開發紀錄:雲台 LOS 優化文獻回顧——量出頻率響應之後,控制端還能做什麼

這是 LocalPapa Notes 開發紀錄系列的第十九篇。上一篇整理了三種 LOS 光學量測架構,並講到「把雲台裝上擾動台,量出擾動抑制的閉迴路頻率響應」這一步。但量到頻率響應之後呢?如果抗擾頻寬不夠、或某個頻段的靈敏度峰值超標,控制端有哪些手段可以優化?這篇整理我們讀過的後續文獻——控制演算法、摩擦補償、機構最佳化,以及一條還在驗證階段的新方向。

為什麼「算出扭力」跟「壓住抖動」是兩件事

雲台馬達選型計算機回答的是「需要多少扭力」,量測驗證區塊回答的是「做出來的東西有沒有達標」。但即使馬達選對了、量測也做了,如果抗擾頻寬還是不夠,下一步不是換更大的馬達,而是優化控制迴路——同一顆馬達在不同控制演算法下,能壓住的擾動頻寬可以差好幾倍。這正是這篇要整理的內容。

一、控制演算法:主動抗擾控制(ADRC)是這幾年的主流

傳統做法用 PID 加上一個手調的擾動觀測器;這幾年的文獻明顯往「主動抗擾控制」(Active Disturbance Rejection Control, ADRC)集中,核心想法是把所有沒被精確建模的東西(摩擦、耦合扭矩、外部擾動、參數誤差)打包成一個「總擾動」,用擴張狀態觀測器(Extended State Observer)即時估計出來再主動抵消,而不是逐項分別建模補償。

  • 混合座標系 + 逐關節擾動觀測器:一篇 2025 年發表於《International Journal of Control, Automation and Systems》的雲台穩定控制論文,把關節座標與慣性座標結合成串級控制器,每個關節各配一個獨立的擾動觀測器,同時消除外部擾動、內部摩擦、軸間耦合扭矩與模型不確定性。這正好接在「量出頻率響應之後」這一步——擾動觀測器的設計本身就需要一個準確的受控體模型,而那個模型的參數(慣量、摩擦係數)正是計算機與量測驗證區塊在做的事。
  • 神經網路/計算力矩模型輔助 ADRC:追蹤誤差最多可降低 85.4%(神經網路輔助)與 40.8%(計算力矩模型輔助)。差距這麼大代表「用什麼方式估計未建模動態」本身就是設計裡的一個重要選擇,不是隨便換一種都差不多。
  • 智慧最佳化演算法自動調參:ADRC 雖然比 PID 抗擾能力強,但參數更多、更難手調。一條明確的解法是用最佳化演算法自動搜尋——粒子群最佳化與差分演化的混合演算法(PSO-DE)用於高精度姿態穩定的 Reduced ADRC;三軸慣性穩定平台則用遺傳演算法(GA)調參,鎖定空拍應用下的多源擾動抑制。
  • 雙補償器架構(Dual-Compensator DOBC):兩個獨立的擾動觀測器並聯運作,抑制能力比單一補償器更強,用來處理慣性穩定平台「非最小相位」特性——這是傳統擾動觀測器設計已知的難題(非最小相位系統的零點在右半平面,觀測器增益不能無限拉高,否則系統本身會不穩定)。

二、滑模控制:處理非線性與模型不確定性的另一條路線

滑模控制(Sliding Mode Control)是另一個常見選擇,特點是對模型誤差與外部擾動有天生的強健性,代價是傳統滑模控制的切換動作會產生高頻抖振(chattering),實務上得用連續化的變體解決:

  • Adaptive super-twisting sliding mode + 擴張狀態觀測器:super-twisting 是二階滑模的一種,把切換動作做成連續函數,緩解傳統滑模的抖振問題。
  • Fast terminal sliding mode + SDRE 觀測器:終端滑模(terminal sliding mode)讓誤差在有限時間內收斂到零,而不是傳統滑模的漸近收斂;SDRE(State-Dependent Riccati Equation)觀測器則處理非線性系統的狀態估計。
  • Proxy-based sliding mode:引入一個「代理」變數取代直接切換,這篇論文有直接跟傳統 PID 比較,量化了改善幅度。

三、摩擦補償:把數字接上我們已經引用的那篇論文

上一篇文章引用的 Sightline Jitter Minimization and Shaping Using Nonlinear Friction Compensation(2007)講的是自準直儀量測架構,這條研究線後續有更明確的量化結果:

