) and optimal dynamic inversion (for aerodynamic control), which assures tracking of the guidance commands for the nominal plant with an optimal control allocation strategy. In this design phase, the bank angle and angle-of-attack commands as issued by the guidance algorithm are first converted to equivalent roll and pitch commands respectively, while simultaneously assuring turn-coordination through the necessary yaw rate command generation. These body rate commands are then tracked in an inner-loop by generating the necessary control surface deflections. Next, an adaptive control is designed that enforces the inner-loop body rates of the actual plant to track the closedloop body rates of the nominal plant. This overall control design structure retains the simplicity in design while simultaneously assuring robust performance of the controller. The control design has been carried out using the full Six-DOF model of the vehicle in velocity frame that imbeds the spherical and rotating earth effects in the vehicle dynamics (which is in harmony with the dynamics used for the vehicle guidance). The promising simulation results with the Six-DOF dynamics along with realistic constraints like actuator dynamics, control bounds, RCS constraints etc. clearly demonstrate the good command following as well as robustness of the overall design approach presented in this paper, making it a viable technique to be implemented in a real vehicle.

Constrained optimal multi-phase lunar landing trajectory with minimum fuel consumption

Abstract: A Legendre pseudo spectral philosophy based multi-phase constrained fuel-optimal trajectory design approach is presented in this paper. The objective here is to find an optimal approach to successfully guide a lunar lander from perilune ( 18 km altitude) of a transfer orbit to a height of 100 m over a specific landing site. After attaining 100 m altitude, there is a mission critical re-targeting phase, which has very different objective (but is not critical for fuel optimization) and hence is not considered in this paper. The proposed approach takes into account various mission constraints in different phases from perilune to the landing site. These constraints include phase-1 (‘braking with rough navigation’) from 18 km altitude to 7 km altitude where navigation accuracy is poor, phase-2 (‘attitude hold’) to hold the lander attitude for 35 sec for vision camera processing for obtaining navigation error, and phase-3 (‘braking with precise navigation’) from end of phase-2 to 100 m altitude over the landing site, where navigation accuracy is good (due to vision camera navigation inputs). At the end of phase-1, there are constraints on position and attitude. In Phase-2, the attitude must be held throughout. At the end of phase-3, the constraints include accuracy in position, velocity as well as attitude orientation. The proposed optimal trajectory technique satisfies the mission constraints in each phase and provides an overall fuel-minimizing guidance command history.

ISRO’s Unprecedented Journey to the Moon

Abstract: Chandrayaan-2, being the sequel of Indian Lunar Mission, differs with Chandrayaan-1 in targeting a specific lunar orbit. The primary ground trajectory design objective is to achieve the desired lunar orbit, from which the lander attempts soft-landing on the pre-selected landing site. The target lunar orbit is designed such that while landing, the Sun elevation rise angle is 6° on the desired site. This is to ensure the lander touchdown is close to sunrise, which in-turn will maximize the lander mission life to one lunar solar day (approximately 14 Earth days). This makes the Chandrayaan-2 trajectory design unique and challenging in itself. The maneuver strategy has been worked out to acquire the specific target lunar orbit. The objective of the powered descent phase is soft-landing over the desired site satisfying all the sensor constraints. This multi-phase lunar landing optimal control problem has been solved for trajectory design of the powered descent phase. Based on this design, the Chandrayaan-2 spacecraft has been launched on 2 2 nd July, 2019 UT and successfully rendezvoused with the Moon on 2 0 th August, 2019 UT and has attempted a soft-landing on 6 th September, 2019 UT.

Unscented MPSP for Optimal Control of a Class of Uncertain Nonlinear Dynamic Systems

Abstract: A new computationally efficient nonlinear optimal control synthesis technique, named as unscented model predictive static programming (U-MPSP), is presented in this paper that is applicable to a class of problems with uncertainties in time-invariant system parameters and/or initial conditions. This new technique is a fusion of two recent ideas, namely MPSP and Riemann–Stieltjes optimal control problems. First, unscented transform is utilized to construct a low-dimensional finite number of deterministic problems. The philosophy of MPSP is utilized next so that the solution can be obtained in a computational efficient manner. The control solution not only ensures that the terminal constraint is met accurately with respect to the mean value, but it also ensures that the associated covariance matrix (i.e., the error ball) is minimized. Significance of U-MPSP has been demonstrated by successfully solving two benchmark problems, namely the Zermelo problem and inverted pendulum problem, which contain parametric and initial condition uncertainties.

