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Control System Toolbox 8 Design and analyze control systems Control System Toolbox provides tools for systematically analyzing, deg, and tuning linear control systems. You can specify a linear model of your system, plot its time and frequency responses to understand how the system behaves, tune the controller parameters using automated and interactive techniques, and performance requirements, such as rise time and gain/phase margins. Workflow-based graphical interfaces (GUIs) guide you through each step of the analysis and design process.

Key features ■ Enables design of single-loop and multi-loop control systems using a variety of classical and state-space techniques ■ Lets you analyze system responses and performance using a GUI or command-line functions ■ Manually or automatically tunes SISO loops in Simulink® models (with Simulink® Control Design, available separately) ■ Optimizes control system performance to meet time- and frequency-based requirements (with Simulink® Response Optimization, available separately) ■ Represents and manipulates linear models as transferfunction, state-space, zero-pole-gain, and frequency-response data objects ■ Converts between model representations, discretizes continuoustime models, and computes low-order approximations of highorder systems ■ Uses state-of-the-art algorithms built on the LAPACK and SLICOT libraries for optimal performance and accuracy

Control and Estimation Tools Manager (above), a workflowbased GUI that lets you perform interactive design, graphical tuning, and analysis of compensators (right).

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Proportional-integral-derivative (PID) tuning with the Control and Estimation Tools Manager, which provides automated tuning algorithms for stable and unstable systems.

Working with Control System Toolbox

Creating and Manipulating Linear Models

Linear control techniques are the foundation of control system design and analysis. Control System Toolbox lets you create linear models of your control system. Using interactive visualization tools, you can analyze these models to gain insight into the control system’s behavior, performance, and limitations. You can also systematically tune the control system parameters using singleand multi-loop design techniques.

Control System Toolbox lets you represent and manipulate linear models of dynamic systems as objects. All standard representations are ed, including transfer function, zero-pole-gain, explicit and descriptor state space, and frequency response data. Linear models can be SISO, MIMO, continuous, or discrete. In addition, you can accurately model and simulate systems with time delays, including loops with delays.

The linear models from Control System Toolbox can be used in other control design products, such as Robust Control Toolbox and Model Predictive Control Toolbox. Together with Simulink Control Design and Simulink Response Optimization, Control System Toolbox provides a comprehensive, GUI-driven toolset for analyzing and tuning control systems built in Simulink.

Control System Toolbox provides commands for: • Performing arithmetic on linear models • Building complex block diagrams by connecting simple models in series, parallel, or • Discretizing continuous-time models • Computing low-order approximations of high-order models You can also use the LTI block to bring linear model objects into Simulink.

Building a linear model of your plant is usually the first step in deg a control system. If no plant model is available, you can build one by fitting test data using System Identification Toolbox, or by linearizing a Simulink model using Simulink Control Design (both available separately). Either model can be imported into Control System Toolbox as an object. Once you have created an object that represents your plant, you can use Control System Toolbox to analyze and control it.

Analyzing Models Control System Toolbox provides extensive GUIs and command-line functions for analyzing linear systems. Using the LTI Viewer, you can view and compare the time and frequency responses of several linear models at once. You can also inspect key performance parameters, such as rise time, maximum overshoot, and stability margins. Available plots include step, impulse, Bode, Nichols, Nyquist, singular value, and pole/ zero plots. You can simulate the response to -defined inputs and initial conditions to further investigate system performance.

Deg Single-Loop Control Systems Control System Toolbox provides command-line and GUI tools for deg SISO control systems. With the SISO Design Tool GUI you can: • Design common control components, such as proportional integral derivatives (PIDs), lead/lag networks, and notch filters • Automatically tune controllers using algorithms, such as Ziegler-Nichols, Internal Model Control (IMC), and LinearQuadratic-Gaussian (LQG) design • Graphically tune SISO loops using classical tools, such as root locus, Bode diagrams, or Nichols charts

• Monitor closed-loop responses and performance requirements in real time while tuning your controller • Evaluate design factors, such as choice of sample time and controller complexity When used with Simulink Control Design, the SISO Design Tool lets you tune controllers directly in Simulink. When used with Simulink Response Optimization, it lets you optimize the control system parameters to enforce time and frequency-based performance requirements. When used with Robust Control Toolbox, it lets you automatically shape open-loop responses using H-infinity algorithms.

Interactive compensator design in Simulink. You can access the Control Systems Toolbox functionality from within Simulink by using Simulink Control Design (available separately).

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Deg Multi-Loop Control Systems Control System Toolbox s established methods for MIMO design, including LQG and pole placement algorithms. It also provides tools for deg observers, including Kalman filters. You can use the SISO Design Tool from within Simulink Control Design to tune multi-loop controllers consisting of several SISO loops. You can close SISO loops sequentially, visualize loop interactions, and iteratively tune each loop for best overall performance. You can then export the tuned parameters to Simulink and further validate the design through nonlinear simulation.

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Related Products Simulink. Simulation and Model-Based Design Robust Control Toolbox. Design robust controllers for plants with uncertain parameters and unmodeled dynamics Simulink Control Design. Design and analyze control systems in Simulink Simulink Response Optimization. Optimize parameters in Simulink models System Identification Toolbox. Create linear and nonlinear dynamic models from measured input-output data

Platform and System Requirements For platform and system requirements, visit www.mathworks.com/products/control ■

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