  • 92 µrad → 30 µrad:摩擦補償器把 LOS jitter 從 92 微弧度壓到 30 微弧度以下。這個數字很有用,因為它給了「摩擦補償這件事值不值得做」一個具體量級——不是抽象地說「有幫助」,而是接近三倍的改善。
  • Time-Delay Control + 二自由度 Internal Model Control:用於磁懸浮控制力矩陀螺(CMG)的雲台系統,結合時延控制估計摩擦扭矩、內模控制做前饋消除。
  • 改良 Coulomb-Viscous 摩擦模型:針對諧波減速器(harmonic drive)的雲台伺服系統,把摩擦扭矩表示成角速度與角位置的函數,而不是簡化成單一庫倫摩擦常數。
  • 雙編碼器融合(load encoder + motor encoder):用負載端與馬達端兩顆編碼器的讀數差補償齒輪傳動的非線性擾動(背隙、彈性變形),這是「用感測器融合取代精確建模」的思路,跟純軟體的摩擦補償是互補而非取代關係。

摩擦比例在我們的計算機裡是一個經驗值(預設 15%),這批文獻說明了為什麼——摩擦本身是強非線性、跟角速度和位置都有關,很難用一個常數完整描述。經驗比例是一階近似,真正要壓低摩擦造成的抖動,得靠上面這些補償演算法。

四、機構設計:輕量化不必然犧牲剛性

前面三節都是控制端的優化,但雲台的抖動抑制能力有一半天花板是機構本身決定的——結構共振頻率越低,控制頻寬能拉多高就越受限(拉高頻寬會激振到共振模態)。這方面找到一個很具體的案例:

  • 雙軸慣性穩定平台內框有限元模態分析最佳化:酬載承載框架減重 35%,同時第一階扭轉振動模態頻率提升 22%,整體動態性能提升 75%。這個案例值得注意的地方是:減重與提升剛性同時做到了,不是「這次犧牲重量換剛性」的取捨,而是找出結構上真正沒必要存在的材料(有限元模態分析能定位哪些區域對整體剛性貢獻低、可以挖空減重)。
  • 同時考慮摩擦、共振、振動三個效應的系統性能模型:把三種擾動源放進同一個分析框架,而不是分開處理。這跟我們上一篇文章第 6 節「RMS 看達標與否、PSD 看根因」的邏輯是同一件事的更完整版本——PSD 分析能分辨的正是這三種效應各自主宰的頻段。

這給馬達選型計算機裡的轉動慣量欄位一個補充觀點:J 只是「有多重、離軸多遠」,但同一個 J 值,結構剛性可以差很多——真正決定控制頻寬上限的往往不是 J 本身,而是第一階共振頻率。這是計算機目前沒有涵蓋、但值得列入知識庫的一個提醒。

五、強化學習:一條還在驗證中的新方向

  • DDPG(Deep Deterministic Policy Gradient)用於雲台目標追蹤(2024,Drones 期刊):在 Unity 模擬環境裡訓練雲台執行追蹤動作,取代傳統的追蹤控制迴路。
  • TD3(Twin-Delayed DDPG)用於控制力矩陀螺陣列的角動量控制(2025,太空應用):嚴格來說不是雲台,但控制問題結構相同——多軸耦合扭矩分配,可以類比到多軸雲台的軸間耦合補償。

老實說,這條線目前多半還停在模擬環境驗證,還沒看到跟我們上一篇文章引用的 JWST 在軌實測同等級的驗證。列進來是因為方向值得追蹤,但目前不建議拿來取代前面提到的 ADRC/滑模控制這些已經有實測數據支撐的方法。

這些文獻在計算機/量測工具裡的落點

  • ADRC/滑模控制量測驗證區塊量出頻率響應之後,控制端優化的下一步;目前計算機本身不涉及控制器設計
  • 摩擦補償量化效果(92→30 µrad) → 計算機的「摩擦阻力比例」經驗值背後的物理依據
  • FEM 模態最佳化案例 → 計算機「轉動慣量 J」欄位的補充提醒——結構剛性與共振頻率同樣重要,但目前未建模
  • 強化學習 → 方向追蹤用,暫不影響工具設計

