- Email: [email protected]
DSP-BASED H∞ CONTROLLED DIGITAL AUTOMATIC VOLTAGE REGULATOR FOR USE ON ENGINE GENERATOR
Copyright © 2002 IFAC 15th Triennial World Congress, Barcelona, Spain
www.elsevier.com/locate/ifac
DSP-BASED H∞ CONTROLLED DIGITAL AUTOMATIC VOLTAGE REGULATOR FOR USE ON ENGINE GENERATOR Masayoshi Asama ∗ Hiroyuki Ukai ∗∗ Mototaka Sone ∗∗∗ Koichi Nakamura ∗∗∗∗ ∗
Department of Electrical and Computer Engineering, Nagoya Institute of Technology, Showa-Ku Nagoya, Japan. E-mail: [email protected] ∗∗ Department of Systems Management and Engineering, Nagoya Institute of Technology, Showa-Ku Nagoya, Japan. E-mail: [email protected] ∗∗∗ Department of Electrical Engineering, Musashi Institute of Technology, 1-28-1 Tamazutsumi Setagaya-Ku Tokyo, Japan. E-mail: [email protected] ∗∗∗∗ Department of Systems Management and Engineering, Nagoya Institute of Technology, Showa-Ku Nagoya, Japan. E-mail: [email protected]
Abstract: This paper presents a DSP-based high performance digital automatic voltage regulator (D-AVR) for use on engine generator. The H∞ control approach is applied to the engine generator excitation control system (ECS) for the purpose of tracking a r.m.s. of sinusoidal ac voltage to a specified value. Since the implementation of the control laws has tended to the digital microprocessor, the paper extends the reformulized H∞ control to the discrete time domain. The design procedure of H∞ based ECS is explained for the purpose of constructing robust, low noise, and high performance tracking system. Simulation and experimental results show that the proposed scheme can supply a high-quality voltage power source in the presence of load disturbance. Copyright © 2002 IFAC Keywords: digital signal processors, H-infinity control, digital automatic voltage regulator, engine generator
1. INTRODUCTION
terparts, but contain sophisticated control functions not readily available in analog excitation systems. Besides, it incorporates a number of preprogrammable settings and also allows for custom settings.
In recent years, owinig to the increasing use of computer, instrumentation equipment, and factory automation systems, a higher quality digital automatic voltage regulators (D-AVR) is required for the digital excitation control systems (ECS) in these systems. (K.J. Runtz et al., 1973)(M.J. D’Antonio et al., 1991)(A. Godhwani et al., 1996). The main reason is that the digital electronics are not just digital versions of their analog coun-
In the case of engine generator, AVR systems is constructed at analog electronics proportional, integral and derivative (PID) controller. In practical scene, skilled engineers need to tune PID parameters by trail and error, because the dy-
283
namic ECS is nonliner and noisy. Moreover, as the demand on the back-up power supply increased in recent years, the precise voltage characteristic is required. To satisfy these requirements, the reformulized H∞ control is presented for the ECS loop. The H∞ control approach comprises an integral, robust controller and low pass filter for low noise system.
These models are identified in condition (sample period: 0.2sec, system width: 10, sampling time for data collection: 0.01sec, switching frequency: 10kHz).
However, in practical point of view, it is difficult to implement on usual devices, because H∞ controller is usually high-dimension. Hence the controller is obliged to be reduced, then the degradation of the control performance is unavoidable. Thus, it require high-accuracy, high-speed computation processor core. In this paper, the H∞ control approach is applied to the engine generator ECS for the purpose of tracking a r.m.s. of sinusoidal ac voltage to a specified value. Considering the implementtion of control law by the digital signal processor (DSP) microprocessor, the reformulized H∞ control has been extended to the discrete time. The design, simulation, and implementation of a ECS using the H∞ control is described. The experimental set-up includes 4-poles 5kVA engine generator, a PWM voltage source excitation curcuit and fixed-point motor controller DSP-based D-AVR. Simulation and experimental results are presented for demonstrating the potential of the proposed scheme.
