An adaptive exponential sliding mode control method for optoelectronic pod based on disturbance observer

Abstract

The present invention discloses an adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer. The method comprises the following steps: first, establishing a mathematical model of the optoelectronic pod system based on the principle of the optoelectronic pod. Then, based on the mathematical model of the optoelectronic pod system, designing an adaptive exponential sliding mode controller based on a disturbance observer. The disturbance observer observes external disturbances and parameter uncertainties to obtain a control input that offsets the aggregated disturbance. An adaptive law is designed to online estimate the switching gain in the sliding mode controller to avoid chattering caused by excessive switching gain. Finally, Lyapunov's stability theorem is used to prove that the optoelectronic pod system has asymptotic stability in a closed-loop state, so that the actual attitude of the optoelectronic pod ultimately converges to the desired attitude.

Description

Technical Field

[0001] The invention belongs to the technical field of photoelectric pod control, in particular to an adaptive exponential sliding mode control method for a photoelectric pod based on a disturbance observer. Background Art

[0002] Electro-optical pods are typically deployed on mobile vehicles such as drones and unmanned watercraft. Equipped with high-precision optoelectronic sensors such as infrared cameras, visible light cameras, and laser rangefinders, they are multi-sensor optoelectronic detection devices capable of target detection, tracking, and aiming. These pods are typically equipped with a variety of optoelectronic payloads, including visible light, infrared, and lasers. During mission execution, regardless of changes in posture and trajectory, the payload's boresight must be controlled to maintain the desired tracking target, thereby achieving the desired tracking accuracy.

[0003] When an electro-optical pod is tracking a target, its line of sight moves and stops, sometimes maintaining low speeds. During this period, the friction torque exhibits strong nonlinearity, constantly switching between static and kinetic friction. The dynamic variation in friction torque causes "jitter" or "creeping" in the pod's scanning, degrading the image quality of the imaging system and the pod's tracking accuracy. When the pod is further disturbed by random factors such as mass imbalance and wind resistance, these disturbances, coupled with the time-varying friction torque, form aggregated disturbances that are transmitted to the inner frame. This significantly impacts the stability of the line of sight, further reducing the pod's tracking accuracy and stability, and may even lead to target loss. Traditional PID control relies too heavily on the control object model, resulting in poor parameter robustness and difficulty achieving high-precision control requirements. When a wide speed range is required, it cannot simultaneously meet the requirements of fast response speed and high steady-state accuracy, and the system may even fail to operate properly at low speeds. Modern control theories such as adaptive neural network control and active disturbance rejection control can effectively improve the performance of electro-optical pods, but the numerous parameters make tuning difficult. Summary of the Invention

[0004] The present invention proposes an adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer, which offsets the influence of external disturbances and parameter uncertainties on the optoelectronic pod and realizes stable control of the optoelectronic pod under the influence of aggregated disturbances.

[0005] The technical solution to realize the present invention is: an adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer, the steps of which are as follows:

[0006] Step 1: Based on the principle of optoelectronic pod, establish the mathematical model of optoelectronic pod system and go to step 2.

[0007] Step 2: Based on the mathematical model of the optoelectronic pod system, establish the dynamic equations and state space equations of the optoelectronic pod; based on the dynamic equations and state space equations of the optoelectronic pod, design the sliding mode controller u smc , and establish a disturbance observer to observe the aggregate disturbance, use Lyapunov stability theorem to verify the stability of the disturbance observer, and finally obtain the control input u to offset the aggregate disturbance D , go to step 3.

[0008] Step 3: The switching gain in the sliding mode controller is improved online through the adaptive law to compensate for the aggregate uncertainty and realize the dynamic correction control quantity. At the same time, in order to avoid excessive adaptation of the switching gain, an adaptive exponential sliding mode controller is proposed. The adaptive exponential sliding mode controller is used to reduce the arrival process of the sliding mode motion, so that the optoelectronic pod system always runs along the sliding mode surface and finally converges to the equilibrium state. Finally, the optimized control quantity U′ is output, which improves the robustness of the optoelectronic pod and realizes precise control, and then proceeds to step 4.