參考文獻

  • Enhanced 2-axis Gimbal Stabilization Control via a Hybrid Coordinate System Approach With Disturbance Observer. International Journal of Control, Automation and Systems (2025). 連結
  • Stabilization of two-axis line-of-sight system using active disturbance rejection control. Multibody System Dynamics (2025). 連結
  • On Dual Compensation to Disturbances and Uncertainties for Inertially Stabilized Platforms. International Journal of Control, Automation and Systems. 連結
  • A GA-based parameters tuning method for an ADRC controller of ISP for aerial remote sensing applications. ScienceDirect. 連結
  • A Robust Double Active Control System Design for Disturbance Suppression of a Two-Axis Gimbal System. Electronics (MDPI). 連結
  • Fast terminal sliding mode control based on SDRE observer for two-axis gimbal with external disturbances. Journal of the Brazilian Society of Mechanical Sciences and Engineering (2022). 連結
  • Adaptive super-twisting sliding mode control for stabilization platform of laser seeker based on extended state observer. Optics & Laser Technology. 連結
  • Proxy-Based Sliding Mode Stabilization of a Two-Axis Gimbal System. Proc. WCECS (2011). 連結
  • Research on Nonlinear Friction Compensation of Harmonic Drive in Gimbal Servo-system of DGCMG. International Journal of Control, Automation and Systems. 連結
  • Friction Compensation Based on Time-Delay Control and Internal Model Control for a Gimbal System in Magnetically Suspended CMG. IEEE Journals & Magazine. 連結
  • Combining Load and Motor Encoders to Compensate Nonlinear Disturbances for High Precision Tracking Control of Gear-Driven Gimbal. PMC. 連結
  • Learning-Based Control Compensation for Multi-Axis Gimbal Systems. arXiv:2112.02561. 連結
  • Design Optimization of the Inner Gimbal for Dual Axis Inertially Stabilized Platform Using Finite Element Modal Analysis. 連結
  • System Performance of an Inertially Stabilized Gimbal Platform with Friction, Resonance, and Vibration Effects. 連結
  • Manipulating Camera Gimbal Positioning by Deep Deterministic Policy Gradient Reinforcement Learning for Drone Object Detection. Drones, 8(5), 174 (2024). DOI: 10.3390/drones8050174
  • Angular Momentum Control Strategy of Control Moment Gyroscope Array Based on Deep Reinforcement Learning in Spacecraft Attitude Control System (2025). 連結

上一篇:雲台 LOS 光學量測系統怎麼架。想試算馬達規格?雲台馬達選型計算機。想追蹤系列後續?把 LocalPapa Notes 加入書籤吧。

Dev Log: A Literature Review of Gimbal LOS Optimization — What Happens After You Measure the Frequency Response

This is the nineteenth post in the LocalPapa Notes dev-log series. The last post covered three optical measurement architectures for LOS jitter, ending with mounting the gimbal on a shaker table to extract the closed-loop disturbance-rejection frequency response. But what happens after you have that frequency response? If the rejection bandwidth falls short, or the sensitivity peak exceeds spec at some frequency, what can the control side actually do about it? This post reviews the follow-on literature — control algorithms, friction compensation, structural optimization, and one still-unproven new direction.

Why "calculating torque" and "suppressing jitter" are two different problems

The Gimbal Motor Sizing Calculator answers "how much torque do I need"; the measurement verification panel answers "does what I built actually hit the target." But even with the right motor and a completed measurement pass, if the rejection bandwidth still falls short, the next move isn't a bigger motor — it's optimizing the control loop. The same motor under different control algorithms can suppress disturbance over bandwidths differing by several times. That's what this post digs into.

I. Control algorithms: Active Disturbance Rejection Control (ADRC) dominates recent work

The traditional approach pairs PID with a hand-tuned disturbance observer. Recent literature clusters heavily around Active Disturbance Rejection Control (ADRC) instead: bundle everything that isn't precisely modeled — friction, coupling torque, external disturbance, parameter error — into a single "total disturbance," estimate it in real time with an Extended State Observer, and cancel it actively, rather than modeling and compensating each term separately.