Fig. 1. Parametric model and non-parametric model of engine generator ECS.
2.2 Design of the H∞ Controller H∞ control algorithm can be standerdized as various control problems such as disturbances restraint problem, sensor noise problem, robustness stability problem, servo problem and etc. In the engine generator ECS, the following four problems are considered, which is shown in Fig. 2.
2. DYNAMIC MODEL OF ENGINE GENERATOR ECS AND DESIGN OF THE H∞ CONTROLLER
• Servomechanism: to track sinusoidal ac voltage with specified amplitude • Disturbance rejection: to restrain voltage amplitude drop at load input • Robust stability: to be robust against the fluctuation of parameters and nonlinearity of the system • Sensor noise reduction: to reduce the sensor noise
2.1 Dynamic Model of Engine Generator ECS The generator under control is fed by a rotary exciter. The plant transfer functon P (s) is geven by P (s) ≈
kg ke (1 + stg )(1 + ste )
(1)
where, kg = the generator open-circuit gain, tg = the generator open-circuit time-constant, ke = the exciter open-circuit gain, te = the exciter open-circuit time-constant. Parametric transfer function model P (s) is identified by predictive error method with ARMAXmodel. To obtain robust system, it is nessesary to define modeling error ∆ in the H∞ control design stage. Here, non-parametric model P˜ is identified by spectral analysis method. And, ∆ is defined by subtraction between the parametric model P (s) and the non-parametric model P˜ . The frequency responses of these models are shown in Fig. 1.
Fig. 2. Block diagram of engine generator ECS. where, K(s) is the controller. The signal r is the reference input voltage, y is the controlled voltage amplitude, e is the error, u is the manipulated input, d is the load disturbances, α is the modeling error input and β is the modeling error output.
284
Now, let G(s) be the generalized plant, the standard H∞ problem is reformularized as a mixed sensitivity problem given by
From Eqs. (10) and (11) S(s) and Ta (s) have a trade-off relation as follows: S(s) + P (s)Ta (s) = 1
z1 z2 = G(s) w u y
(2)
u = K(s)y
(3)
In order to satisfy the tracking performance to the step-wise change of the desired voltage, the weighting function wS (s) also need to have servo response quality: controller K(s) need to have servo response quality. Here, approximation integral method is applied.
where,
wS (s) −P (s)wS (s) wT (s) G(s) = 0 1 −P (s)
The standard H∞ control problem is composited by the designed weighting functions wS (s) (dimension: 3), wT (s) (dimension: 2) and the model P (s) (dimension: 2). And the solution K(s) (γ : 0.9375, dimension: 7) is obtained by K. Glover and J.C. Doyle method (K. Glover et al., 1988).
(4)
w = r, d, β
(5)
z1 = e, y
(6)
z2 = α
(7)
The sensitivity characteristic of the cotrol system appear in Fig. 3. The figure shows that sensitivity of Ta (jω) is better in high-frequency territory. And sensitivity S(jω) is better in low-frequency territory. In other words, complementary sensitivity function Ta (s) shows robust performance, and sensitivity function S(s) shows nominal performance.
wS (s) is the weighting function for sensitivity function; wT (s) is the weighting function for complementary sensitivity function. Signal w contains all external inputs such as r, d and β; output z1 contains e and y; output z2 is the α. The transfer function from w to z1 , z2 and transfer function Gzw (s) are given by delete signal y in equation (2) and (3). z1 = Gzw (s)w (8) z2 where,
Gzw (s) =
wS (s)S(s) wT (s)Ta (s)
(15)
(9)
S(s) is the sensitivity function; Ta (s) is the complementary sensitivity function. S(s) and Ta (s) are given by 1 1 + P (s)K(s) K(s) Ta (s) = 1 + P (s)K(s) S(s) =
Fig. 3. Sensitivity charasteristic of the controller.
(10) (11)
3. IMPLEMENTATION
The solution K(s) we have to find is designed in usual standard H∞ control problem as follows; for given number γ > 0, find all controllers such that the H∞ norm of the closed-loop transfer function is (strictly) less than γ.