Energy Based Suboptimal Reentry Guidance of a Reusable Launch Vehicle Using Model Predictive Static Programming

Abstract: Using the recently-developed computationally efficient model pred ictive static programming (MPSP) and three-dimensional nonlinear vehicle dynamics with spherical and rotating earth, an energy based suboptimal reentry guidance technique is presented in this paper for a reusable launch vehicle (RLV). This guidance essentially shapes the trajectory of the RLV by predicting the necessary angle of attack and bank angle that the vehicle should execute. The path constraints (imposed as ‘soft constraints’) are in the form of structural load and thermal load constraint as well as bounds on angle of attack and bank angle. The terminal constraints (imposed as ‘hard constraints’), on the other hand, are are in th e form of three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle of attack solution comes out of the MPSP guidance directly, the bank angle command generation is done in two steps. First, the required heading angle is considered as an intermediate control variable to steer the vehicle towards the desired final coordinates. Next, the required bank angle is computed through a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis leads to smoothness as well as reversals in the bank angle at appropriate points in the trajectory within the specified bounds. The computationally e fficient MPSP guidance law is primarily based on nonlinear optimal control theory and hence embeds effective trajectory optimization concepts into the guidance law. In addition to the promising results for the nominal case, it has also been demonstrated that the proposed guidance has sufficient robustness for perturbat ions in the states, which may possibly arise from noise input.

Active fault tolerant control design for reusable launch vehicle using adaptive sliding mode technique

Abstract: In this paper, the problem of active fault tolerant control for a reusable launch vehicle (RLV) with actuator fault using both adaptive and sliding mode techniques is investigated. Firstly, the kinematic equations and dynamic equations of RLV are given, which represent the characteristics of RLV in reentry flight phase. For the dynamic model of RLV in faulty case, a fault detection scheme is proposed by designing a nonlinear fault detection observer. Then, an active fault tolerant tracking strategy for RLV attitude control systems is presented by making use of both adaptive control and sliding mode control techniques, which can guarantee the asymptotic output tracking of the closed-loop attitude control systems in spite of actuator fault. Finally, simulation results are given to demonstrate the effectiveness of the developed fault tolerant control scheme.

Generalized Model Predictive Static Programming and Angle-Constrained Guidance of Air-to-Ground Missiles

Abstract: A new generalized model predictive static programming technique is presented for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. Two key features for its high computational efficiency include one-time backward integration of a small-dimensional weighting matrix dynamics, followed bya static optimization formulation that requires only a static Lagrange multiplier to update the control history. It turns out that under Euler integration and rectangular approximation of finite integrals it is equivalent to the existing model predictive static programming technique. In addition to the benchmark double integrator problem, usefulness of the proposed technique is demonstrated by solving a three-dimensional angle-constrained guidance problem for an air-to-ground missile, which demands that the missile must meet constraints on both azimuth and elevation angles at the impact point in addition to achieving near-zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Simulation studies include maneuvering ground targets along with a first-order autopilot lag. Comparison studies with classical augmented proportional navigation guidance and modern general explicit guidance lead to the conclusion that the proposed guidance is superior to both and has a larger capture region as well.

Attitude controller design for reusable launch vehicles during reentry phase via compound adaptive fuzzy H-infinity control

Abstract: In this paper, the attitude control problem of reusable launch vehicles (RLVs) during reentry phase is investigated by using compound adaptive fuzzy H-infinity control (CAFHC) strategy in the presence of parameter uncertainties and external disturbances. Firstly, the control-oriented attitude model is established by a model transformation based on the six-degree-of-freedom (6-DoF) dynamic model of the RLV. Secondly, a novel attitude control scheme is developed and the control strategy consists of two parts to achieve a stable and accurate attitude tracking during reentry flight process. An attitude tracking controller is designed utilizing adaptive fuzzy H-infinity control approach combined with an identification model to improve the attitude tracking performance in the interior of fuzzy approximation region of attitude angle. Next, an attitude stabilization controller based on boundary adaptive technique is employed to assure the robustness of the closed-loop system in the exterior of fuzzy approximation region of attitude angle. Furthermore, the stability of the closed-loop system is guaranteed within the framework of Lyapunov theory and the attitude tracking error converges to a small neighborhood around origin. Finally, the simulation results are presented to demonstrate that the effectiveness of the proposed control scheme for reentry RLV, and its tracking performance performs better than the other control method.

Multi-constrained suboptimal powered descent guidance for lunar pinpoint soft landing

Abstract: A multi-constrained suboptimal guidance method based on an improved zero-effort-miss/zero-effort-velocity (ZEM/ZEV) algorithm and the recently developed model predictive static programming (MPSP) is presented in this paper for lunar pinpoint soft landing. Firstly, the ZEM/ZEV algorithm is improved so that the trajectories generated by the algorithm are always above the surface of the Moon without thrust magnitude and look-angle constraints violated. A concept of virtual control is introduced for the continuity of the guidance commands and the enforcement of the thrust vector constraint at the terminal point. Taking the trajectory generated by the improved ZEM/ZEV algorithm as the initial guess history of the MPSP method, and the virtual control history as its control history, we develop a multi-constrained fuel suboptimal powered descent guidance law with the help of the high computational efficiency of the MPSP technique. Extensive simulations are conducted to verify the design features of the algorithm. The testing results demonstrate that the proposed algorithm is accurate and robust, and has a good capability of retargeting.