[0009] Step 4: In order to prove the stability of the adaptive exponential sliding mode controller in the optoelectronic pod closed-loop system, the Lyapunov stability theorem is proved.

[0010] Compared with the prior art, the present invention has the following significant advantages:

[0011] (1) The present invention adopts a disturbance observer to observe the disturbance of the optoelectronic pod, regards the external disturbance and parameter uncertainty as aggregate disturbance, and obtains the estimated value that offsets the aggregate disturbance through observation by the disturbance observer, thereby realizing accurate estimation and real-time compensation of nonlinear disturbances and improving the robustness and stability of the system.

[0012] (2) The present invention adopts a new adaptive algorithm to estimate the sliding mode switching gain online, thereby avoiding the sliding mode chattering problem caused by excessive switching gain.

[0013] (3) In order to solve the problem of excessive adaptation of the switching gain of the sliding mode control, an adaptive exponential sliding mode controller is adopted, which reduces the arrival process of the sliding mode motion and makes the closed-loop system always move along the sliding mode surface.

[0014] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a block diagram of the optoelectronic pod model of the present invention.

[0016] Figure 2 This is a flow chart of the adaptive exponential sliding mode control method of the optoelectronic pod based on the disturbance observer of the present invention. DETAILED DESCRIPTION

[0017] The present invention will be further described below with reference to the accompanying drawings and specific examples.

[0018] The optoelectronic pod described in the present invention is an airborne optoelectronic pod or a shipborne optoelectronic pod, specifically a two-axis two-frame optoelectronic pod, which is mainly carried on mobile carriers such as unmanned aerial vehicles and unmanned ships.

[0019] Combine Figures 1 and 2 The present invention provides an adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer, comprising the following steps:

[0020] Step 1: Based on the principle of optoelectronic pod, a mathematical model of the optoelectronic pod system is established. The specific process is as follows:

[0021] The photoelectric pod system adopts a two-axis two-frame photoelectric pod, controls the rotation of the photoelectric pod through a permanent magnet synchronous motor, and establishes a transfer function of the photoelectric pod, which is as follows:

[0022]

[0023] Where, the electromagnetic time constant Electromechanical time constant

[0024] Among them, R is the armature resistance of the photoelectric pod rotating motor, L is the inductance of the photoelectric pod rotating motor, C e is the back electromotive force coefficient, C m is the torque coefficient, J is the load moment of inertia, K pwm is the power amplification factor, s is the Laplace variable, θ(s) is the control input, and U(s) is the control output.

[0025] In order to facilitate research, the transfer function of the optoelectronic pod is usually simplified to a second-order model. e Much smaller than the electromechanical time constant T m , can be ignored, that is, s(T e s+1)(T m s+1)≈s(T m s+1), simplify the above formula to obtain the mathematical model of the optoelectronic pod system:

[0026]

[0027] Step 2: Based on the mathematical model of the optoelectronic pod system, combined with Figure 2 , establish the dynamic equations and state space equations of the optoelectronic pod. Based on the dynamic equations and state space equations of the optoelectronic pod, design the sliding mode controller u smc, and establish a disturbance observer to observe the aggregate disturbance, use Lyapunov stability theorem to verify the stability of the disturbance observer, and finally obtain the control input u to offset the aggregate disturbance D , as follows:

[0028] Step 2-1: Considering the influence of external disturbance on the optoelectronic pod, T d represents the external disturbance, which includes the carrier vibration interference torque, friction torque, unbalanced torque, etc. The dynamic equation of the optoelectronic pod can be expressed as:

[0029]

[0030] in, represents the angular acceleration, represents the angular velocity, and U is the control voltage.

[0031] Step 2-2: Use the state space equation of the optoelectronic pod to describe the impact of uncertainty on the system, as follows:

[0032]

[0033] Among them, x1 is the first variable, x2 is the second variable, is the derivative of x1, is the derivative of x2, the first intermediate variable The second intermediate variable D represents the uncertainty of the mathematical model parameters of the optoelectronic pod system and the aggregate uncertainty of the external disturbance torque.

