30.114 Advanced Feedback and Control

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Extending feedback control theory and applications (from 30.101 Systems & Control) to include multi-input & multi-output and discrete-time systems. Mathematical modeling and analysis of discrete time systems in various disciplines using state-space, pulse transfer function and z-transform. Relating controllability and observability and their canonical forms to synthesize and design advanced continuous and discrete-time controllers. Introduction of pole-placement based controller design and formulation of state observers.


Course Lead/Main Instructor


The goal of this class is to build on understanding of linear time-invariant state space systems to synthesize and evaluate advanced feedback controllers as well as digital implementation of such controllers. It has wide applications including, mechatronics, robotics, automation, space technology, transportation & aviation, medical systems, financial markets and energy management.

Learning Objectives

  • Represent physical systems in continuous state-space canonical forms and solve the linear time-invariant (LTI) state equation.
  • Assess the controllability and observability of LTI state-space continuous-time and discrete-time systems for stability analysis, design of controllers and regulators with specific dynamic performances.
  • Extend modelling principles to describe discrete-time systems and represent them using pulse transfer functions and state-space.
  • Analyze and synthesize discrete time control systems using the z transform and root locus.
  • Convert a continuous time system to a discrete-time system and vice-versa.

Measurable Outcomes

  • Given a physical system, conceive a set differential equations and difference equations describing continuous and discrete-time model of the system and representing it state-space. [LO1, LO3]
  • Describe the notion of controllability and observability for both continuous and discrete-time systems and design full and reduced-order state observers and state feedback and integral controllers [LO2].
  • Apply Eigenvalue analysis to determine poles and subsequent stability of state-space system. [LO2]
  • Based on a performance specification, design a suitable digital compensator for a discrete-time system using z-transform and on the z-plane using root-locus analysis. [LO2]
  • Model and represent discrete time signals and systems using the z Transform and solve LTI difference equation and the systems that these equations describe using the inverse z transform and the z plane. [LO4]
  • With a system described in a continuous-time representation, express the corresponding system in a discrete-time representation and be able to map between the s-plane of continuous systems to z-plane of discrete-time systems. [LO5]


Integrated and unified theoretical and practical approach in continuous-time and discrete-time control engineering and their applications. Embedded 1D, and 3D group and individual design activities.

Class structure:

  • Monday (2.5 hr): Active Learning
  • Tuesday (2.5 hr): Active Learning + Design Experience (1D/3D)

All handouts and supplements will be available on eDimension.

Software integration:

  • MATLAB and Control System Toolbox
  • LabVIEW and Control Design Toolkit plus Quanser QNETs
  • C Programming and Ubuntu (Virtual Machine)

Text & References

Primary Texts

  • Feedback Control of Dynamic Systems by Gene F. Franklin, J. David Powell, Abbas Emami-Naeini
  • Modern Control Engineering by Katsuhiko Ogata
  • Discrete-time Control Systems by Katsuhiko Ogata

Additional References:

  • Digital Control of Dynamic Systems by Gene F. Franklin, J. David Powell, Michael Workman
  • Linear Systems Theory by João P. Hespanha.
  • Linear Systems by Thomas Kailath.


Finals – 30%

Mid-term – 25%

1D / 3D Design Experience – 20%

In-class Assignments & Homework – 15%

Instructor Prerogative (e.g. attendance) – 10%


Late submissions will be penalized.