2. Gain Scheduling
• Gain scheduling is a control technique
used when the dynamics of a system
vary significantly under different
operating conditions, making it
challenging to design a single controller
that performs optimally across all
conditions.
• Instead of using a fixed set of control
gains, gain scheduling adjusts these
gains based on the current operating
conditions of the system.
3. Key aspects of gain scheduling include
• Parameterization: Identifying key parameters that describe the
varying dynamics of the system, such as operating conditions or
environmental factors.
• Gain Scheduling Controller: Designing a controller that adjusts its
parameters (gains) based on the values of the identified parameters.
This often involves using a lookup table or a mathematical model to
determine the appropriate gains for specific operating conditions.
• Interpolation/Extrapolation: Determining the control gains for
conditions between those explicitly considered in the scheduling
process, often achieved through interpolation or extrapolation of the
scheduled gains.
4. • Gain scheduling is commonly applied in various fields, including:
• Process Control: Controlling industrial processes where operating
conditions (e.g., temperature, pressure) vary over time.
• Robotics: Adapting robot control algorithms to accommodate
changes in payload, terrain, or environmental conditions.
• Aerospace: Adjusting control gains in aircraft or spacecraft control
systems to account for changes in altitude, speed, or aerodynamic
conditions.
5.
6. Significance of gain scheduling
• The significance of gain scheduling lies in its ability to improve the
performance and robustness of control systems in situations where the
dynamics of the system vary significantly under different operating
conditions.
• This ensures optimal system performance across varying dynamics,
enhancing stability and control accuracy in applications such as
aerospace, automotive, and industrial processes where conditions
fluctuate.
7.
8. Gain scheduling
• Gain scheduling functions by dynamically adjusting control gains based on the current
operating conditions of a system.
• This involves:
1. Identifying key parameters that describe the system's varying dynamics.
2. Designing a controller that maps these parameters to appropriate control gains.
3. Updating the control gains in real-time as the system's operating conditions change.
4. Ensuring smooth transitions between different gain sets to maintain stability and
performance across varying conditions.
9. Gain scheduling- working principle
1. Parameter Identification: Key parameters affecting
system dynamics are identified. These parameters could
include environmental conditions, operating points, or
other relevant factors.
2. Gain Selection: For each set of operating conditions,
appropriate control gains are predetermined or
calculated. This could involve using mathematical
models, experimental data, or empirical relationships.
3. Interpolation/Extrapolation: If the current operating
conditions fall between the predefined sets, interpolation
or extrapolation techniques are used to determine the
appropriate control gains.
4. Adjustment: The control gains are adjusted or updated
in real-time based on the current values of the identified
parameters.
5. Control Action: The control system utilizes the adjusted
gains to regulate the system output, ensuring stability,
performance, and desired behavior under varying
operating conditions.
10. Advantages of Gain Scheduling
1. Adaptability: Gain scheduling allows
control systems to adapt to changing operating
conditions, ensuring optimal performance across a
range of scenarios.
2. Improved Performance: By adjusting
control gains in real-time, gain scheduling can
enhance system stability, response time, and
overall performance.
3. Robustness: It can improve system
robustness by compensating for uncertainties or
variations in system dynamics.
4. Flexibility: Gain scheduling offers
flexibility in controller design, as it can
accommodate nonlinearities and time-varying
dynamics more effectively than fixed-gain
controllers.
5. Optimization: It enables the
optimization of system performance under
varying conditions, leading to more efficient
operation.
Disadvantages of Gain Scheduling:
1.Complexity: Implementing gain scheduling requires a
thorough understanding of the system dynamics and the selection
of appropriate parameters for scheduling.
2.Tuning: Proper tuning of gain scheduling parameters can be
challenging, as it requires careful consideration of the system’s
behaviour under different operating conditions.
3.Interpolation/Extrapolation Errors: Errors in interpolation or
extrapolation techniques used to determine control gains for
intermediate or unexplored operating conditions can lead to
suboptimal performance or instability.
4.Performance Degradation: In some cases, gain scheduling
may not effectively address all variations in system dynamics,
leading to potential performance degradation or instability in
certain operating regimes.
5.Computational Overhead: Real-time adjustment of control
gains based on parameter values requires computational
resources, which may introduce additional computational
overhead, particularly in resource-constrained systems.