  • Hybrid coordinate system with a per-joint disturbance observer: a 2025 paper in International Journal of Control, Automation and Systems combines joint and inertial coordinate frames into a cascade controller for gimbal stabilization, with an independent disturbance observer on each joint eliminating external disturbance, internal friction, cross-axis coupling torque, and model uncertainty in one shot. This picks up exactly where "measuring the frequency response" leaves off — designing a disturbance observer requires an accurate plant model, and the parameters of that model (inertia, friction coefficient) are exactly what the calculator and measurement panel are producing.
  • Neural-network and computed-torque-model assisted ADRC: tracking error reduced by up to 85.4% (neural-network-assisted) and 40.8% (computed-torque-model-assisted). The size of that gap says something on its own — how you estimate the unmodeled dynamics is a real design choice, not an interchangeable detail.
  • Intelligent optimization for automatic parameter tuning: ADRC rejects disturbance better than PID but has more parameters and is harder to hand-tune. One clear answer is automated search — a hybrid Particle Swarm Optimization / Differential Evolution algorithm (PSO-DE) tunes a Reduced ADRC for high-precision attitude stabilization, while a Genetic Algorithm (GA) tunes a three-axis inertially stabilized platform against multi-source disturbance for aerial applications.
  • Dual-Compensator DOBC: two independent disturbance observers running in parallel reject disturbance more strongly than a single compensator, addressing the "nonminimum-phase" property of inertially stabilized platforms — a known limitation of conventional disturbance-observer design (a nonminimum-phase system has right-half-plane zeros, so observer gain can't be pushed arbitrarily high without destabilizing the plant itself).

II. Sliding mode control: another route through nonlinearity and model uncertainty

Sliding Mode Control (SMC) is the other common choice, prized for inherent robustness to model error and external disturbance — at the cost of chattering from the switching action in classical SMC, which in practice gets addressed with continuous variants:

  • Adaptive super-twisting sliding mode with an extended state observer: super-twisting is a second-order sliding mode that replaces the switching action with a continuous function, easing the chattering problem of classical SMC.
  • Fast terminal sliding mode with an SDRE observer: terminal sliding mode drives the error to zero in finite time rather than the asymptotic convergence of classical SMC; the State-Dependent Riccati Equation (SDRE) observer handles state estimation for the nonlinear system.
  • Proxy-based sliding mode: introduces a "proxy" variable in place of direct switching; this paper directly benchmarks against conventional PID and quantifies the improvement.

III. Friction compensation: putting numbers behind a paper we already cited

The previous post cited Sightline Jitter Minimization and Shaping Using Nonlinear Friction Compensation (2007) in the context of autocollimator measurement setups. That research line has more concrete follow-on results:

  • 92 µrad → under 30 µrad: friction compensation reduced LOS jitter from 92 microradians to under 30. That number is useful because it gives "is friction compensation worth doing" a concrete order of magnitude — not an abstract "it helps," but close to a threefold improvement.
  • Time-Delay Control with two-degree-of-freedom Internal Model Control: applied to a magnetically-suspended CMG gimbal system, combining time-delay control to estimate friction torque with internal model control for feedforward cancellation.
  • Improved Coulomb-Viscous friction model: for a harmonic-drive gimbal servo, friction torque is expressed as a function of angular velocity and position rather than reduced to a single Coulomb-friction constant.
  • Dual-encoder fusion (load encoder + motor encoder): the difference between load-side and motor-side encoder readings compensates for nonlinear disturbance from gear-train backlash and elastic deformation — a sensor-fusion approach that complements, rather than replaces, pure software friction compensation.

Our calculator's friction ratio is an empirical value (15% by default), and this literature explains why: friction is strongly nonlinear and depends on both angular velocity and position, so it resists being captured by a single constant. The empirical ratio is a first-order approximation; actually suppressing friction-driven jitter requires the compensation schemes above.

IV. Mechanical design: lighter doesn't have to mean less stiff

The first three sections are all control-side optimization, but half the ceiling on jitter suppression is set by the mechanism itself — the lower the structural resonance frequency, the more it limits how high the control bandwidth can go (pushing bandwidth up risks exciting the resonant mode). One concrete case study stands out here:

  • Finite-element modal-analysis optimization of a dual-axis inertially stabilized platform's inner gimbal: the payload-carrying frame lost 35% of its weight while the first torsional vibration mode's frequency rose 22%, with overall dynamic performance up 75%. What makes this case notable is that weight reduction and stiffness improvement happened together — not "trading weight for stiffness this time," but identifying material that structurally wasn't contributing (modal analysis pinpoints which regions contribute little to overall stiffness and can be hollowed out).
  • A system performance model that treats friction, resonance, and vibration together: putting all three disturbance sources into one analysis framework rather than handling them separately. This is the more complete version of the "RMS tells you pass/fail, PSD tells you why" logic from Section 6 of the previous post — PSD analysis is exactly what distinguishes the frequency bands each of these three effects dominates.

