That's great news. I will include the direct method in my notes as well.
--
This message may contain unintentional errors, as it was typed on a phone
> On 23 Feb 2016, at 22:47, Aaron Meurer <asmeu...@gmail.com> wrote:
>
> 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 <carl.sandr...@gmail.com>
>> 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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