## Web-Based Control System Design and Analysis

This Web service for interactive control system design and analysis is part of Ch Control System Toolkit. Ch Control System Toolkit supports most classical and modern control techniques through object-oriented programming based on a control class. It can seamlessly interface existing C/C++ code in either source code or binary static/dynamical libraries without re-compilation. It can even be embedded in other application programs.

This Web-based system can be used for modeling, design, and analysis of continuous-time or discrete-time linear time-invariant (LTI) control systems. A control system can be modeled in the form of transfer functions, zero-pole-gain, or state-space.

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Function
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Description
Time Domain Response Analysis
Step response Plot step response of a system in time domain.
Impulse response Plot impulse response of a system in time domain.
Initial response Plot time domain initial response of a system represented in state space.
Simulation response Simulate system response to an arbitrary input.
Frequency Domain Analysis
Bode diagram Plot the Bode frequency response of a system.
Gain and phase margin Calculate the gain and phase margins of a system.
Nichols chart Plot the Nichols frequency response of a system.
Nyquist diagram Plot the Nyquist frequency response of a system.
Frequency response Calculate the system frequency response.
Controllability analysis Check whether a system is controllable.
Controllability staircase Compute the controllability staircase form.
Grammian Compute the controllability and observability grammians of a state-space model.
LQE design Kalman estimator design for continuous-time systems.
LQG design Design optimal linear quadratic state-feedback regulator for continuous-time plant.
Lyapunov equation solvers Solve Lyapunov equation.
Observability analysis Check whether a system is observable.
Observability staircase Compute observability staircase form.
Pole placement Compute the feedback gain matrix k such that the closed loop poles are at the desired locations.
Model Reduction and Dynamics
Bandwidth Calculate the bandwidth of a SISO system.
Pole-zero map Plot the pole-zero map of an LTI model.
Damping factors and natural frequencies Compute the damping factors and natural frequencies of system poles.
DC gain Compute low frequency (DC) gain of the system.
Sort poles  Sort the poles of systems.
Minimal realization Find a minimal realization of an LTI model.
Pole-zero cancellation Cancel the pole-zero pairs with same value of a system.
Root Locus Design
Root locus Plot the root locus of a SISO system.
Model Conversion
State-space model Find state-space equations for a system given transfer function or zero-pole-gain representation.
Transfer function model Find transfer function for a system given state-space equations or zero-pole-gain representation.
ZPK model Find zero-pole-gain representation for a system given state-space equations or transfer function.
System Conversion
Coordinate transformation Change state coordinates for state-space models.
Continuous-time to discrete-time Convert continuous-time models to discrete-time models.
Discrete-time to continuous-time  Convert discrete-time models to continuous-time models.
Discrete-time to discrete-time Create an equivalent discrete-time model with new sample time.
Delay2z Map all time delays to poles at z equal to 0 for discrete-time system.
System Interconnection
Series Series interconnection of two LTI models.
Parallel Parallel interconnection of two LTI models.
Feedback Feedback interconnection of two LTI models.
Append Group LTI models by appending their inputs and outputs.
Connect Connect two LTI models, user can define inputs and outputs of the connected system.