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| 1 | +#pragma once |
| 2 | + |
| 3 | +#if defined(__GNUC__) || defined(__clang__) |
| 4 | +#pragma GCC optimize("O3", "fast-math") |
| 5 | +#endif |
| 6 | + |
| 7 | +#include "numerical/math/CompilerOptimizations.hpp" |
| 8 | +#include "numerical/math/LinearTimeInvariant.hpp" |
| 9 | +#include "numerical/math/Matrix.hpp" |
| 10 | +#include <array> |
| 11 | +#include <cstddef> |
| 12 | +#include <type_traits> |
| 13 | + |
| 14 | +namespace control_analysis |
| 15 | +{ |
| 16 | + template<typename T, std::size_t n> |
| 17 | + struct TransferFunction |
| 18 | + { |
| 19 | + static_assert(std::is_floating_point_v<T>, "TransferFunction supports floating-point types"); |
| 20 | + |
| 21 | + std::array<T, n + 1> numerator{}; |
| 22 | + std::array<T, n + 1> denominator{}; |
| 23 | + }; |
| 24 | + |
| 25 | + template<typename T, std::size_t n> |
| 26 | + class TransferFunctionStateSpace |
| 27 | + { |
| 28 | + static_assert(std::is_floating_point_v<T>, "TransferFunctionStateSpace supports floating-point types"); |
| 29 | + |
| 30 | + public: |
| 31 | + using Realization = math::LinearTimeInvariant<T, n, 1, 1>; |
| 32 | + using TF = TransferFunction<T, n>; |
| 33 | + using StateMatrix = math::Matrix<T, n, n>; |
| 34 | + using InputMatrix = math::Matrix<T, n, 1>; |
| 35 | + using OutputMatrix = math::Matrix<T, 1, n>; |
| 36 | + using FeedMatrix = math::Matrix<T, 1, 1>; |
| 37 | + |
| 38 | + OPTIMIZE_FOR_SPEED static Realization ToControllableCanonical(const TF& tf); |
| 39 | + OPTIMIZE_FOR_SPEED static Realization ToObservableCanonical(const TF& tf); |
| 40 | + OPTIMIZE_FOR_SPEED static TF ToTransferFunction(const Realization& sys); |
| 41 | + |
| 42 | + private: |
| 43 | + static std::array<T, n + 1> NormalizeDenominator(const std::array<T, n + 1>& den); |
| 44 | + static std::pair<T, std::array<T, n + 1>> ProperSplit( |
| 45 | + const std::array<T, n + 1>& num, const std::array<T, n + 1>& monicDen); |
| 46 | + static StateMatrix CharacteristicPolynomialCoefficients(const Realization& sys); |
| 47 | + static std::array<T, n + 1> LeVerrierNumerator( |
| 48 | + const Realization& sys, const std::array<T, n + 1>& charPoly); |
| 49 | + }; |
| 50 | + |
| 51 | + //// Implementation //// |
| 52 | + |
| 53 | + template<typename T, std::size_t n> |
| 54 | + std::array<T, n + 1> TransferFunctionStateSpace<T, n>::NormalizeDenominator( |
| 55 | + const std::array<T, n + 1>& den) |
| 56 | + { |
| 57 | + std::array<T, n + 1> result{}; |
| 58 | + T leading{ den[0] }; |
| 59 | + if (leading == T(0)) |
| 60 | + leading = T(1); |
| 61 | + for (std::size_t i{ 0 }; i <= n; ++i) |
| 62 | + result[i] = den[i] / leading; |
| 63 | + return result; |
| 64 | + } |
| 65 | + |
| 66 | + template<typename T, std::size_t n> |
| 67 | + std::pair<T, std::array<T, n + 1>> TransferFunctionStateSpace<T, n>::ProperSplit( |
| 68 | + const std::array<T, n + 1>& num, const std::array<T, n + 1>& monicDen) |
| 69 | + { |
| 70 | + T leading{ num[0] }; |
| 71 | + std::array<T, n + 1> remainder{}; |
| 72 | + for (std::size_t i{ 0 }; i <= n; ++i) |
| 73 | + remainder[i] = num[i] - leading * monicDen[i]; |
| 74 | + return { leading, remainder }; |
| 75 | + } |
| 76 | + |
| 77 | + template<typename T, std::size_t n> |
