Related Experiment Video
Updated: May 3, 2026
08:35
Interactive and Visualized Online Experimentation System for Engineering Education and Research
Published on: November 24, 2021
2.3K
Global stability analysis in a class of second-order nonlinear uncertain systems controlled by non-ideal PD
Mahdi Samadani1, Mohammad Saleh Tavazoei1
1Electrical Engineering Department, Sharif University of Technology, Tehran, Iran.
ISA Transactions
|May 1, 2026
Summary
Implementing a non-ideal derivative in proportional-derivative (PD) controllers can impact system stability. This study identifies controller parameters to ensure global stability for nonlinear uncertain systems.
Area of Science:
- Control Systems Engineering
- Nonlinear System Analysis
- Robotics and Automation
Background:
- Practical proportional-derivative (PD) controllers often use first-order filters for the derivative term.
- This approximation can negatively affect closed-loop system stability and control performance.
- The impact of non-ideal derivatives on controlling nonlinear uncertain systems requires thorough investigation.
Purpose of the Study:
- To analyze the implications of using a non-ideal derivative in PD controllers.
- To investigate the control of second-order nonlinear uncertain systems with non-ideal PD controllers.
- To determine tunable parameters for non-ideal PD controllers that guarantee global stability.
Main Methods:
- Mathematical modeling of second-order nonlinear uncertain systems.
- Analysis of closed-loop system dynamics with non-ideal PD controllers.
- Stability analysis techniques to guarantee global fixed-point stability.
Main Results:
- Quantification of stability and performance degradation due to non-ideal derivative implementation.
- Identification of specific parameter ranges for the non-ideal PD controller.
- Demonstration of guaranteed global stability under determined parameter settings.
Conclusions:
- The use of non-ideal derivatives in PD controllers presents significant challenges for system stability.
- Careful tuning of controller parameters is crucial for ensuring reliable control of nonlinear uncertain systems.
- This research provides a method to achieve global stability guarantees for such systems.
Related Concept Videos
01:20Second Order systems I
824
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
By reinterpreting the system, one can derive the closed-loop transfer function, which...
824
01:07Time-Domain Interpretation of PD Control
500
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
500
01:26PD Controller: Design
761
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,...
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
761
01:21Control System Problem
578
In an open-loop system, such as a basic thermostat, the poles of the transfer function influence the system's response but do not determine its stability. However, when feedback is introduced to form a closed-loop system, such as an advanced thermostat that adjusts heating based on room temperature, stability is governed by the new poles of the closed-loop transfer function.
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...
578
01:26Feedback control systems
800
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
800
01:18Second Order systems II
557
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
557