The proposed H∞ controlled D-AVR has been implemented as a full-digital control system, that includes 4-poles 5kVA engine generator, power amplifire stage and DSP-based D-AVR, as shown in Fig. 4.
Gzw (s)∞ < γ
4-poles 5kVA engine generator is single phase two wire, brush-less, revolving-field type synchronous system. The specifications of the engine generator are followings; rated voltage: 100V , rated current: 50A, rated frequency: 50Hz, rated power-factor: 1.0. As a Fig. 4 indicates, the structure can be shared into main generator (G), exciter (Ex), PWM voltage source excitation circuit and diesel
(12)
Therefore, weighting functions wS (s), wT (s) have to satisfy following equations. |∆(jω)| ≤ |wT (jω)|
(13)
|d(jω)| ≤ |wS (jω)|
(14)
285
Fig. 4. Proposed drive circuit. and produced at Analog Devices Inc., America. The system is capable of a performance of 26MIPS and hosts all the peripherals, which includes a 12bit pipeline flash A/D module for voltage/current acquisition and 16-bit PWM generation unit. The specification of ADMC401 is shown in Table 1.
engine system. The main generator output side has an UV line terminal (U, V) and an AB line terminal (A, B). UV line terminal is connected to the load, AB line is connected to the PWM voltage source excitation circuit, and the phase of UV line output sinusoidal ac voltage v(t) is shifted 90deg the phase of AB line output sinusoidal ac voltage. That is self-excited AC generator.
Table 1. Specification of ADMC401 DSP motor controller.
The exciter is running with rated frequency (50Hz), which is controlled by diesel engine openloop control system. PWM DC voltage is fed by PWM voltage source excitation circuit, is inputted to the exciter (J, K). Thus, single-phase sinusoidal ac voltage with rated frequency is generated at main generator output side (U, V and A, B). The generated UV line voltage (v(t)) is regulated to specified voltage amplitude (100V) by D-AVR system.
ADSP-2171 core
Peripheral
16-bit fixed point type 26MIPS (38.5ns) 2kword PM, 1kword DM 16-bit 3-phase PWM generator 12-bit, 8ch ADC 12-bit PIO SPORT × 2 Encoder interface
As reported in the flow chart of Fig. 6, after initialization, the program waits for a dedicated PWM timer that synchronizes all the algorithm operations. In particular, the phase voltage acquisitions have been synchronized with the beginning of the PWM switching period. After the v(t) , VDC acquisition and voltage auto calibration, rms value of UV line sinusoidal voltage Vrms is calculated by shifting average method given by
A schematic of the proposed PWM voltage source excitation circuit in Fig. 5. As the Fig. 5 indicates, the circuit can be shared into rectifier circuit (Rec.), insulated gate bipolar transistor (IGBT) and 12V DC battery (Bat.). The system depicted, AB line sinusoidal ac voltage for use on exciting power supply is converted to the DC link voltage (VDC ) on the AC-DC rectifier. The VDC is converted to the PWM signal by an IGBT, and fed to exciter input (J, K). The controlled UV line ac voltage v(t) and VDC are sensed by voltage sensor. 12V DC battery is used as the starting voltage source.
π |v(t)| + |v(t − 1)| · · · |v(t − n)| Vrms = √ (16) n 2 2 Where, v(t): instantaneous value of UV line voltage, n: zero-cross to zero-cross sampling point of UV line voltage. The next step, controlled error Verror is obtained by equation (17), H∞ control calculation in equation (18). The PWM duty, which is calculated by equation (19), is set to the PWM generation unit in the ADMC401 DSP system. Verror = Vref − Vrms
Fig. 5. PWM voltage source excitation circuit.
