Transfer matrix method for multibody systems (MS-TMM) is a rife method to multi-rigid-flexible-body systems dynamics model deduction due to that there are no needs to establish the global dynamics equations of the system. Its basic idea is transferring a state vector between the body input(s) and output(s); this idea is close to the linear theories in control analysis and design. In this paper, three controllers’ parameters tuning techniques for the proposed system model using MS-TMM are utilized; one technique is applied to get the stability regions via the frequency response of MS-TMM derived model. Another technique considers a classical PID controller design through the analysis of step input response of the system, and the last technique can be applied in both time and frequency domains if the model has a known mathematical model. A car suspension system is considered to represent modeling and tuning problems. In-depth study of MS-TMM with control techniques and defining the controllers’ parameters stability regions provide an opportunity to formulate a relationship between MS-TMM and control design for novel control applications due to the powerful strength of MS-TMM dealing with more complex problems of the controlled multibody systems.

A precise guided system needs an efficient control depending on a precise navigation algorithm, with the ability of getting an accurate initial attitude determination to guarantee the mission success. A navigation system is presented in this paper based on integration between inertial measuring unit and Global Positioning System via Kalman filter approach to satisfy an acceptant accuracy. The two well known Euler and Quaternion attitude determination techniques are implemented to evaluate the body orientation during motion. The carried out system is validated using both simulation data and experimental work. The simulation data is obtained using a six-degree-of-freedom model for a 122mm artillery rocket to obtain all ballistic trajectory parameters during flight. The experimental work is done using a land vehicle taking into consideration the initial attitude determination problem. The results showed high accuracy improvements with high data rates 200 Hz for full state navigation information (position, velocity and attitude).

Any trajectory calculation method has three primary sources of errors, which are model error, parameter error, and initial state error. In this paper, based on initial projectile flight trajectory data measured using Doppler radar system; a new iterative method is developed to estimate the projectile attitude and the corresponding impact point to improve the second shot hit probability. In order to estimate the projectile initial state, the launch dynamics model of practical 155 mm self-propelled artillery is defined, and hence, the vibration characteristics of the self-propelled artillery is obtained using the transfer matrix method of linear multibody system MSTMM. A discrete time transfer matrix DTTM-4DOF is developed using the modified point mass equations of motion to compute the projectile trajectory and set a direct algebraic relation between any two successive radar data. During iterations, adjustments to the repose angle are made until an agreement with acceptable tolerance occurs between the Doppler radar measurements and the estimated values. Simulated Doppler radar measurements are generated using the nonlinear six-degree-of-freedom trajectory model using the resulted initial disturbance. Results demonstrate that the data estimated using the proposed algorithm agrees well with the simulated Doppler radar data obtained numerically using the nonlinear six-degree-of-freedom model.

Due to the importance of the ballistic trajectory computation including the estimation of launch point and impact point problems, a fast and accurate model is needed to increase the weapon precession. A discrete time transfer matrix method is developed and presented in this paper to compute the trajectory for both fin- and spin-stabilized artillery projectiles. This method is based on discretizing the projectile continuous nonlinear system into a set of linear equations using a second-order Taylor series. These equations are collected into one transfer matrix which can be used in trajectory prediction with high computation speed by evaluating a set of algebraic equations instead of integrating differential equations. Results demonstrate that the presented formulation agrees very well with those obtained numerically using the well-known nonlinear 6-degree-of-freedom model.

Vibration effects for space crafts has a great influence during the launching phase and also after launching. Active vibration isolation techniques have good results to protect such systems from vibration problems in wide frequency bands. But, these active systems increase the total weight of space craft. That will increase the need of power supplies, which may affect the mission life time due to batteries and solar cell charging consuming. Passive control for such problem is designed using Transfer Matrix Method for Multibody Systems (MSTMM) that can provide an easy method to analyze a passive vibration isolation technique with simple design. The main objective of this paper is to study the different models effect in isolation design using MSTMM and passive control techniques to conserve the power consumption for enlarging the power batteries life. That means longer mission intervals for such systems. Simulation results are given to demonstrate the effectiveness of the offered technique.