Control Systems

What you'll learn

• Explain open- and closed-loop control, identify the elements of a feedback loop, and use the sensitivity and complementary sensitivity functions to show how feedback rejects disturbances and reduces the effect of plant changes.
• Derive dynamic models of electrical, electromechanical and thermal systems from physical laws, including a DC motor with gearbox, and linearize nonlinear plants about an operating point.
• Reduce block diagrams and signal-flow graphs to closed-loop transfer functions for references, disturbances and sensor noise, and design cascade loops.
• Relate first- and second-order step-response specifications to pole locations, express specifications as regions of the s-plane, and judge when dominant poles describe a higher-order system.
• Determine closed-loop stability and the stable range of a gain or time constant with the Routh–Hurwitz criterion, including systems with delay approximated by Padé forms.
• Classify loops by system type, compute error constants and steady-state errors to references and disturbances, and explain where integral action must sit to reject a disturbance.
• Sketch and compute root loci, apply the angle and magnitude conditions, and use the locus to decide whether gain alone can meet a specification.
• Design lead, lag, lead-lag and PID compensators by root locus, and compare designs by simulation of transient response, steady-state error, disturbance rejection and actuator effort.
• Construct Bode and Nyquist plots, apply the Nyquist criterion, and read gain margin, phase margin and peak sensitivity from a loop's frequency response, including pure delay.
• Shape loop gains with lead and lag compensators in the frequency domain, and evaluate robustness to sampling delay, structural resonance and parameter variation.
• Tune PID controllers from step tests and closed-loop experiments, prevent integrator windup, and implement continuous controllers as difference equations with adequate numerical precision.
• Design state-feedback controllers with integral action and observers by pole placement, check their margins, and combine them with trajectory planning and feedforward to meet a complete servo specification.