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Commitfe4589b

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Merge pull request#895 from jrforbes/main
Add H2 and Hinf synthesis examples
2 parents1b84d80 +ecc9116 commitfe4589b

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‎doc/examples.rst‎

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phaseplots
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robust_siso
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robust_mimo
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scherer_etal_ex7_H2_h2syn
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scherer_etal_ex7_Hinf_hinfsyn
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cruise-control
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steering-gainsched
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steering-optimal

‎doc/scherer_etal_ex7_H2_h2syn.py‎

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../examples/scherer_etal_ex7_H2_h2syn.py

‎doc/scherer_etal_ex7_H2_h2syn.rst‎

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H2 synthesis, based on Scherer et al. 1997 example 7
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----------------------------------------------------
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Code
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....
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..literalinclude::scherer_etal_ex7_H2_h2syn.py
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:language: python
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:linenos:
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Notes
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.....
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1. The environment variable `PYCONTROL_TEST_EXAMPLES` is used for
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testing to turn off plotting of the outputs.
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../examples/scherer_etal_ex7_Hinf_hinfsyn.py
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Hinf synthesis, based on Scherer et al. 1997 example 7
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------------------------------------------------------
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Code
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....
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..literalinclude::scherer_etal_ex7_Hinf_hinfsyn.py
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:language: python
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:linenos:
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Notes
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.....
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1. The environment variable `PYCONTROL_TEST_EXAMPLES` is used for
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testing to turn off plotting of the outputs.
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"""H2 design using h2syn.
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Demonstrate H2 desing for a SISO plant using h2syn. Based on [1], Ex. 7.
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[1] Scherer, Gahinet, & Chilali, "Multiobjective Output-Feedback Control via
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LMI Optimization", IEEE Trans. Automatic Control, Vol. 42, No. 7, July 1997.
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[2] Zhou & Doyle, "Essentials of Robust Control", Prentice Hall,
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Upper Saddle River, NJ, 1998.
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"""
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# %%
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# Packages
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importnumpyasnp
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importcontrol
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# %%
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# State-space system.
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# Process model.
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A=np.array([[0,10,2],
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[-1,1,0],
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[0,2,-5]])
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B1=np.array([[1],
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[0],
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[1]])
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B2=np.array([[0],
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[1],
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[0]])
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# Plant output.
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C2=np.array([[0,1,0]])
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D21=np.array([[2]])
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D22=np.array([[0]])
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# H2 performance.
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C1=np.array([[0,1,0],
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[0,0,1],
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[0,0,0]])
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D11=np.array([[0],
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[0],
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[0]])
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D12=np.array([[0],
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[0],
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[1]])
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# Dimensions.
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n_u,n_y=1,1
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# %%
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# H2 design using h2syn.
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# Create augmented plant.
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Baug=np.block([B1,B2])
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Caug=np.block([[C1], [C2]])
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Daug=np.block([[D11,D12], [D21,D22]])
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Paug=control.ss(A,Baug,Caug,Daug)
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# Input to h2syn is Paug, number of inputs to controller,
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# and number of outputs from the controller.
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K=control.h2syn(Paug,n_y,n_u)
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# Extarct controller ss realization.
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A_K,B_K,C_K,D_K=K.A,K.B,K.C,K.D
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# %%
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# Compute closed-loop H2 norm.
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# Compute closed-loop system, Tzw(s). See Eq. 4 in [1].
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Azw=np.block([[A+B2 @D_K @C2,B2 @C_K],
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[B_K @C2,A_K]])
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Bzw=np.block([[B1+B2 @D_K @D21],
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[B_K @D21]])
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Czw=np.block([C1+D12 @D_K @C2,D12 @C_K])
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Dzw=D11+D12 @D_K @D21
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Tzw=control.ss(Azw,Bzw,Czw,Dzw)
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# Compute closed-loop H2 norm via Lyapunov equation.
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# See [2], Lemma 4.4, pg 53.
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Qzw=control.lyap(Azw.T,Czw.T @Czw)
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nu=np.sqrt(np.trace(Bzw.T @Qzw @Bzw))
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print(f'The closed-loop H_2 norm of Tzw(s) is{nu}.')
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# Value is 7.748350599360575, the same as reported in [1].
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# %%
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"""Hinf design using hinfsyn.
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Demonstrate Hinf desing for a SISO plant using h2syn. Based on [1], Ex. 7.
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[1] Scherer, Gahinet, & Chilali, "Multiobjective Output-Feedback Control via
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LMI Optimization", IEEE Trans. Automatic Control, Vol. 42, No. 7, July 1997.
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"""
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# %%
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# Packages
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importnumpyasnp
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importcontrol
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# %%
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# State-space system.
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# Process model.
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A=np.array([[0,10,2],
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[-1,1,0],
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[0,2,-5]])
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B1=np.array([[1],
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[0],
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[1]])
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B2=np.array([[0],
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[1],
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[0]])
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# Plant output.
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C2=np.array([[0,1,0]])
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D21=np.array([[2]])
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D22=np.array([[0]])
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# Hinf performance.
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C1=np.array([[1,0,0],
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[0,0,0]])
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D11=np.array([[0],
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[0]])
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D12=np.array([[0],
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[1]])
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# Dimensions.
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n_x,n_u,n_y=3,1,1
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# %%
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# Hinf design using hinfsyn.
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# Create augmented plant.
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Baug=np.block([B1,B2])
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Caug=np.block([[C1], [C2]])
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Daug=np.block([[D11,D12], [D21,D22]])
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Paug=control.ss(A,Baug,Caug,Daug)
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# Input to hinfsyn is Paug, number of inputs to controller,
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# and number of outputs from the controller.
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K,Tzw,gamma,rcond=control.hinfsyn(Paug,n_y,n_u)
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print(f'The closed-loop H_inf norm of Tzw(s) is{gamma}.')
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# %%

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