[0034] Step 2-3: Design the sliding mode controller u smc :

[0035] 2-3-1. Design a sliding mode function to describe the degree of deviation of the angular position and angular velocity of the optoelectronic pod, so that the optoelectronic pod system converges to the desired control point of the system after entering the sliding mode motion, ensuring that the optoelectronic pod system has good dynamic quality.

[0036] According to the state space equation, let the first deviation e1 = x1-θ d , the second deviation where θ d is the desired angular position, For the desired angular velocity, design the sliding mode function S:

[0037] S=e2+ke1

[0038] Wherein k is the first gain, and k>0.

[0039] 2-3-2. Design a sliding mode control law to make the system state of the optoelectronic pod slide quickly to the desired state along the sliding mode surface, thereby achieving accurate tracking and robust control of the state of the optoelectronic pod system.

[0040] Before the system state of the optoelectronic pod moves along the sliding surface, there will be a period of approaching motion. The movement of the optoelectronic pod system from any initial state to the sliding surface until it reaches the sliding surface is called approaching motion. The use of a suitable approaching law can improve the dynamic quality of the approaching motion and suppress the influence of sliding mode chattering. Here, the exponential approaching law is used. express:

[0041]

[0042] Wherein, η is the switching gain, λ is the second gain, both are positive numbers, and sgn(·) represents the sign function.

[0043] 2-3-3. Design sliding mode controller u smc for:

[0044]

[0045] Step 2-4: Use the disturbance observer to observe the aggregate uncertainty in the optoelectronic pod system. Take x1 as the actual position signal and x2 as the actual speed signal. Send the above two as inputs to the disturbance observer to obtain the control input u that offsets the aggregate uncertainty. D .

[0046] The input of the disturbance observer is the actual signal of the control system, namely the actual position signal and the actual speed signal. The disturbance observer is used to obtain the estimated value of the aggregate uncertainty. Based on the actual signal, it is possible to make real-time estimates of external disturbances and parameter uncertainties, and use the estimated values ​​to compensate for the impact of aggregate disturbances on the control accuracy of the optoelectronic pod.

[0047] Defining auxiliary variables l is the third gain, and the designed disturbance observer is as follows:

[0048]

[0049] in, represents the derivative of z.

[0050] Step 2-5: In order to verify the stability of the disturbance observer designed by the present invention, an observation error with aggregated uncertainty is given as Assume that the aggregate uncertainty changes slowly, so can be close to zero and Take the derivative:

[0051]

[0052] in, Expressed as The derivative of .

[0053] Assume that the Lyapunov function Derivative of the Lyapunov function:

[0054]

[0055] because By solving the equation, we can get Among them, the variable C0 is a constant, and When the action time t→∞, That is, the disturbance observer observes the estimated value of the aggregate disturbance It converges to the actual aggregate uncertainty D in an exponential form, and l represents the convergence rate of the disturbance observer. For the convenience of calculation, l here is a positive constant.

[0056] Step 2-6: When the optoelectronic pod system is disturbed by external factors, the disturbance observer can be used to observe the estimated value of the aggregate uncertainty. After adjusting the second intermediate variable, the control input to offset uncertainty can be obtained. The specific formula is as follows:

[0057]

[0058] Step 3. The switching gain in the sliding mode controller is improved online through the adaptive law to compensate for the aggregate uncertainty and realize the dynamic correction control quantity. At the same time, in order to avoid excessive adaptation of the switching gain, an adaptive exponential sliding mode controller is proposed. The adaptive exponential sliding mode controller is used to reduce the arrival process of the sliding mode motion, so that the optoelectronic pod system always runs along the sliding mode surface and finally converges to the equilibrium state. Finally, the optimized control quantity U′ is output, which improves the robustness of the optoelectronic pod and realizes precise control.

[0059] Step 3-1: The switching gain in the sliding mode controller is highly dependent on the uncertainty upper bound. However, due to the complexity and unpredictability of external disturbances and parameter uncertainty, it is usually difficult to obtain an accurate uncertainty upper bound. Therefore, it is difficult to accurately obtain the switching gain. In this part, adaptive technology is used to adjust the switching gain online. Assume that there is an optimal switching gain The control requirements of the optoelectronic pod system in a closed loop state are met, and is the upper bound of the residual perturbation uncertainty.