Vinput = K(z)Verror Vinput VP W M = VDC
The H∞ voltage regulator, as well as rms value calculation, analog to digital conversion and PWM generation, have been implemented on a 16bit fixed-point motor controller DSP (ADMC401 Analog Devices Motor Control Family), designed
(17) (18) (19)
The discrete-time H∞ controller K(z) is obtained from K(s) by bilinear approximation, which is
286
4. SIMULATION AND EXPERIMENTAL RESULTS The effectiveness of the proposed H∞ controlled D-AVR is varified by both simulation and experiment. Simulation result is shown in Fig. 7. The figure includes Vrms and Vinput response. After the generated sinusoidal ac voltage with specified amplitude (Vrms =Vref =100[V]), step load disterbance (linear register load), is inputted to the Vrms . In this case, the result is compared with classical PID controller tuned by direct design method (A. Godhwani et al., 1996). The direct design method is easy to tune for servo system. As the figure shows, H∞ controller has high disturbance response, is robust against sensor noise. The Vrms response means that H∞ controller is similer to that of PID. The Vinput response means robust noise response. The PID includes noises, however H∞ controller is robust against with noises.
Fig. 6. Program flow chart. first order sampling controller. For hign-accuracy computaion system, the discrete-time H∞ controller is devided to 2nd order sections, and it is adapted to the DSP controller as the cascade connection type 2nd-order sections controller. As the result, 7th order Hi nf ty controller is consist of 4 cascade 2nd order sections.
Fig. 7. Simulation results.
In this case, because discrete-time H∞ controller calculation needs high-accuracy, high-speed computation, it is implemented at 48-bit data words. As reported in Table 2, the complete algorithm is executed in only 67.297us, but H∞ controller usually takes much computation time (54.516us). This system can be increasing the sampling rate up to 10kHz.
Experimental result is obtained with closed-loop ECS using ADMC401-based D-AVR. The diesel engine open-loop control system is set to the specified frequency (50Hz), and regulated reference voltage amplitude is set to the specified voltage (Vref =100[V]). In this case, the voltage transient response against 50% load input implemented. The results of test is shown in Fig. 8. The figure also includes Vinput , VDC , exciter running frequency (F req) and load ac currrent rms value (ILOAD ). The figure shows that proposed system has good performance, which is similar to simulated results. These response satisfy with the Japan Electrical Manufacture (JEM) standard provided by The Japan Electrical Manufacture’s Association (JEMA).
Table 2. Computation time. v(t), VDC acquisition Vrms , Verror calculation (n=200) H∞ control (7th-order, 48bit) VP W M calculation Total execution
0.809 9.972 54.516 2.000 67.297
µs µs µs µs µs
287
Fig. 8. Experimental results. 5. CONCLUSIONS
for Generator Voltage Control, American Power Conference, Chicago, IL. A. Godhwani, M.J. Basler, (1996). A Digital Excitation Control System for use on Brushless Excited Synchronous Generators, IEEE Transactions on Energy Conversion, Vol. 11, No. 3, pp 616-620. K. Glover and J.C. Doyle, (1988). State-space Formulae for All Stabilizing Controllers that Satisfy an H∞ -norm Bound and Relations to Risk Sensitivity, System & Control Letters, 11-2, pp.167-172.
