High-Frequency Rotary Control Strategy

• High-frequency rotary control is a set of strategies that actuate systems at rates surpassing dominant dynamic frequencies to optimize performance.
• Techniques like cascaded feedback, phase-based control, and model predictive control ensure robust handling of nonlinearities and measurement noise.
• Real-time frequency-domain excitation and learning-based approaches deliver significant gains in energy efficiency, vibration suppression, and system stability.

High-frequency rotary control strategy refers to a broad class of feedback and feedforward control methodologies that actuate rotary systems at frequencies sufficient to excite, stabilize, or optimize high-bandwidth dynamic phenomena. These strategies are deployed across a range of applications, including flight control for small rotorcraft, fluid flow manipulation, active vibration suppression, electric machine actuation, power electronics, and advanced robotics. The technical requirements for high-frequency rotary control generally include rapid and precise input command generation, robust rejection or exploitation of system nonlinearities and measurement noise, bandwidth-aware tuning, and often the integration of safety or performance constraints.

1. Core Principles and Definitions

High-frequency rotary control comprises control architectures that execute actuation or feedback loops at rates comparable to or exceeding the dominant frequency components of the target dynamics. Typical implementations include cascaded PID or PI velocity/torque controllers with high-bandwidth motor drivers (Qian et al., 2022), real-time phase-based controllers designed for rapid perturbation of periodic flows (&&&1&&&), and open- or closed-loop high-frequency feedback (e.g., >1 kHz for torque-controlled manipulators (Zhang et al., 26 Sep 2024), >40 kHz for whole-body robot actuators (Kourdis et al., 29 Sep 2025)). In these systems, "high frequency" is relative to the dynamic time constants of the plant and may range from a few Hz (as in physical human–robot interfaces) up to tens of kHz (as in direct torque control or inverter modulation).

Central to many high-frequency rotary control strategies is the notion of frequency-domain system identification and bandwidth allocation. For instance, in the context of rotary wing UAVs, automated frequency-sweep excitation with precise bandwidth coverage yields high-coherence frequency response measurements, critical for linear model extraction and subsequent control design (0804.3881). In rotary fluidic systems, the timing of rotary actuation is designed to exploit natural phase response and vortex dynamics, with inputs tailored at the oscillation frequency of the flow (Nair et al., 2020, Sababha et al., 29 Sep 2025).

2. Methodologies for High-Frequency Rotary Actuation

The methodologies utilized in this domain can be grouped as follows:

Methodology	Key Feature	Typical Applications
Cascaded Feedback	Decoupling of torque and velocity control; bandwidth separation	Series elastic actuators, rotary drives (Qian et al., 2022)
Frequency-Sweep Excitation	Predefined frequency content excitation for sysID	Rotorcraft flight test, wind turbines (0804.3881, Strom et al., 2016)
Model Predictive Control	Dynamic model updates and constraint handling at high rate	VSPS frequency response (Xu et al., 2022), robotic MPC (Zhang et al., 26 Sep 2024)
Phase-Optimization	Actuation synchronized to system phase evolution	Vortex shedding control (Nair et al., 2020), AFC (Sababha et al., 29 Sep 2025)
High-Frequency PWM/Carrier	Modulation to shift/control spectral content	Induction motor vibration (Ruiz-Gonzalez et al., 25 Jan 2024)
DRL-Driven Rotary Control	Policy-learned high-frequency actuation with delay compensation	AFC/VIV suppression (Sababha et al., 29 Sep 2025)

The core implementation steps include: (1) selection of high-bandwidth actuators and sensors, (2) design of inner–outer feedback loops with bandwidth allocation, (3) integration of excitation or actuation strategies (sinusoidal, arbitrary, or adaptive), and, for learning-based or data-driven approaches, (4) continuous adaptation or augmentation of control inputs based on real-time feedback, recent actuation history, and time-series constraints.

3. Frequency-Domain Excitation and System Identification

A key motif in high-frequency rotary control is excitation using frequency-swept or band-limited inputs for system identification (sysID). In (0804.3881), a cascaded PID autopilot is structured to maintain hover while injecting automated, exponentially swept frequency excitation on individual axes. The control input is defined by:

$$u(t) = u_{min} + K(u_{max} - u_{min}), \quad K = C_2[\exp(T_{rec} t_{rec}) - 1]$$

Flight data gathered at 50 Hz is processed algorithmically (e.g., using the Chirp-Z transform and CIFER FRESPID utility) to yield frequency response functions with quantified coherence. This ensures that linear models extracted represent the true frequency-dependent dynamics of the rotary system, underpinning both controller synthesis and safety parameterization.

The same philosophy extends to optimized intracycle control for turbines (Strom et al., 2016), where the instantaneous angular velocity is parameterized as a function of the blade azimuth to maximize instantaneous power extraction, directly leveraging frequency-dependent aerodynamic effects such as dynamic stall. Profiles such as

$$\omega(\theta) = A_0 + \sum_{i=1}^3 A_i \sin(iN\theta + \phi_i)$$

are optimized in situ to align actuation energy with periods of peak physical excitation, which enhances average efficiency by up to 79% relative to constant-speed methods.

4. Advanced Feedback Architectures: Cascade, Phase-Based, and Predictive

Cascade controllers for modern rotary electromechanical systems consist of an inner high-bandwidth velocity or current loop combined with an outer torque or position loop, often leveraging series elasticity and nonlinear stiffness properties (Qian et al., 2022). For the reconfigurable rotary series elastic actuator (RRSEAns), the control architecture is:

• Outer loop (torque):

$$\dot{\theta}_d = \left(K_{pt} + \frac{K_{it}}{s}\right)(\tau_d - \tau_e)$$

• Inner loop (velocity):

$$2k_m i_m = \left(K_{pv} + \frac{K_{iv}}{s}\right)(\dot{\theta}_d - \dot{\theta})$$

High-frequency operation is crucial for both disturbance rejection and transparent pHRI, with bandwidths ranging 2.5–7.2 Hz in closed- and open-loop, respectively (Qian et al., 2022).

