In master I get the solution
In [46]: sympy.solve(eq.coeffs(), [K_C, tau_I, tau_D])
Out[46]:
⎡ ⎧ -(τ₁ + τ₂) τ₁⋅τ₂ ⎫⎤
⎢{K_C: 0, τ_I: 0}, ⎨K_C: ───────────, τ_D: ───────, τ_I: τ₁ + τ₂⎬⎥
⎣ ⎩ K⋅(φ - τ_c) τ₁ + τ₂ ⎭⎦
It looks like whatever fixed it will be included in 1.0 (it's also
fixed in the 1.0 release branch).
Aaron Meurer
On Tue, Feb 23, 2016 at 12:43 AM, Carl Sandrock <[email protected]> wrote:
> I am attempting to work a problem from a textbook in sympy, but sympy fails
> to find a solution which appears valid. For interest, it is the design of a
> PID controller using direct synthesis with a second order plus dead time
> model.
>
> The whole problem can be reduced to finding K_C, tau_I and tau_D which will
> make
>
> K_C*(s**2*tau_D*tau_I + s*tau_I + 1)/(s*tau_I) = (s**2*tau_1*tau_2 + s*tau_1
> + s*tau_2 + 1)/(K*s*(-phi + tau_c))
>
>
> for given tau_1, tau_2, K and phi.
>
>
> I have tried to solve this by matching coefficients:
>
>
> import sympy
>
>
> s, tau_c, tau_1, tau_2, phi, K = sympy.symbols('s, tau_c, tau_1, tau_2, phi,
> K')
>
> target = (s**2*tau_1*tau_2 + s*tau_1 + s*tau_2 + 1)/(K*s*(-phi + tau_c))
>
> K_C, tau_I, tau_D = sympy.symbols('K_C, tau_I, tau_D', real=True)
> PID = K_C*(1 + 1/(tau_I*s) + tau_D*s)
>
> eq = (target - PID).together()
> eq *= sympy.denom(eq).simplify()
> eq = sympy.poly(eq, s)
>
> sympy.solve(eq.coeffs(), [K_C, tau_I, tau_D])
>
> This returns an empty matrix. However, the textbook provides the following
> solution:
>
> booksolution = {K_C: 1/K*(tau_1 + tau_2)/(tau_c - phi),
> tau_I: tau_1 + tau_2,a
> tau_D: tau_1*tau_2/(tau_1 + tau_2)}
>
> Which appears to satisfy the equations I'm trying to solve:
>
> [c.subs(booksolution).simplify() for c in eq.coeffs()]
>
> returns
>
> [0, 0, 0]
>
> Can I massage this into a form which sympy can solve? What am I doing wong?
>
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