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Control System Design

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Maple has tools for linear control system design in the DynamicSystems package. You can



Work with transfer functions, state space models, or differential equations


Linearize systems


Analyze the controllability, observability, phase and gain margin, and more


Generate control plots, including Bode, root-locus and Nyquist plots


Work symbolically or numerically

In this example, we will calculate the controllability matrix of a model of a DC motor, and generate a root-locus plot.

DC Motor System


restart: withDynamicSystems:

eq_symLi.t+R⋅it=vt−K⋅θ.t,Jθ..t+b⋅θ.t+Ks⋅θt=K⋅it :

paramsJ=0.1, b=0.1, K=0.01, R=1, L=0.5, Ks = 1:


Controllability Matrix and Root-Locus Plot



sys_num  StateSpaceeq_num, inputvariable=vt, outputvariable=thetat,it:





Symbolic Controllability Matrix


You can also work symbolically, and maintain the parameter relationships present in the original equation system. Here, for example, we generate a symbolic controllability matrix.

sys_sym  StateSpaceeq_sym, inputvariable=vt, outputvariable=thetat,it:





Robot Arm Code Generation

LQR Controller for Inverted Pendulum