[0060] η is the switching gain in the sliding mode function S. Its value is related to the stability of the optoelectronic pod system. A better switching gain can improve the stability of the optoelectronic pod. The optimal switching gain will also change according to the changes of the optoelectronic pod system. It is assumed that there is an optimal switching gain that meets the control requirements of the actual optoelectronic pod system; is the optimal switching gain Make an estimate.

[0061] Using adaptive law To get an online estimate:

[0062]

[0063] Where: the fourth gain κ>0, is the estimated value of the optimization gain, t0 represents the initial time, t m It represents the time for the optoelectronic pod to reach the sliding mode surface in the closed-loop state, where S represents the sliding mode function of the controller.

[0064] Step 3-2: In order to solve the over-adaptation problem caused by the adaptive law, an adaptive exponential sliding mode controller is designed. The conventional sliding mode is optimized so that the optoelectronic pod system is on the sliding mode surface in the initial state, that is, S(t0) = 0. and When the sliding surface cannot be reached, there will be a deviation from the sliding surface. As the sliding function S(t) increases, the estimated switching gain also increases until The arrival condition of sliding mode control cannot be met and the vehicle returns to the sliding surface.

[0065] The designed adaptive exponential sliding mode function S′ is shown as follows:

[0066]

[0067] Where: the first intermediate function Q = e2(t0) + ke1(t0), the fifth gain β>0, and the adaptive exponential sliding mode function is derived:

[0068]

[0069] In the above formula, is the derivative of S′, is the derivative of e2, is the derivative of e1. In order to maintain the approaching speed, the exponential approaching law is adopted, and the adaptive exponential sliding mode controller is designed as follows:

[0070]

[0071] Step 4: In order to prove the stability of the adaptive exponential sliding mode controller in the optoelectronic pod closed-loop system, the Lyapunov stability theorem is proved.

[0072] The Lyapunov function V is defined as:

[0073]

[0074] Taking the derivative of V, we can get:

[0075]

[0076] Substituting the adaptive exponential sliding mode controller into the above equation, we have:

[0077]

[0078] because λ>0, so we know Because V is positive, Lyapunov's stability theory shows that the stability of this system is asymptotic. Based on the principle of the overall sliding model, under optimal conditions, the optoelectronic pod system always slides along the sliding surface in the closed loop state, that is, S'(t) = 0. So we have:

[0079]

[0080] Solving the above first-order differential equation, we can obtain:

[0081]

[0082] Among them, θ e (t0) represents the deviation between the desired angular position and the actual angular position at time t0.

[0083] From the above formula, we can see that when t→∞, e1(t)→0. Therefore, when t→∞, That is, the optoelectronic pod system is asymptotically stable in a closed-loop state.

[0084] Since S′(t) = 0 always holds true for t∈[t0,∞], the optoelectronic pod system exhibits global sliding mode characteristics in the closed-loop state. To suppress the chattering caused by the sliding mode transition and make the optoelectronic pod system asymptotically stable under non-asymptotically stable conditions, a saturation function is used instead of a sign function. Furthermore, to address the effects of parameter uncertainty, a sigma correction method is used. The modified adaptive exponential sliding mode exponential controller is:

[0085]

[0086] The saturation function sat(S′) in the formula is specifically expressed as follows:

[0087]

[0088] Where the boundary layer thickness ε>0, the estimated switching gain The specific expression is:

[0089]

[0090] Finally, the output of the adaptive exponential sliding mode controller based on the disturbance observer can be expressed as:

[0091] U′=u D +u smc

[0092] In the formula, U′ is the output of the adaptive exponential sliding mode controller based on the disturbance observer to realize the control of the optoelectronic pod, where u D is the output of the disturbance observer, which is mainly used to offset the aggregate uncertainty, u smc is the output of the adaptive exponential sliding mode controller, which is used to achieve global robust control of the desired angular position rotation of the optoelectronic pod under the influence of residual disturbances.

