Advanced Control Systems

Problem

• A single degree-of-freedom (DOF) rotating joint is asked to behave like a precision tool, moving rapidly between targets rather than drifting or oscillating

• The challenge is to make the joint settle exactly where intended, every time, under realistic dynamic constraints

Why it matters

• Precise joint-level control is the foundation of industrial robotics. Without it, pick-and-place systems become slow, inaccurate, and unsafe

• Single-joint control problems scale directly to multi-DOF robotic arms, making this a core building block of modern automation systems

Approach

• Leveraged Symmetric Root Locus-informed LQR design to systematically translate time-domain specifications into optimal state weighting, ensuring fast, critically damped responses while minimising steady-state error

• Incorporated discrete-time Kalman filtering (LQG) for optimal state estimation under noisy measurements, applying the separation principle to independently tune controller and observer while maintaining guaranteed closed-loop stability

• Implemented constrained MPC with receding horizon optimisation, integrating input/state constraints and prediction horizons to balance aggressive tracking with actuator limitations and achieve robust, real-time reference following

Key Insight

• Achieving precise control requires careful trade-offs between state tracking performance and control effort, systematically tuned through Q/R ratios in LQR and W/V ratios in Kalman filtering

• Augmenting the system to include integrators and disturbance models allows principled application of the Internal Model Principle for zero steady-state error and predictable disturbance rejection

• Optimal performance emerges from holistic integration of control, estimation, and predictive strategies, highlighting the value of rigorous theoretical foundations applied to practical nonlinear systems

• Tuning parameters such as MPC horizon length, input change penalties, and observer gains directly impact transient behaviour and robustness, demonstrating that detailed engineering choices materially affect system-level performance

Result

• Achieved near-zero steady-state error across all controllers with maximum overshoot limited to 3–4° and sub-second settling times

• LQG observer accurately estimated states under process and measurement noise, with estimation error <1.5° even during reference reversals

• MPC with receding horizon and constraints maintained reference tracking with negligible overshoot, demonstrating predictive control under physical input limits

• Input signals remained well within actuator limits, confirming robust, energy-efficient operation without saturation