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Related Concept Videos

Controller Configurations01:22

Controller Configurations

Controller configurations are crucial in a car's cruise control system because they manage speed over time to maintain a consistent pace regardless of road conditions, thereby meeting design goals. In traditional control systems, fixed-configuration design involves predetermined controller placement. System performance modifications are known as compensation.
Control-system compensation involves various configurations, most commonly series or cascade compensation, in which the controller aligns...
PD Controller: Design01:26

PD Controller: Design

In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
Time and frequency -Domain Interpretation of PI Control01:27

Time and frequency -Domain Interpretation of PI Control

Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...
Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
First Order Systems01:21

First Order Systems

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
Phase-lead and Phase-lag Controllers01:22

Phase-lead and Phase-lag Controllers

Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass filters, manage...

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Related Experiment Video

Updated: Jul 3, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

Fixed, low-order controller design with time response specifications using non-convex optimization.

Lihua Jin1, Young Chol Kim

  • 1Department of Electronics Engineering, Graduate School, Chungbuk National University, 12 Gaesin-dong, Cheongju, 361-763, Republic of Korea. jinlihua@chungbuk.ac.kr

ISA Transactions
|July 9, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a new algorithm for designing fixed, low-order controllers for linear time-invariant (LTI) systems to meet time response specifications. The method optimizes controller parameters using least squares estimation and polynomial constraints, ensuring closed-loop stability.

Related Experiment Videos

Last Updated: Jul 3, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

Area of Science:

  • Control Systems Engineering
  • Optimization Theory
  • Linear Systems Analysis

Background:

  • Designing controllers for linear time-invariant (LTI) systems with specific time response requirements is a significant challenge.
  • Existing methods may struggle with fixed, low-order controllers, particularly in SISO plants.
  • Controller zeros can complicate achieving desired time responses in cascade feedback configurations.

Purpose of the Study:

  • To develop a novel algorithm for designing fixed, low-order controllers for single-input, single-output (SISO) LTI plants.
  • To meet precise time response specifications through an optimized control design process.
  • To formulate the controller design problem as a constrained optimization problem.

Main Methods:

  • The problem is reformulated as a least squares estimation (LSE) within partial model matching (PMM) for a two-parameter feedback configuration.
  • Closed-loop stability is enforced using polynomial matrix inequality (PMI) constraints.
  • Controller design for cascade feedback structures incorporates polynomial constraints to manage controller zeros.
  • The overall problem is solved as an optimization problem with a quadratic objective function and polynomial constraints using SeDuMi with the YALMIP interface.

Main Results:

  • A unified optimization framework is presented for designing fixed, low-order controllers that satisfy time response and stability criteria.
  • The algorithm effectively handles challenges posed by controller zeros in cascade feedback systems.
  • The SeDuMi/YALMIP tool is demonstrated as a viable solver for this class of control design problems.

Conclusions:

  • The proposed algorithm provides an effective method for designing fixed, low-order controllers for LTI SISO systems with stringent time response specifications.
  • The formulation as a constrained optimization problem simplifies the design process and ensures stability.
  • The use of computational tools like SeDuMi/YALMIP facilitates the practical implementation of the proposed control design method.