[0093] The present invention provides an adaptive exponential sliding mode control method for an electro-optical pod based on a disturbance observer. This method utilizes a disturbance observer to observe aggregated uncertainty, deriving control inputs that offset the aggregated uncertainty and mitigating the high-frequency chattering caused by the aggregated disturbance in the sliding mode variable structure control. Finally, a novel adaptive law is used to online estimate the sliding mode switching gain, avoiding the sliding mode chattering problem caused by excessive switching gain. An adaptive exponential sliding mode controller is also employed to address the issue of excessive gain adaptation, allowing the actual attitude of the electro-optical pod to converge asymptotically to the desired attitude, thereby achieving precise control of the pod.

Claims

1. An adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer, characterized in that: Here are the steps: Step 1: Based on the principle of optoelectronic pod, establish the mathematical model of optoelectronic pod system and proceed to step 2; Step 2: Based on the mathematical model of the optoelectronic pod system, establish the dynamic equations and state space equations of the optoelectronic pod; based on the dynamic equations and state space equations of the optoelectronic pod, design the sliding mode controller u smc , and establish a disturbance observer to observe the aggregate disturbance, use Lyapunov stability theorem to verify the stability of the disturbance observer, and finally obtain the control input u to offset the aggregate disturbance D , go to step 3; Step 3: The switching gain in the sliding mode controller is improved online through an adaptive law to compensate for the aggregate uncertainty and achieve dynamic correction of the control variable. To avoid excessive adaptation of the switching gain, an adaptive exponential sliding mode controller is proposed. This controller eliminates the arrival stage in the sliding mode motion, ensuring that the optoelectronic pod system always moves along the sliding mode surface and eventually converges to an equilibrium state. The optimized control variable U′ is ultimately output, improving the robustness of the optoelectronic pod and achieving precise control. In step 3, the details are as follows: Step 3-1: Assume there is an optimal switching gain The control requirements of the optoelectronic pod system in a closed loop state are met, and is the upper bound of the residual perturbation uncertainty; Using adaptive law To get an online estimate: Where: the fourth gain κ>0, is the estimated value of the optimization gain, t represents the action time, t0 represents the initial time, t m It represents the time for the optoelectronic pod to reach the sliding mode surface in the closed-loop state, where S represents the sliding mode function of the controller; Step 3-2: Design the adaptive exponential sliding mode function S′ as follows: Wherein: the first intermediate function Q=e2(t0)+ke1(t0), the fifth gain β>0, e1 is the first deviation, e2 is the second deviation, and k is the first gain; Derivative of the adaptive exponential sliding mode function: In the above formula, is the derivative of S′, is the derivative of e2, is the derivative of e1. In order to maintain the approaching speed, the exponential approaching law is adopted, and the adaptive exponential sliding mode controller is designed as follows: Among them, u smc represents the sliding mode controller, a represents the first intermediate variable, b represents the second intermediate variable, θ d is the desired angular position, is the desired angular velocity, is the desired angular acceleration, λ is the second gain; The saturation function sat(S′) in the formula is specifically expressed as follows: Wherein, the boundary layer thickness ε>0; Finally, the output U′ of the adaptive exponential sliding mode controller based on the disturbance observer is expressed as: U′=u D +in smc u D represents the control input that offsets the aggregate uncertainty; Go to step 4; Step 4: In order to prove the stability of the adaptive exponential sliding mode controller in the optoelectronic pod closed-loop system, the Lyapunov stability theorem is proved.

2. The adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer according to claim 1, characterized in that: In step 1, the mathematical model of the optoelectronic pod system is: Electromagnetic time constant Electromechanical time constant Among them, R is the armature resistance of the photoelectric pod rotating motor, L is the inductance of the photoelectric pod rotating motor, C e is the back electromotive force coefficient, C m is the torque coefficient, J is the load moment of inertia, K pwm is the power amplification factor, s is the Laplace variable, θ(s) is the control input, and U(s) is the control output.

