Lumped Parameter State Space Observer Implementation for Embedded Sensor Compensation
Lumped parameter state space observers reconstruct true sensor inputs by modeling internal transducer dynamic lag in firmware to eliminate delay and phase lag.
Discrete Pole Placement
Controller Synthesis
Design of state feedback control systems by positioning the closed-loop poles of a system in the discrete z-plane determines the transient response of digital controllers. The technique of discrete pole placement allows engineers to dictate the decay rate and damping ratio of the closed-loop system directly. By solving the characteristic equation, the feedback gain matrix is computed to move the open-loop poles to their desired discrete coordinates.
This method assumes that all system states are available for feedback, either through direct measurement or by utilizing a state observer.
Gain Calculation
Solving Ackermann’s formula or using matrix inversion techniques provides the feedback coefficients required to achieve the target response. High feedback gains can saturate the actuators of the physical system, causing non-linear behaviour and leading to instability. For this reason, poles must not be placed arbitrarily far from the origin of the z-plane.
Robustness Margin
Sensitivity to variation in system parameters increases when poles are grouped too close to each other or to the unit circle boundary. Modest deviations in sensor gain or physical loads can render the feedback loop unstable if the design margin is too narrow. Verification requires computing the gain and phase margins of the discrete system.
Observer Integration
Estimation of unmeasured states is necessary when physical sensors are missing or too expensive to deploy. The state observer runs in parallel with the controller, using the output of the system to update its internal state estimates. These estimated states are then used in the pole placement feedback loop instead of direct measurements.