The paper describes D-AVR system for use on engine generator. Here, high-dimension H∞ controller is adapted to the fixed point DSP (ADMC401), not reduce the dimension. The results obtained in this paper are summarized as follows: • H∞ control problem is formulated as mixed sensitivity problem: servo problem, disturbances restraint problem and robustness stability problem. And 7th-order H∞ controller is obtained. • 16-bit fixed-point DSP motor controller is adapted to the D-AVR, which can regulate rms value of sinusoidal ac voltage to the rated voltage amplitude. In this case, operation accuracy need 48-bits, and it takes many (54.516us) computation time. • Experimental setup is implemented; H∞ controller has high robust performance and high nominal performance. The proposed controller satisfied with JEM standard. REFERENCES K.J. Runtz, A.S.A. Farag, D.W. Huber, G.S. Hope, O.P. Malik, (1973). Digital Control Scheme for a Generating Unit, IEEE Transactions PAS, Vol PAS-92 (2), pp 478-483. M.J. D’Antonio, R.A. Lawson, W.R. Pearson, G.W. Speer, M.L. Crenshaw, A. Murdoch, (1991). A Digital-Based Excitation System
288
www.elsevier.com/locate/ifac
DSP-BASED H∞ CONTROLLED DIGITAL AUTOMATIC VOLTAGE REGULATOR FOR USE ON ENGINE GENERATOR Masayoshi Asama ∗ Hiroyuki Ukai ∗∗ Mototaka Sone ∗∗∗ Koichi Nakamura ∗∗∗∗ ∗
Department of Electrical and Computer Engineering, Nagoya Institute of Technology, Showa-Ku Nagoya, Japan. E-mail: [email protected] ∗∗ Department of Systems Management and Engineering, Nagoya Institute of Technology, Showa-Ku Nagoya, Japan. E-mail: [email protected] ∗∗∗ Department of Electrical Engineering, Musashi Institute of Technology, 1-28-1 Tamazutsumi Setagaya-Ku Tokyo, Japan. E-mail: [email protected] ∗∗∗∗ Department of Systems Management and Engineering, Nagoya Institute of Technology, Showa-Ku Nagoya, Japan. E-mail: [email protected]
Abstract: This paper presents a DSP-based high performance digital automatic voltage regulator (D-AVR) for use on engine generator. The H∞ control approach is applied to the engine generator excitation control system (ECS) for the purpose of tracking a r.m.s. of sinusoidal ac voltage to a specified value. Since the implementation of the control laws has tended to the digital microprocessor, the paper extends the reformulized H∞ control to the discrete time domain. The design procedure of H∞ based ECS is explained for the purpose of constructing robust, low noise, and high performance tracking system. Simulation and experimental results show that the proposed scheme can supply a high-quality voltage power source in the presence of load disturbance. Copyright © 2002 IFAC Keywords: digital signal processors, H-infinity control, digital automatic voltage regulator, engine generator
1. INTRODUCTION
terparts, but contain sophisticated control functions not readily available in analog excitation systems. Besides, it incorporates a number of preprogrammable settings and also allows for custom settings.
In recent years, owinig to the increasing use of computer, instrumentation equipment, and factory automation systems, a higher quality digital automatic voltage regulators (D-AVR) is required for the digital excitation control systems (ECS) in these systems. (K.J. Runtz et al., 1973)(M.J. D’Antonio et al., 1991)(A. Godhwani et al., 1996). The main reason is that the digital electronics are not just digital versions of their analog coun-
In the case of engine generator, AVR systems is constructed at analog electronics proportional, integral and derivative (PID) controller. In practical scene, skilled engineers need to tune PID parameters by trail and error, because the dy-
283
namic ECS is nonliner and noisy. Moreover, as the demand on the back-up power supply increased in recent years, the precise voltage characteristic is required. To satisfy these requirements, the reformulized H∞ control is presented for the ECS loop. The H∞ control approach comprises an integral, robust controller and low pass filter for low noise system.
These models are identified in condition (sample period: 0.2sec, system width: 10, sampling time for data collection: 0.01sec, switching frequency: 10kHz).
However, in practical point of view, it is difficult to implement on usual devices, because H∞ controller is usually high-dimension. Hence the controller is obliged to be reduced, then the degradation of the control performance is unavoidable. Thus, it require high-accuracy, high-speed computation processor core. In this paper, the H∞ control approach is applied to the engine generator ECS for the purpose of tracking a r.m.s. of sinusoidal ac voltage to a specified value. Considering the implementtion of control law by the digital signal processor (DSP) microprocessor, the reformulized H∞ control has been extended to the discrete time. The design, simulation, and implementation of a ECS using the H∞ control is described. The experimental set-up includes 4-poles 5kVA engine generator, a PWM voltage source excitation curcuit and fixed-point motor controller DSP-based D-AVR. Simulation and experimental results are presented for demonstrating the potential of the proposed scheme.
Fig. 1. Parametric model and non-parametric model of engine generator ECS.