3. The adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer according to claim 2, characterized in that: In step 2, based on the mathematical model of the optoelectronic pod system, the dynamic equations and state space equations of the optoelectronic pod are established; based on the dynamic equations and state space equations of the optoelectronic pod, the sliding mode controller u is designed. smc , and establish a disturbance observer to observe the aggregate disturbance, use Lyapunov stability theorem to verify the stability of the disturbance observer, and finally obtain the control input u to offset the aggregate disturbance D , as follows: Step 2-1: Considering the influence of external disturbances on the optoelectronic pod, the dynamic equation of the optoelectronic pod is expressed as: in, represents the angular acceleration, represents the angular velocity, U is the control voltage; Step 2-2: Use the state space equation of the optoelectronic pod to describe the impact of uncertainty on the system, as follows: Among them, x1 is the first variable, x2 is the second variable, is the derivative of x1, is the derivative of x2, the first intermediate variable The second intermediate variable D represents the uncertainty of the mathematical model parameters of the optoelectronic pod system and the aggregate uncertainty of the external disturbance torque; Among them, θ d is the desired angular position, is the desired angular velocity; Step 2-3: Design the sliding mode controller u smc ; Where S is the designed sliding mode function; η is the switching gain, λ is the second gain, both are positive numbers, and sgn(·) represents the sign function; Step 2-4: Use the disturbance observer to observe the aggregate uncertainty in the optoelectronic pod system. Take x1 as the actual position signal and x2 as the actual speed signal. Send the above two as inputs to the disturbance observer to obtain the control input u that offsets the aggregate uncertainty. D ; Step 2-5: In order to verify the stability of the disturbance observer, an observation error with aggregated uncertainty is given as Assume that the aggregate uncertainty changes slowly, so Close to zero, and Take the derivative: in, is a disturbance observer to obtain an estimate of the aggregate uncertainty, Expressed as The derivative of ; l is the third gain; represents the derivative of the auxiliary variable z; Assume that the Lyapunov function Derivative of the Lyapunov function: because By solving the equation, we get Among them, the variable C0 is a constant, and is related to the initial value; when the action time t→∞, That is, the disturbance observer observes the estimated value of the aggregate disturbance Converges exponentially to the actual aggregate uncertainty D; Step 2-6: When the optoelectronic pod system is disturbed by external factors, the disturbance observer can be used to observe the estimated value of the aggregate uncertainty. After adjusting the second intermediate variable, the control input to offset uncertainty can be obtained. The specific formula is as follows:

4. The adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer according to claim 3 is characterized in that: In step 2-3, design the sliding mode controller u smc , as follows: 2-3-1. Design a sliding mode function to describe the degree of deviation between the angular position and angular velocity of the optoelectronic pod, so that the optoelectronic pod system converges to the desired control point after entering the sliding mode motion, ensuring that the optoelectronic pod system has good dynamic quality. According to the state space equation, let the first deviation e1 = x1-θ d , the second deviation where θ d is the desired angular position, For the desired angular velocity, design the sliding mode function S: S=e2+ke1 Where k is the first gain, and k>0; 2-3-2. Design a sliding mode control law to make the system state of the optoelectronic pod slide quickly along the sliding mode surface to the desired state, thereby achieving accurate tracking and robust control of the state of the optoelectronic pod system; Before the system state of the optoelectronic pod moves along the sliding surface, there will be a period of approaching motion. The movement of the optoelectronic pod system from any initial state to the sliding surface until it reaches the sliding surface is called approaching motion. A suitable approaching law is used to improve the dynamic quality of the approaching motion and suppress the influence of sliding mode chattering. Here, the exponential approaching law is used. express: Where η is the switching gain, λ is the second gain, both are positive numbers, and sgn(·) represents the sign function; 2-3-3. Design sliding mode controller u smc for:

5. The adaptive exponential sliding mode control method for an optoelectronic pod based on a disturbance observer according to claim 4 is characterized in that: In step 2-4, a disturbance observer is used to observe the aggregate uncertainty in the optoelectronic pod system. x1 is used as the actual position signal and x2 as the actual speed signal. The two are fed into the disturbance observer as inputs to obtain the control input u that offsets the aggregate uncertainty. D : The input of the disturbance observer is the actual signal of the control system, namely the actual position signal and the actual speed signal; the disturbance observer is used to obtain the estimated value of the aggregate uncertainty Based on the actual signal, it can make real-time estimates of external disturbances and parameter uncertainties, and use the estimated values ​​to compensate for the influence of aggregate disturbances on the control accuracy of the optoelectronic pod. Defining auxiliary variables l is the third gain, and the designed disturbance observer is as follows: in, represents the derivative of z.

Images