This adds a useful angle to the inertia field in the motor sizing calculator: J only captures "how heavy, how far from the axis," but two payloads with identical J can have very different structural stiffness — what actually caps the achievable control bandwidth is often the first resonance frequency, not J itself. That's not something the calculator currently models, but it's worth adding to the knowledge base.

V. Reinforcement learning: a promising direction still being validated

  • DDPG (Deep Deterministic Policy Gradient) for gimbal target tracking (2024, Drones): trains a gimbal to execute tracking actions in a Unity simulation environment, replacing a conventional tracking control loop.
  • TD3 (Twin-Delayed DDPG) for control-moment-gyroscope-array angular momentum control (2025, spacecraft applications): not strictly a gimbal, but structurally the same control problem — multi-axis coupled torque allocation — and analogous to cross-axis coupling compensation in multi-axis gimbals.

Honestly, this line of work is still largely validated in simulation, and hasn't yet reached the on-orbit measurement rigor of the JWST work cited in the previous post. It's included here because the direction is worth tracking, but it isn't ready to replace the ADRC/sliding-mode methods above, which already have measured results behind them.

Where this literature lands in our tools

  • ADRC / sliding mode control → the next step after the measurement panel produces a frequency response — control-side optimization the calculator itself doesn't currently touch
  • Quantified friction compensation (92→30 µrad) → the physical basis behind the calculator's empirical "friction ratio"
  • FEM modal optimization case study → a reminder for the calculator's "inertia J" field — structural stiffness and resonance frequency matter just as much, but aren't currently modeled
  • Reinforcement learning → worth tracking; doesn't affect tool design yet

References

  • Enhanced 2-axis Gimbal Stabilization Control via a Hybrid Coordinate System Approach With Disturbance Observer. International Journal of Control, Automation and Systems (2025). Link
  • Stabilization of two-axis line-of-sight system using active disturbance rejection control. Multibody System Dynamics (2025). Link
  • On Dual Compensation to Disturbances and Uncertainties for Inertially Stabilized Platforms. International Journal of Control, Automation and Systems. Link
  • A GA-based parameters tuning method for an ADRC controller of ISP for aerial remote sensing applications. ScienceDirect. Link
  • A Robust Double Active Control System Design for Disturbance Suppression of a Two-Axis Gimbal System. Electronics (MDPI). Link
  • Fast terminal sliding mode control based on SDRE observer for two-axis gimbal with external disturbances. Journal of the Brazilian Society of Mechanical Sciences and Engineering (2022). Link
  • Adaptive super-twisting sliding mode control for stabilization platform of laser seeker based on extended state observer. Optics & Laser Technology. Link
  • Proxy-Based Sliding Mode Stabilization of a Two-Axis Gimbal System. Proc. WCECS (2011). Link
  • Research on Nonlinear Friction Compensation of Harmonic Drive in Gimbal Servo-system of DGCMG. International Journal of Control, Automation and Systems. Link
  • Friction Compensation Based on Time-Delay Control and Internal Model Control for a Gimbal System in Magnetically Suspended CMG. IEEE Journals & Magazine. Link
  • Combining Load and Motor Encoders to Compensate Nonlinear Disturbances for High Precision Tracking Control of Gear-Driven Gimbal. PMC. Link
  • Learning-Based Control Compensation for Multi-Axis Gimbal Systems. arXiv:2112.02561. Link
  • Design Optimization of the Inner Gimbal for Dual Axis Inertially Stabilized Platform Using Finite Element Modal Analysis. Link
  • System Performance of an Inertially Stabilized Gimbal Platform with Friction, Resonance, and Vibration Effects. Link
  • Manipulating Camera Gimbal Positioning by Deep Deterministic Policy Gradient Reinforcement Learning for Drone Object Detection. Drones, 8(5), 174 (2024). DOI: 10.3390/drones8050174
  • Angular Momentum Control Strategy of Control Moment Gyroscope Array Based on Deep Reinforcement Learning in Spacecraft Attitude Control System (2025). Link

Previous post: How to Build an Optical LOS Measurement Rig. Want to size a motor? Gimbal Motor Sizing Calculator. Want to follow the rest of the series? Bookmark LocalPapa Notes.

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