2.2 Design of the H∞ Controller H∞ control algorithm can be standerdized as various control problems such as disturbances restraint problem, sensor noise problem, robustness stability problem, servo problem and etc. In the engine generator ECS, the following four problems are considered, which is shown in Fig. 2.
2. DYNAMIC MODEL OF ENGINE GENERATOR ECS AND DESIGN OF THE H∞ CONTROLLER
• Servomechanism: to track sinusoidal ac voltage with specified amplitude • Disturbance rejection: to restrain voltage amplitude drop at load input • Robust stability: to be robust against the fluctuation of parameters and nonlinearity of the system • Sensor noise reduction: to reduce the sensor noise
2.1 Dynamic Model of Engine Generator ECS The generator under control is fed by a rotary exciter. The plant transfer functon P (s) is geven by P (s) ≈
kg ke (1 + stg )(1 + ste )
(1)
where, kg = the generator open-circuit gain, tg = the generator open-circuit time-constant, ke = the exciter open-circuit gain, te = the exciter open-circuit time-constant. Parametric transfer function model P (s) is identified by predictive error method with ARMAXmodel. To obtain robust system, it is nessesary to define modeling error ∆ in the H∞ control design stage. Here, non-parametric model P˜ is identified by spectral analysis method. And, ∆ is defined by subtraction between the parametric model P (s) and the non-parametric model P˜ . The frequency responses of these models are shown in Fig. 1.
Fig. 2. Block diagram of engine generator ECS. where, K(s) is the controller. The signal r is the reference input voltage, y is the controlled voltage amplitude, e is the error, u is the manipulated input, d is the load disturbances, α is the modeling error input and β is the modeling error output.
284
Now, let G(s) be the generalized plant, the standard H∞ problem is reformularized as a mixed sensitivity problem given by
From Eqs. (10) and (11) S(s) and Ta (s) have a trade-off relation as follows: S(s) + P (s)Ta (s) = 1
z1 z2 = G(s) w u y
(2)
u = K(s)y
(3)
In order to satisfy the tracking performance to the step-wise change of the desired voltage, the weighting function wS (s) also need to have servo response quality: controller K(s) need to have servo response quality. Here, approximation integral method is applied.
where,
wS (s) −P (s)wS (s) wT (s) G(s) = 0 1 −P (s)
The standard H∞ control problem is composited by the designed weighting functions wS (s) (dimension: 3), wT (s) (dimension: 2) and the model P (s) (dimension: 2). And the solution K(s) (γ : 0.9375, dimension: 7) is obtained by K. Glover and J.C. Doyle method (K. Glover et al., 1988).
(4)
w = r, d, β
(5)
z1 = e, y
(6)
z2 = α
(7)
The sensitivity characteristic of the cotrol system appear in Fig. 3. The figure shows that sensitivity of Ta (jω) is better in high-frequency territory. And sensitivity S(jω) is better in low-frequency territory. In other words, complementary sensitivity function Ta (s) shows robust performance, and sensitivity function S(s) shows nominal performance.
wS (s) is the weighting function for sensitivity function; wT (s) is the weighting function for complementary sensitivity function. Signal w contains all external inputs such as r, d and β; output z1 contains e and y; output z2 is the α. The transfer function from w to z1 , z2 and transfer function Gzw (s) are given by delete signal y in equation (2) and (3). z1 = Gzw (s)w (8) z2 where,
Gzw (s) =
wS (s)S(s) wT (s)Ta (s)
(15)
(9)
S(s) is the sensitivity function; Ta (s) is the complementary sensitivity function. S(s) and Ta (s) are given by 1 1 + P (s)K(s) K(s) Ta (s) = 1 + P (s)K(s) S(s) =
Fig. 3. Sensitivity charasteristic of the controller.
(10) (11)
3. IMPLEMENTATION
The solution K(s) we have to find is designed in usual standard H∞ control problem as follows; for given number γ > 0, find all controllers such that the H∞ norm of the closed-loop transfer function is (strictly) less than γ.
