Target concepts (C), skills (S) & abilities (A) should be: Essentials ========== - Preliminaries - Ability to identify elements of control systems and specify their interconnections through block diagrams. (A) - Understand pros/cons of the feedback architecture. (C) - Have a conceptual understanding of typical requirements of feedback control systems (C) - Appreciate the issue of dynamic system behaviour and the need to compensate for it in control design. Notion of stability and transient/steady-state behaviour(C) - Mathematical machinery: Have the mathematical background to analyse and work with linear, constant-coefficient ordinary differential equations - LTI systems that describe single-input, single-output systems. (A) - standard representations: single linear ODE, state-space descriptions of LTI systems - importance of linearity and time-invariance - homogenous solution, particular solution for first-order systems - characteristic polynomial: location of roots on the complex plane and its influence on stability, nature of transient response - convolution integral, impulse response, step response - transient response, typical performance metrics: rise time, setting time, overshoot, steady-state error - Laplace Transforms - transfer functions, poles and zeros, algebra of transfer functions, loading effect - Frequency response: significance, relation to impulse response and TFs, Bode Plots, Nyquist Plots - Simulation Tools - Be able to simulate the response of dynamic systems in a computational environment such as MATLAB/SciLab. (A) - Modeling: - Appreciate the requirements of a control-oriented model (C) - Have the ability to invoke physical laws with appropriate assumptions and approximations to arrive at control-oriented models (described by ODEs) - Understand the significance and the process of model linearization - Understand the concept of eqbm points - Have the ability to derive the (Jacobian) linearized system given the non-linear ODE describing the dynamics of the system under investigation - Robustness: - Understand the notion of robustness in control design/analysis (C) - Appreciate the terms signal and model uncertainty (C) - Be familiar with established notions of robustness for SISO systems such as gain/phase margins, percentage variation etc. - Control Design: - Understand the process of control design (C) - Be familiar with typical control system design specifications: time-domain specifications, frequency-domain specifications - Appreciate the elements of the PID controller - Be able to synthesize simple control algorithms for LTI plants: using Root Loci, Bode Plots and pole placement techniques. (S) - Understand the importance of incorporating robustness into the design process (C) - Be able to accommodate effect of sensor noise, time delay, actuator saturation - Digital implementation of controllers - Understanding why digital implementation is useful - Basic understanding of the sampling/hold processes (A/D, D/A) - Appreciate the Nyquist sampling theorem/aliasing - Be able to arrive at discrete realizations of continuous time controllers - Appreciate the effect of sampling time on the control performance - Multivariable control - Be exposed to the state-space framework to deal with multi-input, multi-output linear systems - Elementary linear algebra: vector spaces, linear independence, basis, eigen values, eigen vectors - LTI systems (open loop) aspects: realizations, relation to transfer functions, stability, controllability, observability - LTI systems (closed loop) aspects: state-feedback controller, Luenberger Observers - Introduction to linear optimal control