Phase-based control, as formalized in (Nair et al., 2020), leverages phase sensitivity functions $Z(\theta)$ derived from impulsive experiments to design minimum-energy control laws for rapid phase shifting within periodic flows. The control problem is posed as:

• Phase dynamics: $d\theta/dt = \omega_n + Z(\theta)u(t)$
• Cost function: $C[u(t)] = \int_0^{T^*} [u(t)]^2 dt$

The optimal input $u(t)$ is obtained by solving associated Euler–Lagrange equations, resulting in precise control of phase-locked aerodynamic structures such as vortex shedding.

Adaptive Model Predictive Control (AMPC) for VSPS units (Xu et al., 2022) uses on-the-fly linearization of machine and grid dynamics, with real-time Kalman filter state estimation and quadratic programming. The dual channels (electrical and mechanical) for power adjustment are coordinated to stabilize grid frequency during high-frequency excursions, with tight enforcement of operational constraints derived from electromagnetic model linearization.

5. Control under Nonlinearities, Disturbances, and Practical Constraints

High-frequency rotary systems are susceptible to nonlinear actuator dynamics, measurement noise, sensor interference, and real-world phenomena such as actuator delay and vibrational modes.

• Control conditioning approaches for current-mode systems explicitly model structured sensor interference as deterministic uncertainty rather than simply filtering it (Cui et al., 2022). Static and dynamic current mappings are repaired via techniques such as "first-event triggering with latching," resulting in globally stable operation and optimized transient response even at multi-megahertz switch rates.
• Harmonic-specific feedback: The internal model principle is applied in (Novičenko et al., 18 Mar 2024), embedding harmonic oscillators into the controller to selectively reject only the first Fourier harmonic induced by tilt or imbalance in high-speed AFM experiments, even under unknown feedback delays up to 15% of the oscillation period.
• PWM with frequency modulation: HIPWM-FMTC3 adjusts the carrier frequency discontinuously in relation to the modulating wave’s slope, redistributing output harmonics to higher frequencies and minimizing excitation of structural resonances in asynchronous machines. For optimal parameters, this results in ~4 dB reduction in vibration levels (Ruiz-Gonzalez et al., 25 Jan 2024).

6. Data-Driven and Learning-Based High-Frequency Rotary Control

Recent advancements leverage model-free or data-driven methods for real-time rotary actuation in fluid and mechanical domains. DRL-based controllers such as those employing proximal policy optimization (PPO) (Sababha et al., 29 Sep 2025) are deployed in high-frequency active flow control (AFC) for vortex-induced vibration (VIV) suppression.

• Policy learning is enhanced by augmenting state vectors with prior actuation commands, enabling compensation for known actuation delay (~200 ms in (Sababha et al., 29 Sep 2025)).
• Experimental validation shows that agents leveraging memory of past control signals can achieve >95% vibration attenuation, surpassing open-loop or state-only based approaches.
• The high-frequency rotary control modifies vortex shedding patterns by synchronizing ("locking on") cylinder rotation to the flow, confirmed by Particle Image Velocimetry.

In robotic torque control, high-frequency linear interpolation bridges the gap between infrequent nonlinear controller updates and the need for real-time stabilization (Kourdis et al., 29 Sep 2025). Linearized Jacobian feedback at up to 40 kHz greatly reduces violent vibrations associated with direct high-gain torque commands, allowing deployment of both inverse dynamics and neural policy controllers at previously unstable gains.

In high-frequency MPC contexts, first-order (gradient-based) optimization algorithms, particularly those augmented with ADAM adaptive momentum, have been shown to match the performance of classical second-order (DDP-like) algorithms but with higher iteration rates and lower computational complexity at 1 kHz control rates (Zhang et al., 26 Sep 2024).

7. Applications and Implications

The high-frequency rotary control paradigm pervades several engineering fields:

• Aerospace and Small UAVs: Automated frequency-response system identification supports development of robust stability augmentation systems and empirical state-space models (0804.3881).
• Wind and Hydrokinetic Energy: Intracycle angular velocity control of turbines synchronizes high-frequency actuation with unsteady aerodynamic loads to maximize energy capture (Strom et al., 2016).
• Power Electronics and Drives: Control conditioning in current-mode power stages extends robust operation to MHz-class switching, with direct applicability in high-frequency motor drives (Cui et al., 2022, Ruiz-Gonzalez et al., 25 Jan 2024).
• Assistive Robotics: Rotary series elastic actuators tuned for both compliance (human-robot safety) and performance (high-frequency torque tracking) (Qian et al., 2022).
• Fluid Mechanics: Phase-based rotary actuation in AFC provides precise, energy-minimal manipulation of coherent fluid structures and flow-induced vibrations (Nair et al., 2020, Sababha et al., 29 Sep 2025).

This suggests that convergence on high-frequency rotary control strategies is enabling new levels of agile, robust performance in complex, uncertainty-laden environments, particularly where plant nonlinearities, multi-physical couplings, or advanced learning-based controllers are involved. The continued evolution of actuation bandwidth, learning-enabled adaptation, robust constraint handling, and hardware-in-the-loop feedback architectures is shaping the emerging landscape of high-frequency rotary systems.