The proposed H∞ controlled D-AVR has been implemented as a full-digital control system, that includes 4-poles 5kVA engine generator, power amplifire stage and DSP-based D-AVR, as shown in Fig. 4.
Gzw (s)∞ < γ
4-poles 5kVA engine generator is single phase two wire, brush-less, revolving-field type synchronous system. The specifications of the engine generator are followings; rated voltage: 100V , rated current: 50A, rated frequency: 50Hz, rated power-factor: 1.0. As a Fig. 4 indicates, the structure can be shared into main generator (G), exciter (Ex), PWM voltage source excitation circuit and diesel
(12)
Therefore, weighting functions wS (s), wT (s) have to satisfy following equations. |∆(jω)| ≤ |wT (jω)|
(13)
|d(jω)| ≤ |wS (jω)|
(14)
285
Fig. 4. Proposed drive circuit. and produced at Analog Devices Inc., America. The system is capable of a performance of 26MIPS and hosts all the peripherals, which includes a 12bit pipeline flash A/D module for voltage/current acquisition and 16-bit PWM generation unit. The specification of ADMC401 is shown in Table 1.
engine system. The main generator output side has an UV line terminal (U, V) and an AB line terminal (A, B). UV line terminal is connected to the load, AB line is connected to the PWM voltage source excitation circuit, and the phase of UV line output sinusoidal ac voltage v(t) is shifted 90deg the phase of AB line output sinusoidal ac voltage. That is self-excited AC generator.
Table 1. Specification of ADMC401 DSP motor controller.
The exciter is running with rated frequency (50Hz), which is controlled by diesel engine openloop control system. PWM DC voltage is fed by PWM voltage source excitation circuit, is inputted to the exciter (J, K). Thus, single-phase sinusoidal ac voltage with rated frequency is generated at main generator output side (U, V and A, B). The generated UV line voltage (v(t)) is regulated to specified voltage amplitude (100V) by D-AVR system.
ADSP-2171 core
Peripheral
16-bit fixed point type 26MIPS (38.5ns) 2kword PM, 1kword DM 16-bit 3-phase PWM generator 12-bit, 8ch ADC 12-bit PIO SPORT × 2 Encoder interface
As reported in the flow chart of Fig. 6, after initialization, the program waits for a dedicated PWM timer that synchronizes all the algorithm operations. In particular, the phase voltage acquisitions have been synchronized with the beginning of the PWM switching period. After the v(t) , VDC acquisition and voltage auto calibration, rms value of UV line sinusoidal voltage Vrms is calculated by shifting average method given by
A schematic of the proposed PWM voltage source excitation circuit in Fig. 5. As the Fig. 5 indicates, the circuit can be shared into rectifier circuit (Rec.), insulated gate bipolar transistor (IGBT) and 12V DC battery (Bat.). The system depicted, AB line sinusoidal ac voltage for use on exciting power supply is converted to the DC link voltage (VDC ) on the AC-DC rectifier. The VDC is converted to the PWM signal by an IGBT, and fed to exciter input (J, K). The controlled UV line ac voltage v(t) and VDC are sensed by voltage sensor. 12V DC battery is used as the starting voltage source.
π |v(t)| + |v(t − 1)| · · · |v(t − n)| Vrms = √ (16) n 2 2 Where, v(t): instantaneous value of UV line voltage, n: zero-cross to zero-cross sampling point of UV line voltage. The next step, controlled error Verror is obtained by equation (17), H∞ control calculation in equation (18). The PWM duty, which is calculated by equation (19), is set to the PWM generation unit in the ADMC401 DSP system. Verror = Vref − Vrms
Fig. 5. PWM voltage source excitation circuit.