| 78 | + OPTIMIZE_FOR_SPEED typename TransferFunctionStateSpace<T, n>::Realization |
| 79 | + TransferFunctionStateSpace<T, n>::ToControllableCanonical(const TF& tf) |
| 80 | + { |
| 81 | + T leading{ tf.denominator[0] }; |
| 82 | + if (leading == T(0)) |
| 83 | + leading = T(1); |
| 84 | + auto monic{ NormalizeDenominator(tf.denominator) }; |
| 85 | + std::array<T, n + 1> scaledNum{}; |
| 86 | + for (std::size_t i{ 0 }; i <= n; ++i) |
| 87 | + scaledNum[i] = tf.numerator[i] / leading; |
| 88 | + auto [d, bhat]{ ProperSplit(scaledNum, monic) }; |
| 89 | + |
| 90 | + StateMatrix A{}; |
| 91 | + for (std::size_t i{ 0 }; i < n - 1; ++i) |
| 92 | + A.at(i, i + 1) = T(1); |
| 93 | + for (std::size_t j{ 0 }; j < n; ++j) |
| 94 | + A.at(n - 1, j) = -monic[n - j]; |
| 95 | + |
| 96 | + InputMatrix B{}; |
| 97 | + B.at(n - 1, 0) = T(1); |
| 98 | + |
| 99 | + OutputMatrix C{}; |
| 100 | + for (std::size_t j{ 0 }; j < n; ++j) |
| 101 | + C.at(0, j) = bhat[n - j]; |
| 102 | + |
| 103 | + FeedMatrix D{}; |
| 104 | + D.at(0, 0) = d; |
| 105 | + |
| 106 | + Realization result{}; |
| 107 | + result.A = A; |
| 108 | + result.B = B; |
| 109 | + result.C = C; |
| 110 | + result.D = D; |
| 111 | + return result; |
| 112 | + } |
| 113 | + |
| 114 | + template<typename T, std::size_t n> |
| 115 | + OPTIMIZE_FOR_SPEED typename TransferFunctionStateSpace<T, n>::Realization |
| 116 | + TransferFunctionStateSpace<T, n>::ToObservableCanonical(const TF& tf) |
| 117 | + { |
| 118 | + auto ccf{ ToControllableCanonical(tf) }; |
| 119 | + Realization result{}; |
| 120 | + result.A = ccf.A.Transpose(); |
| 121 | + result.B = ccf.C.Transpose(); |
| 122 | + result.C = ccf.B.Transpose(); |
| 123 | + result.D = ccf.D; |
| 124 | + return result; |
| 125 | + } |
| 126 | + |
| 127 | + template<typename T, std::size_t n> |
| 128 | + OPTIMIZE_FOR_SPEED typename TransferFunctionStateSpace<T, n>::TF |
| 129 | + TransferFunctionStateSpace<T, n>::ToTransferFunction(const Realization& sys) |
| 130 | + { |
| 131 | + using SqMat = math::Matrix<T, n, n>; |
| 132 | + |
| 133 | + std::array<T, n + 1> charPoly{}; |
| 134 | + charPoly[0] = T(1); |
| 135 | + |
| 136 | + SqMat M{ SqMat::Identity() }; |
| 137 | + |
| 138 | + for (std::size_t k{ 1 }; k <= n; ++k) |
| 139 | + { |
| 140 | + M = sys.A * M; |
| 141 | + charPoly[k] = -M.Trace() / static_cast<T>(k); |
| 142 | + for (std::size_t i{ 0 }; i < n; ++i) |
| 143 | + M.at(i, i) += charPoly[k]; |
| 144 | + } |
| 145 | + |
| 146 | + std::array<T, n + 1> numCoeffs{}; |
| 147 | + numCoeffs[0] = sys.D.at(0, 0); |
| 148 | + |
| 149 | + SqMat N{ SqMat::Identity() }; |
| 150 | + for (std::size_t k{ 1 }; k <= n; ++k) |
| 151 | + { |
| 152 | + auto CB{ sys.C * N * sys.B }; |
| 153 | + numCoeffs[k] = CB.at(0, 0); |
| 154 | + N = sys.A * N; |
| 155 | + for (std::size_t i{ 0 }; i < n; ++i) |
| 156 | + N.at(i, i) += charPoly[k]; |
| 157 | + } |
| 158 | + |
| 159 | + TF result{}; |
| 160 | + result.numerator = numCoeffs; |
| 161 | + result.denominator = charPoly; |
| 162 | + return result; |
| 163 | + } |
| 164 | + |
| 165 | +#ifdef NUMERICAL_TOOLBOX_COVERAGE_BUILD |
| 166 | + extern template class TransferFunctionStateSpace<float, 2>; |
| 167 | +#endif |
| 168 | +} |
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