(控制理论课程设计及Matlab代码.docxVIP

Project ObjectiveThis project is for the students to learn how to linearize a practical dynamical system for simple analysis,evaluate a given linear system (e.g. controllability and observability), apply feedback control and observ-er designing, use PID control to improve the performance of the system, design a LQR controller to solve the optimal problem, etc.Given the state vector and the control input vector as and ,Then, the longitudinal equations of motion for the aircraft can be written in the following form: ,Where W, , are constants, , , are the functions of u, w, q, ,, and , and and .Linearize the longitudinal equations, we have ,Around the trim condition and ,Where A and B are , ,Now consider an autopilot designing problem. The linearized equations can be expressed in state-space form aswhere , , ,Plot the unit step response (Figure 1), Bode plot(Figure 2), and Nyquist plot(Figure 3) of the given open-loop system in MATLAB.Determine the controllability of the given system.The controllability matrix of the given open-loop system,The given system is controllable since the determinant of the controllability matrixAssume all the states are measurable, design a state feedback controller , where , such that the resultant system is asymptotically stableand at the same time, meet the following requirements on rise time , the settling time and the overshoot OS%; The closed-loop system need to satisfy four conditions above, we can use trail and error method to find two poles of the closed-loop system, then use ‘place’ MATLAB command find the corresponding gain , then write a MATLAB function that take gain K as input and output the eigenvalues of the matrix, step response information and check whether the resultant system indeed satisfy all the conditions.The real parts of eigenvalues of the resultant system dynamic matrix are -17.8064 and -2.2394, both lie in the left hand plane of the complex plane, so the closed loop system is asymptotically sta