Vinput = K(z)Verror Vinput VP W M = VDC
The H∞ voltage regulator, as well as rms value calculation, analog to digital conversion and PWM generation, have been implemented on a 16bit fixed-point motor controller DSP (ADMC401 Analog Devices Motor Control Family), designed
(17) (18) (19)
The discrete-time H∞ controller K(z) is obtained from K(s) by bilinear approximation, which is
286
4. SIMULATION AND EXPERIMENTAL RESULTS The effectiveness of the proposed H∞ controlled D-AVR is varified by both simulation and experiment. Simulation result is shown in Fig. 7. The figure includes Vrms and Vinput response. After the generated sinusoidal ac voltage with specified amplitude (Vrms =Vref =100[V]), step load disterbance (linear register load), is inputted to the Vrms . In this case, the result is compared with classical PID controller tuned by direct design method (A. Godhwani et al., 1996). The direct design method is easy to tune for servo system. As the figure shows, H∞ controller has high disturbance response, is robust against sensor noise. The Vrms response means that H∞ controller is similer to that of PID. The Vinput response means robust noise response. The PID includes noises, however H∞ controller is robust against with noises.
Fig. 6. Program flow chart. first order sampling controller. For hign-accuracy computaion system, the discrete-time H∞ controller is devided to 2nd order sections, and it is adapted to the DSP controller as the cascade connection type 2nd-order sections controller. As the result, 7th order Hi nf ty controller is consist of 4 cascade 2nd order sections.
Fig. 7. Simulation results.
In this case, because discrete-time H∞ controller calculation needs high-accuracy, high-speed computation, it is implemented at 48-bit data words. As reported in Table 2, the complete algorithm is executed in only 67.297us, but H∞ controller usually takes much computation time (54.516us). This system can be increasing the sampling rate up to 10kHz.
Experimental result is obtained with closed-loop ECS using ADMC401-based D-AVR. The diesel engine open-loop control system is set to the specified frequency (50Hz), and regulated reference voltage amplitude is set to the specified voltage (Vref =100[V]). In this case, the voltage transient response against 50% load input implemented. The results of test is shown in Fig. 8. The figure also includes Vinput , VDC , exciter running frequency (F req) and load ac currrent rms value (ILOAD ). The figure shows that proposed system has good performance, which is similar to simulated results. These response satisfy with the Japan Electrical Manufacture (JEM) standard provided by The Japan Electrical Manufacture’s Association (JEMA).
Table 2. Computation time. v(t), VDC acquisition Vrms , Verror calculation (n=200) H∞ control (7th-order, 48bit) VP W M calculation Total execution
0.809 9.972 54.516 2.000 67.297
µs µs µs µs µs
287
Fig. 8. Experimental results. 5. CONCLUSIONS
for Generator Voltage Control, American Power Conference, Chicago, IL. A. Godhwani, M.J. Basler, (1996). A Digital Excitation Control System for use on Brushless Excited Synchronous Generators, IEEE Transactions on Energy Conversion, Vol. 11, No. 3, pp 616-620. K. Glover and J.C. Doyle, (1988). State-space Formulae for All Stabilizing Controllers that Satisfy an H∞ -norm Bound and Relations to Risk Sensitivity, System & Control Letters, 11-2, pp.167-172.
The paper describes D-AVR system for use on engine generator. Here, high-dimension H∞ controller is adapted to the fixed point DSP (ADMC401), not reduce the dimension. The results obtained in this paper are summarized as follows: • H∞ control problem is formulated as mixed sensitivity problem: servo problem, disturbances restraint problem and robustness stability problem. And 7th-order H∞ controller is obtained. • 16-bit fixed-point DSP motor controller is adapted to the D-AVR, which can regulate rms value of sinusoidal ac voltage to the rated voltage amplitude. In this case, operation accuracy need 48-bits, and it takes many (54.516us) computation time. • Experimental setup is implemented; H∞ controller has high robust performance and high nominal performance. The proposed controller satisfied with JEM standard. REFERENCES K.J. Runtz, A.S.A. Farag, D.W. Huber, G.S. Hope, O.P. Malik, (1973). Digital Control Scheme for a Generating Unit, IEEE Transactions PAS, Vol PAS-92 (2), pp 478-483. M.J. D’Antonio, R.A. Lawson, W.R. Pearson, G.W. Speer, M.L. Crenshaw, A. Murdoch, (1991). A Digital-Based Excitation System
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