Automatic Control and Stabilized Platform Investigation
【摘要】：Inertially stabilized platforms (ISPs) are so widespread used in several applications to point the line of sight (LOS) of sensors, antennas, cameras, instruments or weapons. All these applications have in common the use of this kind of system vehicle onboard such as, ground vehicles, helicopters, unmanned either ground or aerial vehicles, and even space satellites. Although the requirements from the ISPs are vary widely depending on the application, they all have a common goal, which is to hold the LOS of one object relative to another object. The function of LOS stabilization systems is to maintain the LOS of sensors when it is subjected to any external disturbances caused by the carrier vehicle motion. Gyro stabilized platform can be considered as the most useful device for both ground and airborne application. It forms the basis of a wide range of practical instruments which used for the purposes of sighting and tracking target. The number of stabilized axes required by the system depends on the application requirements and it normally ranges from two to five axes. For most applications it is required to stabilize at least two orthogonal axes.
On the other hand, multi-gimbals system such as dual axes inertially stabilized platforms is a complex nonlinear multivariable problem. Several factors, such as mechanical resonance, random drift of inertial sensors, make the modeling of this kind of system difficult. The main goal of the thesis is to investigate the best control strategy that can deals with such nonlinearity and uncertainty for the ISPs. A mathematical model for the dual axis stabilizer platform, based on Euler's equations of motion, is presented.
Two different control strategies are introduced to control the platform. The first control strategy is based on the classical control theory by decomposing the system into pair of single input single output (SISO) system. The double loop configuration was considered for each axis, consisting of stabilization loop and position loop. Since physical systems and external environment is somewhat difficult to model precisely, the external environment may change in an unpredictable manner, and may be subject to significant disturbances. So the design of the control systems in the presence of significant uncertainty requires the designer to seek about a robust system. A robust proportional integral (PI) based on the minimization of integral of time-weighted absolute error index (ITAE) is proposed for the stabilization loop.
On the other hand, under the linear conditions of the process, conventional PID control can achieve the desired performance requirement. Otherwise, under the conditions with nonlinear constraints and uncertainties only using the conventional PID control is very difficult to realize the system desired performance with high accuracy. So the non-linear fuzzy proportional integral (NLFPI) controller with only four rule base is proposed in stead of the proportional integral (PI) controller. The idea is to start with a tuned, conventional PI controller that achieve a certain desired performance, replace it with an equivalent linear fuzzy proportional integral (LFPI) controller, and finally convert the linear fuzzy controller to nonlinear fuzzy controller.
The position loop of the ISP is a third order system and most of researches seek to deal with the second order system due to the simplicity to describe and control its behavior with classical methods. The third order system response can be approximated by the dominant roots of the second order system when the real part of the dominant root is less than one tenth of the real part of the third root. Otherwise, the third root will affect on the system response and the system can not be approximated by second order system. For this case, the selected controller must be gives the opportunity to control all coefficient of the characteristic equation. Although PID controller is considered as one of the most controllers widely used in the control system, it is difficult to design the PID controller for a third order system because the order of system is greater than the number of zeros provided by the PID controller. For the first time, a proportional derivative double derivative (PDD2) controller was proposed for the position loop to solve the problem of third order system without reducing the system order. The second control strategy is based on modern control theory. Full state feedback controller has been designed through two different methods namely, pole placement and linear quadratic regulator (LQR).
Comparison between the all different designed controllers has been done through simulation, experiment, sensitivity analysis, and robustness analysis. The simulation results showed the superiority of non linear fuzzy PI controller for controlling the ISP with stabilization precession of0.015°/s. It can improve the system performance, robustness, and disturbances rejection. It also showed the effectiveness of the proposed PDD2controller with the third order system, which offers an excellent performance and robustness in the presence of uncertainty. The system robustness and performance can be adjusted by only tuning the proportional part of the PDD2controller.
Since the single inverted pendulum is a classical problem in the field of non-linear control theory; the experiments for all proposed controllers have been performed on a real time inverted pendulum. It offers a good example for control engineers to verify a modern control theory. The ability of each controller to stabilize and reject the outer disturbances has been checked. The experimental results are found to be in agreement with the simulation. Moreover, the results showed the ability of NLFPID controller to stabilize the inverted pendulum after introducing any external disturbances in less than2seconds with zero overshoot and zero steady state error.