On Nonlinear Control Of High-Precision Optical Tracking System With Disturbance Rejection Technique

Optical tracking system is widely used in military fields such as electronic countermeasures and missile guidance,as well as in civil fields such as fire protection and environmental monitoring.How to achieve rapid capture and high-precision tracking of maneuvering targets on moving carriers has always been the research focus on optical tracking systems.Due to the existence of various influencing factors,such as cross-coupling torque,mass imbalance torque,friction torque,external disturbance,parameter uncertainty,unknown target depth,etc.,the development of the high-performance optical tracking system is always a challenging task.This paper mainly focuses on the inertial stabilization of the light of sight(LOS)and visual servoing technologies of the optical tracking system.Firstly,the basic composition and working principle of the two-axis optical tracking system are carried out in detail from the aspects of the mechanical structure,control structure,electronic control unit and visual processing unit.The coupling dynamic model of the inertially stabilized system(ISP)is derived by using Newton-Euler theory and the dynamic model of the visual servo system is established by using perspective projection theory.The uncertainties affecting tracking performances are analyzed.On the basis of the design philosophy of the sliding mode control(SMC)theory,the active disturbance rejection control(ADRC)theory and the model predictive control(MPC)theory,this paper completes the research from the following three directions:(1)To eliminate the influences induced by time-varying multi-source disturbances for the ISP,a sliding mode decoupling control method based on the higher-order extended state observer(HOESO)is proposed.Firstly,motivated by the concepts of the ADRC,the multi-source disturbances including mass imbalance torque,cross-coupling torque,friction torque and external disturbance are lumped as the total disturbance such that the approximately dynamic decoupling between the pitch and yaw channels is realized.This makes it possible to design the controllers separately for the two independent subsystems.Considering that the motor current is unavailable,a new HOESO is proposed to reconstruct the unmeasured auxiliary states and time-varying disturbances synchronously.Furthermore,by incorporating the estimates,an output feedback sliding mode controller derived.It is shown by Lyapunov stability analysis that the proposed controller can drive the output tracking errors to an ultimately bounded region,which can be regulated arbitrarily by assigning a tunable scaling gain.Finally,the effectiveness of the proposed algorithm is verified by comparing with the traditional PI control and the ESO-based sliding mode controller.The contributions are summarized as follows: 1)The proposed HOESO provides a feasible way for the higher-order disturbance estimation such that it is suitable for the applications subjected to the multi-source time-varying disturbances;2)The upper bound of disturbances is not necessarily required as a priori for the sliding mode controller design and the switching gain is adjusted based on the estimation error such that the chattering effects are significantly reduced.(2)When there is a rapid change in the posture of moving carriers or a relative movement between different gimbal frames,the existence of mass imbalance and cross-coupling will have serious impacts on the stabilization of the LOS.To further improve the control precision and response speed of the LOS stabilization loop,a finite-time control method based on the higher-order sliding mode observer(HOSMO)and the integral-type continuous terminal sliding mode(CTSM)is proposed.Firstly,the situation that the mass distribution of an ISP is non-symmetrical with respect to the mass center is emphatically analyzed.In this case,coupling dynamics are finely modeled.For the known and nominal coupled dynamic model,the direct compensation is performed in the control law design whereas for the unknown coupling dynamics,it is collected together with the residual disturbances/uncertianites such as the lumped disturbance.Considering that only the inertial angular rate is available,a HOSMO is constructed for the online observation of the unknown angular acceleration and the lumped disturbance.By incorporating the estimated information,an integral-type terminal sliding surface is established,and the second-order sliding mode dynamics of the control system is realized.Finite time convergence property of the closed-loop system is analyzed by Lyapunov stability theory.Finally,experimental comparisons with the traditional boundary layer-based CTSM control and the ADRC are carried out.The contributions are summarized as follows: 1)The coupling dynamics compensation and disturbances estimation compensation in the inertially stabilized platform are synchronously considered,which reduces the estimated burden of the observer;2)In comparison with the conventional SMC,a positive chattering alleviation effect is achieved because of the continuous control action and also the upper bound of the uncertain dynamics is not necessarily known as a priori;3)Compared with the asymptotic stability control method,the finite time convergence of the inertial angular rate tracking error is achieved.(3)The existence of uncertain kinematics caused by uncalibrated camera parameters,inertial angular rate tracking errors,and unknown target movement imposes the exogenous disturbance on the input channel of the visual servoing system.To improve the target tracking precision in the presence of the mentioned factors,a robust visual servoing method based on the disturbance observer(DOB)and MPC is proposed.Firstly,the“partitioned method”is employed to transform the kinematic model of the system,resulting in a partial interaction matrix that is independent of the feature depth and only related to rotational motions.The remainder uncertain kinematics are treated as the lumped disturbance,which are subsequently estimated in real-time by constructing a discrete-time DOB.A corrected prediction model is thus obtained by incorporating the disturbance estimates.By virtue of the design principle of multi-step prediction and receding optimization,the optimal control sequence of the system is derived.It is proved by the Lyapunov stability analysis that the target tracking error can asymptotically converge to a bounded region which can be adjusted by the controller parameters.Finally,the tuning principle of the horizon length,the weighting matrix and the observer gain in the proposed control method is illustrated by experiments.The experimental comparisons with the traditional PI control and integrator-based MPC methods are also conducted.The contributions are summarized as follows: The influence of uncertain kinematics in the system is dynamically estimated and embedded in the prediction model.The resulting desired inertial angular rate ensures the receding optimization performance of target tracking in the presence of uncertainties.